## Abstract Entrepreneurs make consequential decisions under extreme uncertainty, yet traditional startup advice lacks personalization and actionability. This research introduces STRAP (Sequential Threshold Reduction for Actionable Perceptions), a decision framework built on a powerful insight: reducing uncertainty directly increases your probability of success—these are mathematically equivalent goals. This fundamental principle reshapes how founders should approach venture-building, transforming it into a systematic cycle of perception (understanding stakeholder uncertainties), action (running targeted experiments), and confirmation (aligning stakeholder expectations). STRAP provides a practical rule for choosing which experiments to run next: always target the "bottleneck" uncertainty that offers the highest information gain per dollar spent. This approach reveals that coordinating stakeholder expectations breaks deadlocks, using resources efficiently matters more than raising large amounts, and successful ventures naturally evolve from unpredictable to predictable outcomes. Case study on comparing Segway's STRAP-guided (balanced uncertainty reduction across stakeholders) and its actual (over-investing in technology while neglecting market validation) operation, demonstrate that STRAP-guided ventures achieve better outcomes with fewer resources by systematically eliminating critical uncertainties in the optimal sequence. cInstead of relying on a static map and a one-dimensional compass, entrepreneurs need the equivalent of a GPS that dynamically combines sensor and motion – in other words, a navigation system that adapts in real time to the founder’s perspective and surroundings. Bayesian Entrepreneurship is an attempt to orient the field around entrepreneurs' prior beliefs about their opportunity space and how those beliefs evolve over the course of their entrepreneurial journey. If we take a Bayesian perspective, then entrepreneurship is more about "establishing hypotheses rather than having the right "vision", and running the right experiments rather than writing one-hundred-page business plans" (Stern et al, 2025). This thesis contribute to Bayesian entrepreneurship, by suggesting a blueprint for Bayesian decision making tool for entrepreneurs. After identifying there's no entrepreneurial decision making model that are personalized and realistically tractable I identify three core needs for developing such an adaptive tool: 📽️ **Perception** – the ability to clearly sense and interpret how different stakeholders view the venture; ⚡ **Sequencing** – the foresight to take the right steps in the right order under resource constraints; and 🔄 **Confirmation** – the capacity to align and synergize these stakeholders’ actions and expectations. These three needs form the backbone of my framework. In the following **Need Analysis** and **Solution Design** sections, I delve into each need and show how a rigorous decision model can function as that adaptive entrepreneurial GPS, I call this 🪢STRAP (Sequential Threshold Reduction for Actionable Perceptions) framework. To motivate the economic effect of my work, I apply this framework to the mobility sector. Mobility ventures require complex, multi-stakeholder alignment across regulators, infrastructure partners, and technology providers—making them ideal for testing Confirmation strategies under real-world constraints. Their moderate clockspeed—slower than software but faster than heavy industry—grants entrepreneurs time to strategically sequence experiments without being overtaken by market shifts. The sector’s remarkable breadth, from batteries to built environment (micromobility, electric vehicles, fleet/sharing, autonomy, elecaviation, marintime and public transit/infrastructure, allows us to validate generalizability across heterogeneous contexts. Crucially, mobility sits at the intersection of AI, robotics, and climate tech—fast-evolving, signal-rich domains that challenge my ability to model stakeholder perception under uncertainty. These qualities make mobility ventures not just an appropriate case, but a high-leverage proving ground for adaptive, evidence-based decision support. ## 2. Entrepreneurial Decision-Making Under Uncertainty This section defines the core challenges – differing stakeholder perceptions, circular dependencies, and resource constraints – and maps them to the requirements for a solution. It reviews literature on entrepreneurial decision-making under uncertainty, pointing out gaps that STRAP will address. ### 2.1 Entrepreneurial Decision-Making Under Uncertainty Literature Review This section introduces the fundamental challenge: entrepreneurs lack decision making model that is personalized, realistically tractable, actionable — promoting imitating other's behavior and unsystematic experimenting that lowers entrepreneuring quality. Entrepreneurial decision models span a spectrum of complexity defined by two key dimensions: **operational complexity** (decisions unfolding over time) and **multi-stakeholder complexity** (multiple interacting agents or criteria). At the simplest end of this spectrum are single-stakeholder static strategy models, which consider a one-off strategic choice by a lone decision-maker. These simple models are highly tractable but offer poor reality fit, since they ignore dynamic feedback and the involvement of other stakeholders (e.g., Sarasvathy, 2001; McMullen & Shepherd, 2006). Increasing the operational complexity yields single-stakeholder dynamic models that incorporate sequences of decisions and learning over time. Such models capture how an entrepreneur adapts through multiple stages (for instance, via staged investment or real options reasoning) while still focusing on one primary actor (Håkansson, 1971; McGrath, 1999). To better reflect real venture conditions, other models introduce **multi-stakeholder complexity** even in static settings. These multi-stakeholder strategy models consider how an entrepreneur coordinates or negotiates with various actors (investors, customers, competitors) within a single decision context, adding richer criteria to the choice (Gans, Hsu & Stern, 2002; Van den Steen, 2016). This boosts reality fit by acknowledging diverse interests, but tractability remains manageable only because the decision is not sequential. The most comprehensive models embrace both interacting stakeholders and dynamic operations, portraying entrepreneurship as an ongoing process co-created with partners, markets, and investors (Schindehutte & Morris, 2009; Garud & Karnøe, 2003; Roundy, 2018). These high-complexity models achieve a strong fit to entrepreneurial reality (phenomenological richness) but become computationally intractable – indeed, the full **EDMNO** formulation that accounts for all stakeholders over time is NP-complete (as shown in Section 1.1). In essence, the progression from static single-actor to dynamic multi-actor models reveals an engineering-versus-phenomenological trade-off: as I add realism, I lose tractability. Bridging this tractability–reality gap requires new approaches that retain high reality fit while restoring usability. Rather than abandoning formal modeling, I propose an **engineering** solution that balances these extremes through targeted simplifications and optimization strategies. In this thesis, a three-part framework is introduced to tackle each complexity dimension: **phase-based learning** breaks the decision process into stages to manage operational complexity over time, **proactive hypothesis proposal** uses probabilistic experimentation to navigate multi-stakeholder uncertainty, and **calibrated federated learning** allows entrepreneurs to collectively improve models without sacrificing individual context. Together, these strategies form a mid-complexity decision framework designed to maintain realism (capturing multi-stage, multi-stakeholder dynamics) while remaining computationally tractable. This approach sets the stage for the use cases and solution scope detailed in Section 1.3, aiming to empower entrepreneurs with decision tools that match the actual challenges they face. | Model Type | Multi-stakeholder Complexity | Dynamic operational Complexity | Tractability | Reality Fit | Key Need | Reference | | ----------------------------- | ---------------------------- | ------------------------------ | ------------ | ----------- | ------------------------------ | ------------------------------------------------------------------ | | Single-Stakeholder Static | No | No | High | Poor | More realistic representation | Sarasvathy (2001); McMullen & Shepherd (2006) | | Single-Stakeholder Dynamic | No | Yes | Medium | Medium | Multiple stakeholder view | Håkansson (1971); McGrath (1999) | | Multi-Stakeholder Static | Yes | No | Medium | Medium | Sequential decision capability | Van den Steen (2016); Gans, Hsu & Stern (2002) | | **Multi-Stakeholder Dynamic** | Yes | Yes | Low→Medium | High | **Computational tractability** | Schindehutte & Morris (2009); Garud & Karnøe (2003); Roundy (2018) | ### 2.2 The Entrepreneurial Decision-Making Under Uncertainty Need Analysis In this section, I identify the root causes of entrepreneurial decision-making challenges across three levels and three dimensions, structured as a need matrix, and show how each need maps to specific elements in My mathematical formulations: Each cell in this matrix represents not just a conceptual challenge but also maps directly to specific mathematical elements in My formulations, connecting entrepreneurial needs to formal optimization structures: 1. **Perception Challenges** (📽️): These map to uncertainty terms $\textcolor{#3399FF}{U_j}$ in the probabilistic formulation and entropy terms $H(p_j|\textcolor{red}{a})$ in the primal-dual approach. Perception asymmetry is captured by stakeholder-specific distributions $p_j$ and expectation terms $\textcolor{#3399FF}{\mu_j}(\textcolor{red}{a})$. Entrepreneurs struggle to understand how stakeholders perceive their ventures. Different stakeholders (investors, customers, partners) project identical startup attributes onto different perceptual dimensions, creating a fundamental information asymmetry problem. Traditional approaches either assume perfect information or rely on intuitive reading of stakeholder signals. My framework uses perceptual projection models to decode how observable venture attributes map to stakeholder decision spaces, enabling entrepreneurs to optimize information gathering and signal presentation. 2. **Sequencing Challenges** (⚡): These map to the resource constraints $C,\textcolor{red}{A} \leq \textcolor{#8B0000}{R}$ and action variable $\textcolor{red}{a}$, along with the state transition function $D(\textcolor{green}{S},,\textcolor{red}{a})$. The dual decision rule provides a computationally tractable approach to this otherwise NP-complete problem by determining which experiments to run based on their information value per cost. Entrepreneurs must sequence actions optimally under severe resource constraints. However, they cannot directly compute the uncertainty reduction per cost for each possible action sequence due to combinatorial explosion. Standard optimization approaches become computationally intractable as variables increase. My bottleneck-driven framework allows entrepreneurs to make near-optimal myopic decisions by decomposing complex metrics into estimable components, focusing resources on experiments that provide maximum information value. This mapping demonstrates how My mathematical formulations capture each dimension of the entrepreneurial decision challenge. The probabilistic formulation emphasizes uncertainty minimization across stakeholders, while the primal-dual approach transforms this into maximizing stakeholder satisfaction likelihood under resource constraints. 3. **Confirmation Challenges** (🔄): These correspond to the interdependencies between stakeholder states in $B,\textcolor{green}{S}$ and the consistency constraints on expectations $\textcolor{#3399FF}{\mu_j}(\textcolor{red}{a})$ across stakeholders. In the dual formulation, Confirmation is addressed through likelihood maximization that aligns all stakeholders' expectations. Entrepreneurs face circular dependencies where stakeholders make simultaneous, interdependent decisions. Investors wait for customer validation, customers require operational proof, and partners need investment signals, creating deadlock situations. Conventional methods tackle stakeholders sequentially, but this approach cannot resolve inherent circularity. My framework enables entrepreneurs to act as central coordinators who leverage information spillovers across stakeholder networks, breaking decision deadlocks through parallel engagement strategies. This dual formulation provides critical insights by transforming the uncertainty minimization problem into a likelihood maximization problem—revealing how entrepreneurs can maximize the probability of stakeholder satisfaction while optimizing resource allocation. ## 3. Solution design This section introduces how the needs identified in the previous section is addressed with a **Perception → Action → Confirmation** logic. STRAP integrates two complementary mathematical approaches – probabilistic Bayesian inference and optimization (primal-dual formulations) – to systematically guide entrepreneurial decisions. In essence, STRAP behaves like a “venture GPS” that perceives the stakeholder landscape, plans optimal actions (experiments), and confirms stakeholder alignment, iterating this cycle as the venture learns. I first discuss the theoretical foundations behind this approach, then detail each component (perception modeling, bottleneck sequencing, and stakeholder Confirmation) in turn. The following table presents My comprehensive solution approach across the three dimensions and three levels of entrepreneurial decision-making: ## 2.2 The Primal Formulation: Uncertainty Minimization At its core, entrepreneurial decision-making involves reducing critical uncertainties with limited resources. I formalize this as an optimization problem where the entrepreneur seeks to minimize a weighted sum of stakeholder-specific uncertainties: $\begin{aligned} \min_{\textcolor{red}{a} \in \textcolor{red}{A}} \quad & \textcolor{violet}{W_d}\cdot\textcolor{#3399FF}{U_d} + \textcolor{violet}{W_s}\cdot\textcolor{#3399FF}{U_s} + \textcolor{violet}{W_i}\cdot\textcolor{#3399FF}{U_i} \ \text{subject to} \quad & \sum_{j} c_j \textcolor{red}{a_j} \leq \textcolor{#3399FF}{R} \end{aligned}$ Where: - $\textcolor{#3399FF}{U_d}$, $\textcolor{#3399FF}{U_s}$, $\textcolor{#3399FF}{U_i}$ represent uncertainties facing demand-side, supply-side, and investor stakeholders - $\textcolor{violet}{W_d}$, $\textcolor{violet}{W_s}$, $\textcolor{violet}{W_i}$ are the weights reflecting each stakeholder's importance - $\textcolor{red}{a_j}$ indicates whether action/experiment $j$ is chosen - $c_j$ is the cost of action $j$ - $\textcolor{#3399FF}{R}$ is the available resource budget This primal formulation captures the essence of entrepreneurial decision-making: systematically reducing the most important uncertainties given limited resources. Each uncertainty $\textcolor{#3399FF}{U_j}$ can be mathematically represented as the entropy of a stakeholder's belief distribution: $\textcolor{#3399FF}{U_j} = H(p_j(\textcolor{red}{a})|\textcolor{red}{a})$, where $p_j$ is stakeholder $js probability distribution over possible outcomes. NEED EXAMPLE!! ## 2.3 The Dual Formulation: Success Probability Maximization Through mathematical transformation, this primal problem yields a revealing dual formulation: $\begin{aligned} \max_{\lambda, \beta, \gamma} \quad & \sum_{j \in {d,s,i}} \textcolor{violet}{w_j}[\lambda_j + \beta_j^T \textcolor{#3399FF}{\mu_j}(\textcolor{red}{a_j}) - \log Z_j(\beta_j)] - \gamma \textcolor{#3399FF}{R} \ \text{subject to} \quad & \gamma \geq 0 \end{aligned}$ Where: - $\lambda_j$ is the dual variable for stakeholder $js normalization constraint - $\beta_j$ is the dual variable for stakeholder $js expectation constraint - $\gamma$ is the dual variable for the resource constraint - $\textcolor{#3399FF}{\mu_j}(\textcolor{red}{a_j})$ is stakeholder $js expected outcome given action $a_j$ - $Z_j(\beta_j)$ is the partition function (normalizer) of stakeholder $js decision model **The key insight**: This dual formulation represents **maximizing the weighted log-likelihood that all stakeholders will be satisfied** with the venture's outcome, minus the opportunity cost of resources. In other words, the primal goal of minimizing uncertainty is mathematically equivalent to maximizing the probability of success. This duality transforms how we understand entrepreneurial decision-making: 1. Reducing a stakeholder's uncertainty directly increases the probability they will be satisfied 2. The more important a stakeholder (higher $\textcolor{violet}{w_j}$), the more their satisfaction influences overall success probability 3. Resource constraints ($\textcolor{#3399FF}{R}$) create an opportunity cost ($\gamma$) that must be balanced against information gains | **Level** | **Solution 1: Perception (📽️)** | **Solution 2: Action (⚡)** | | ----------------- | -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | Nature | **Inference Approach**: Initial <span style="color:green;">belief distributions</span> reflecting <span style="color:violet;">stakeholder weights</span> and <span style="color:green;">initial state</span><br><br>**Optimization Approach**: <span style="color:violet;">Value-weighted</span> success likelihood optimization | **Inference Approach**: Planning consistent experimental trajectories<br><br>**Optimization Approach**: <span style="color:#3399FF">Resource</span>-constrained <span style="color:red;">action</span> sequence optimization | | Stakeholder Level | **Inference Approach**: Mental model mapping to understand stakeholder decision spaces<br><br>**Optimization Approach**: Maximizing convincing power per <span style="color:#3399FF">resource unit</span> | **Inference Approach**: <span style="color:#3399FF;">Information value</span> calculation by stakeholder<br><br>**Optimization Approach**: <span style="color:violet;">Stakeholder-weighted</span> experiment prioritization | | Venture Level | **Inference Approach**: Targeting maximum learning per experiment<br><br>**Optimization Approach**: Optimizing evidence acquisition within <span style="color:#3399FF">resource constraints</span> | **Inference Approach**: Dynamic <span style="color:#3399FF;">uncertainty</span> updating after experiments<br><br>**Optimization Approach**: Linear programming relaxation for near-optimal experimental paths | ### 3.1 Theoretical Foundations Supporting Perception → Action Several streams of theory inform the STRAP framework’s structure of **Perception → Action → Confirmation**. At its heart, STRAP treats **strategy as a sequence of core decisions** under uncertainty. This echoes the view that strategy is not a static plan but a **pattern of pivotal decisions** an entrepreneur makes in response to feedback and changing information. Each decision (which experiment to run, which stakeholder to engage next) reshapes the venture’s trajectory – an idea aligning with modern strategic management perspectives that emphasize decision-making over static analysis. **Bayesian decision theory** provides the normative backbone for STRAP’s perception and action components. Under extreme uncertainty, entrepreneurs benefit from treating their actions as experiments and updating their beliefs about the venture’s viability in a Bayesian manner. STRAP’s **perception modeling** explicitly uses Bayesian inference to capture how stakeholders form beliefs and how those beliefs update with new evidence. Each stakeholder’s decision can be seen as a Bayesian update: they have prior beliefs about the venture, observe the entrepreneur’s actions (signals), and update to a posterior belief that informs their willingness to commit. By embracing Bayesian decision theory, STRAP ensures that new information (e.g. a successful prototype test or market trial) is systematically incorporated into the venture’s strategy. This brings mathematical rigor to the learning process that entrepreneurs undertake intuitively, casting it as **belief update and evidence-based optimization**. At the same time, STRAP is influenced by **effectuation logic** – the empirical observation that many successful entrepreneurs do not follow a grand predictive plan, but rather **iterate flexibly**, leveraging what they have and co-creating the venture with stakeholders. Notably, Sarasvathy’s effectuation emphasizes forming partnerships (commitments from customers, investors, etc.) early on to reduce uncertainty and create a self-reinforcing path forward. STRAP’s **confirmation (Confirmation) component** mirrors this: rather than assuming stakeholders will independently line up once the product is “proven,” STRAP actively seeks to align stakeholder expectations and trigger joint commitment once a critical threshold of evidence is reached. In other words, it formalizes the effectual principle of **stakeholder co-commitment** by mathematically determining when and how stakeholders can be brought on board together after key uncertainties are resolved. Moreover, effectuation preaches an “affordable loss” approach – focus on experiments you can afford and learn from, rather than aiming for an optimal predicted outcome. STRAP’s **bottleneck sequencing** aligns with this by prioritizing low-cost, high-learning actions first (the essence of affordable loss in a quantitative sense). It combines a predictive logic (using Bayesian probabilities to estimate an action’s information value) with a control logic (adapting the action sequence based on intermediate results), thus bridging classic planning and effectual learning-by-doing. In summary, these theoretical foundations reinforce STRAP’s Perception → Action → Confirmation cycle. I treat **strategy as a dynamic decision process** (not a static roadmap), use **Bayesian inference** to rigorously update and guide those decisions, and incorporate **effectual insight** by engaging stakeholders in a progressive commitment as uncertainty is reduced. The result is a framework that is both **analytically grounded** and **practically cognizant** of how real ventures evolve. STRAP’s mathematical formulation will show that by perceiving stakeholder needs accurately, acting on the biggest uncertainty-reducing steps, and confirming multilateral buy-in, an entrepreneur can navigate uncertainty in a structured yet flexible way. ### 3.2 Perception Modeling (📽️ Bayesian Stakeholder Modeling) – From Uncertainty to Convincing Power The first component of STRAP addresses the challenge of understanding how different stakeholders perceive the venture. I develop a **hierarchical Bayesian model** to represent each stakeholder’s decision-making process. The entrepreneur treats each stakeholder’s evaluation of the venture as a random utility model with latent parameters. Concretely, suppose stakeholder $i$ (e.g. a particular investor or customer) will decide whether to support the venture (action like “invest” or “buy”) based on signals $x$ (observable aspects of the venture such as performance metrics, team experience, prototypes, etc.). I model the utility stakeholder $i$ derives from the venture’s current state as: $Ui=βiTx+εi,U_i = \beta_i^T x + \varepsilon_i,$ where $\beta_i$ is a vector of **stakeholder-specific preference weights** and $\varepsilon_i$ is a random error term reflecting unmodeled factors and noise. If I assume $\varepsilon_i$ follows a Gumbel distribution (standard assumption in logistic models), the probability that stakeholder $i$ will say “yes” (e.g. invest, buy, partner) is given by a logistic function: $Pi(accept∣x)  =  exp⁡(βiTx)1+exp⁡(βiTx) ,P_i(\text{accept}|x) \;=\; \frac{\exp(\beta_i^T x)}{1 + \exp(\beta_i^T x)} \,$, which can be generalized to multi-option choices if needed (softmax over multiple outcomes). The vector $\beta_i$ encodes that stakeholder’s **latent preferences** – how strongly they weight various venture attributes when deciding. Because I rarely know $\beta_i$ upfront, I employ a **hierarchical Bayesian approach**: I place a prior distribution on each stakeholder’s $\beta_i$ (for instance, $\beta_i \sim \mathcal{N}(\bar{\beta}, \Sigma_\beta)$ around some average investor or customer profile). As the entrepreneur gathers data (stakeholder reactions, feedback, decisions), they update the posterior for $\beta_i$. This way, the model “learns” each stakeholder’s idiosyncrasies over time. For example, an investor might turn out to care far more about team experience than market size; the Bayesian model will adjust the posterior of $\beta_{\text{investor}}$ accordingly after observing that investor’s responses to various signals. **Interpreting and leveraging the model:** In essence, this perception model treats each stakeholder’s decision as a rational (but noisy) inference about the venture’s quality. Each stakeholder is acting on their perception of whether the venture will succeed, and the entrepreneur’s task is to **manage those perceptions by providing evidence**. By mapping observable signals $x$ (like a successful pilot, a patent award, or a key hire) to changes in $P_i(\text{accept})$, the entrepreneur can **predict how likely a given action is to convince each stakeholder**. I quantify stakeholder $i$’s **uncertainty** about the venture’s success as, say, the entropy $H(p_i)$ of their belief distribution $p_i$ or simply the variance of their utility $U_i$. High uncertainty means $P_i(\text{accept})$ is very sensitive to new information (their $\beta_i$ isn’t well-pinned down, or many outcomes are possible in their mind), whereas low uncertainty means the stakeholder’s mind is mostly made up (for good or ill). The **primal formulation** of the perception problem can be viewed as **minimizing these uncertainties** $U_j$ across stakeholders, subject to resource limits (I can’t answer every question at once). However, through a dual lens, an equivalent goal emerges: **maximize the likelihood of stakeholder approval**. In fact, a key insight of My framework is that **reducing a stakeholder’s uncertainty is mathematically equivalent to increasing the probability of meeting that stakeholder’s expectations** (Insight 1). By Bayesian duality, **minimizing entropy corresponds to maximizing the concentration of belief on a successful outcome**. Put simply, if an investor is very uncertain, the venture has to cover many bases to satisfy them (many potential concerns); as uncertainty shrinks, the venture’s story can hit exactly what the investor needs to hear, boosting the chance of a yes. **From “What do they want?” to “What will make them say yes?”** – By modeling stakeholder perception, the entrepreneur shifts from guessing stakeholder desires to **optimizing “convincing power.”** Using the hierarchical model, the entrepreneur can simulate how a given action $a$ (e.g. running a lab test, launching a beta product, securing a customer pilot) will shift stakeholder $j$’s expected outcome $\mu_j(a)$ – essentially the stakeholder’s updated belief of venture success if action $a$ is done. STRAP incorporates a **mean outcome constraint** for each stakeholder: the venture must eventually deliver an expected performance $\mu_j$ that meets stakeholder $j$’s requirement for a yes. In the Bayesian model this relates to ensuring $\beta_j^T \mu_j$ is high enough relative to their decision threshold. The **Lagrange multiplier** associated with this constraint is denoted $\lambda_j$ – one can think of $\lambda_j$ as stakeholder $j$’s **“uncertainty penalty” or demand for evidence**. If $\lambda_j$ is large, stakeholder $j$ currently remains unconvinced and even a decent outcome might not satisfy them; if $\lambda_j$ is near zero, it means that stakeholder’s expectations have effectively been met or they have low remaining skepticism. STRAP’s optimization formulation leverages this: in the **dual objective**, terms like $- \log Z_j(\beta_j)$ appear for each stakeholder, where $Z_j(\beta_j)$ is the partition function (normalizer) of stakeholder $j$’s decision model. Intuitively, $Z_j$ is larger when stakeholder $j$ sees many possible outcomes (high uncertainty) and smaller when their belief is narrowly focused on a particular outcome. Maximizing $- \log Z_j$ is thus equivalent to **concentrating stakeholder $j$’s belief on the favorable outcome**. The dual formulation effectively says: _subject to satisfying basic expected performance for each stakeholder (the constraints), allocate effort to maximize each stakeholder’s approval probability_. To make this concrete, consider an early-stage **sustainable materials startup (Sublime Systems)** dealing with a **scientist**, a **pilot customer**, and an **impact investor**. Initially, each stakeholder has doubts: the scientist isn’t sure the material will pass lab tests, the customer isn’t sure it will meet cost or quality needs, the investor isn’t sure there’s a market. These are different uncertainties (technical, customer, market), each represented by a $U_j$ and a latent $\beta_j$. Through the perception model, the founder identifies that a **lab validation** will most significantly change the scientist’s and customer’s beliefs (it proves the concept works and is one step closer to a product), whereas a **market survey** might more directly nudge the investor’s belief. By quantifying these effects, the founder sees that the lab test has higher combined “convincing power” per dollar – it drastically reduces two stakeholders’ uncertainty at once. Indeed, when Sublime ran a critical lab test (an action $a_1$), the **scientist’s** perceived technical risk plummeted, and seeing the technical success, the **pilot customer’s** confidence shot up as well (the customer’s expected value $\mu_{\text{cust}}(a_1)$ jumped). In turn, the **investor**, observing both the scientific validation and the customer’s increased interest, updated their own expectations upward (even before any direct market result, the investor infers that “if a reputable customer is excited and the tech works, this could be big”). My Bayesian model captures these **cross-stakeholder belief updates**: one action can send ripples through the stakeholder network. By formally modeling each stakeholder, the entrepreneur can anticipate these ripple effects. In summary, **perception modeling** provides a quantitative map of the venture’s stakeholder landscape – revealing which uncertainties are most critical and how actions will shape each stakeholder’s belief. This map is the foundation for deciding where to act next. ### 3.3 Bottleneck Sequencing (⚡ LP–POMDP Hybrid) – From Information Value to Optimal Action The second component of STRAP focuses on **what to do next**. Given multiple uncertainties and limited resources, the entrepreneur must decide which experiment or action will yield the **highest payoff in uncertainty reduction**. This is essentially a planning problem under uncertainty – one that can be framed as a **Partially Observable Markov Decision Process (POMDP)** if I consider the venture’s state of knowledge as the “state” and experiments as actions. However, POMDPs for real ventures quickly become intractable due to the huge state and action space. STRAP circumvents this by using a **bottleneck-driven heuristic that closely approximates the optimal planning**: at each step, tackle the biggest remaining uncertainty (the bottleneck) in a resource-efficient way. I formulate this as a **linear program (LP)** that selects the action maximizing information gain per cost, effectively a **greedy optimization** that I justify through primal-dual analysis. **Formulation:** Let $a_j$ be a binary decision variable indicating whether I execute action/experiment $j$ (e.g. run test $j$) in the next step, and let $c_j$ be the cost of that action (in dollars, time, or any critical resource). I define $\Delta U_j$ as the expected uncertainty reduction in stakeholder $j$’s belief if action $j$ is performed (this can be computed from the perception model as the expected drop in entropy or variance for stakeholder $j$). My objective is to maximize total **weighted uncertainty reduction** $\sum_j w_j, \Delta U_j$ (where $w_j$ is the weight representing stakeholder $j$’s importance in the venture’s success). I are constrained by a limited budget $R$ for this stage, e.g. I can only afford a certain total cost: $\sum_j c_j a_j \le R$. I also typically only choose one action at a time (one major experiment in the next step), so one could add a constraint $\sum_j a_j = 1$ for a strict sequential approach. Solving this simple LP picks the action $j$ with the highest $w_j \Delta U_j / c_j$ ratio – in other words, the **highest information gain per dollar**. This greedy selection is in fact the classic solution to a fractional knapsack problem, and it can be proven that if actions are divisible, taking a little of each would equalize their information-per-cost ratios to a common value (the dual optimal $\gamma$). Since actions here are indivisible (you either run the experiment or not), the greedy strategy of picking the largest ratio first is optimal or near-optimal in most cases. **Dual insight (primal-dual interpretation):** The dual of this LP introduces a Lagrange multiplier $\gamma$ for the resource constraint $\sum_j c_j a_j \le R$. This $\gamma$ represents the **shadow price of resources**, i.e. how much additional total uncertainty reduction I could achieve if I had one more unit of budget. At the optimum, $\gamma$ will equal the information-per-cost ratio of the chosen action (if there were a significantly better ratio action, I would have picked that instead). Thus, $\gamma$ is essentially the **marginal value of an extra dollar** given My current knowledge state. A high $\gamma$ means resources are extremely scarce relative to the uncertainties – every dollar is precious and yields a big jump in knowledge if spent well. A lower $\gamma$ means either I have abundant resources or diminishing returns (the biggest wins are already achieved). As the venture progresses and the easy uncertainties are resolved, $\gamma$ tends to decrease – this reflects diminishing returns on learning (Insight 4: efficiency of learning matters more than sheer spending). In STRAP’s context, $\gamma$ provides a quantitative handle for **when to raise more resources**: if $\gamma$ remains very high, it implies that more funding could significantly boost learning (so earlier-stage ventures often have high $\gamma$, justifying fundraising to enable crucial experiments). If $\gamma$ has fallen low, additional funds won’t help as much because only minor or less critical uncertainties remain. Combining the perception and sequencing formulations, I derive a **decision rule** for action selection that balances all these factors. The condition for an action $j$ to be optimal (to set $a_j^* = 1$) is: $ a_j^* = \begin{cases} 1 & \text{if } w_j\left[\,\lambda_j + \beta_j^T \mu_j(1) - \log Z_j(\beta_j)\right] > \gamma\, c_j \\[6pt] 0 & \text{otherwise} \end{cases} $ This rule deserves unpacking. The left-hand side is the **weighted benefit** of action $j$: inside the brackets, $\beta_j^T \mu_j(1)$ is the expected utility stakeholder $j$ would get from the venture after action $j$ (i.e. how much $j$’s situation improves), $\log Z_j(\beta_j)$ (with a minus sign) represents the **uncertainty reduction** for stakeholder $j$ (as discussed earlier, a smaller $Z_j$ means more certainty for $j$), and $\lambda_j$ is the current penalty on stakeholder $j$ not yet being fully satisfied (if stakeholder $j$ is very unconvinced, $\lambda_j$ is high, so the framework gives extra weight to persuading that stakeholder). Thus $[\lambda_j + \beta_j^T \mu_j(1) - \log Z_j]$ is a composite measure of how much action $j$ moves the needle for stakeholder $j$’s confidence. Multiplying by $w_j$ factors in how important stakeholder $j$ is overall. The right-hand side $\gamma, c_j$ is the **opportunity cost** of the action in terms of scarce resources – essentially the “budget cost” weighted by the current value of budget. If the inequality holds, action $j$ offers more benefit (in terms of increased success likelihood via uncertainty reduction) than its cost, so it’s a go. This condition neatly captures **bottleneck prioritization** (Insight 3): the actions that go forward are those with the highest ratio of uncertainty reduction to cost, adjusted for stakeholder importance. **Illustrative example – Segway vs. a bottleneck-driven approach:** To see why this sequencing matters, consider the famous case of **Segway**, the two-wheeled personal transporter often cited as a cautionary tale. Segway in the early 2000s had tremendous hype and funding. However, they **sequenced their strategic actions poorly** relative to uncertainties. They poured resources into scaling up manufacturing and marketing (an _investor- and supply-side_ action focus) before resolving the most critical unknown: _Would everyday consumers actually adopt this device at scale?_ In My terms, Segway faced at least three major uncertainties: **demand uncertainty** ($U_{\text{demand}}$: will consumers buy it?), **supply/regulatory uncertainty** ($U_{\text{supply}}$: can it be used safely on streets? will cities allow it?), and **business model uncertainty** ($U_{\text{investor}}$: can this be profitable given costs?). Of these, demand was the **bottleneck** – if demand wasn’t there, it wouldn’t matter if regulations or cost were fine. A STRAP-guided approach would have **prioritized an affordable experiment to test demand** (e.g. produce a small batch and release to a pilot market or a specific segment, such as tech enthusiasts or city tMy companies). If that pilot showed people love the product at the intended price, it would greatly reduce $U_{\text{demand}}$ and send a strong positive signal to investors and regulators (making them more willing to accommodate). If the pilot flopped or revealed lukewarm interest, the company could pivot or save its remaining resources instead of having wasted them on mass production. In reality, Segway did the opposite: they spent _vast resources_ building inventory and hype (multiple **costly actions executed in parallel** on the supply side) without real market validation. The outcome was that by the time Segway tried to sell broadly, they discovered the demand was not as hoped; they had burned through their capital (very high $c_j$ spent on the wrong $j$) for very little uncertainty reduction on the key question (people’s willingness to use it). My framework’s action rule likely would not have picked those scaling actions early, because for the **customer stakeholder** the term $[\lambda_{\text{cust}} + \beta_{\text{cust}}^T \mu_{\text{cust}}(1) - \log Z_{\text{cust}}]$ for a _demand-test action_ would have outweighed that of a manufacturing scale-up. In fact, Segway’s story illustrates Insight 4 vividly: **it’s not the total amount of money raised or spent that determines success, but how effectively each dollar is converted into knowledge and traction**. They had plenty of capital, but low _capital efficiency_ – high $\gamma$ persisted even after spending, meaning each new dollar was still not resolving much uncertainty (it was going into building more units that might not sell). # 3.4 Segway Case Study: STRAP Components in Action To illustrate the STRAP framework's practical application, let's examine how Segway could have benefited from this approach with three key stakeholders: tech-savvy urban commuters (demand), manufacturing partners (supply), and venture capitalists (investors). For each stakeholder, we model their belief distribution $p_{jk}$ across three possible outcomes: rejection ($k=1$), partial adoption ($k=2$), and full adoption ($k=3$). Early urban commuters might have assigned 40% probability to rejection, 40% to occasional use, and 20% to daily commuting adoption, reflecting high uncertainty about the product's practical value. Each outcome carries different value to the venture ($f_{jk}$): zero for rejection, 50 for occasional use, and 100 for daily commuting, yielding an initial expected outcome $\textcolor{green}{\mu_{\text{commuter}}}(0) = 40$ before any action is taken. The dual formulation provides a clear decision rule: take action $\textcolor{red}{a_j}$ only if $\textcolor{purple}{w_j}[\lambda_j + \beta_j^T \textcolor{green}{\mu_j}(1) - \log Z_j(\beta_j)] > \gamma c_j$, where $\textcolor{purple}{w_j}$ represents stakeholder importance (e.g., $\textcolor{purple}{w_{\text{commuter}}}=0.6$), $\lambda_j$ is the uncertainty penalty (e.g., $\lambda_{\text{commuter}}=8.0$ initially), $\beta_j^T \textcolor{green}{\mu_j}(1)$ represents expected benefit after the action, $-\log Z_j(\beta_j)$ captures uncertainty reduction, $\gamma$ reflects resource scarcity (e.g., $\gamma=5.0$ early on), and $c_j$ is the action cost in relation to total resources $\textcolor{#3399FF}{R}$. Comparing three potential actions (limited pilot, manufacturing partnership, mass production), the calculation for a pilot with 100 test units yields $\textcolor{purple}{w_{\text{commuter}}}[\lambda_{\text{commuter}} + \beta_{\text{commuter}}^T \textcolor{green}{\mu_{\text{commuter}}}(1) - \log Z_{\text{commuter}}] = 6.12 > \gamma c_{\text{pilot}} = 2.5$, making it worthwhile, while scaling manufacturing produces $0.65 < 50.0$, clearly not justifiable yet. After running a pilot, urban commuters' beliefs might shift to 60% rejection, 30% occasional use, and 10% daily commuting, reducing entropy from 1.52 to 1.30 but crucially revealing that most wouldn't use Segway for daily transportation. A successful venture shows decreasing $\lambda_j$ values as uncertainty is systematically reduced, decreasing $\gamma$ as resource efficiency improves, and increasingly deterministic state transitions. Segway's critical mistake was scaling while customer adoption uncertainty ($\lambda_{\text{commuter}}$) remained high and outcomes were still highly stochastic rather than deterministic. The STRAP framework would have identified urban commuter adoption as the critical bottleneck, prioritizing affordable experiments to resolve this uncertainty before committing massive resources $\textcolor{#3399FF}{R}$ to manufacturing and scaling, potentially saving the venture from its ultimately disappointing outcome. ## 4. Results: Empirical Validation and Performance Analysis The following section evaluates the STRAP framework, using case studies and simulations to demonstrate its efficacy. I particularly compare scenarios inspired by **Segway** (which did not use such a framework) and **Sublime Systems** (which aligns with STRAP principles) to highlight differences. ### 4.1 Setup and Methodology _(Summary)_ _I constructed a simulation of an early-stage venture decision process with three key stakeholders (representing, for example, **Demand**, **Supply**, and **Investor** dimensions). The simulation uses the Bayesian models and decision rules from STRAP to drive an optimal policy, and I also simulate a counterfactual policy that mimics the mis-sequenced approach (like Segway’s actual path). I track key metrics: the stakeholder uncertainty penalties $\lambda_j$ over time, the resource shadow price $\gamma$ over funding rounds, and the state transition matrix $D(S, A)$ evolution as the venture moves from idea to growth. Two panels of visualization are produced for comparison._ ### 4.2 Validation and Performance Analysis To interpret STRAP’s impact, I present a two-panel visualization comparing the **STRAP-guided approach (exemplified by Sublime Systems)** against a **naive approach (exemplified by Segway)**. The left panel of **Figure 1** tracks the evolution of the key parameters $\lambda$ and $\gamma$ across venture stages, and the right panel shows snapshots of the **state transition matrix** in early vs. later stages for each case. ![[Pasted image 20250507221031.png|center|1000]] _Figure 1: Comparison of parameter evolution and state transition dynamics for a venture following STRAP principles (Sublime) vs. a misaligned strategy (Segway). The left side plots each stakeholder’s uncertainty penalty $\lambda$ (solid lines for Sublime, dashed for Segway) declining as the venture progresses from Ideation through Growth, as well as the resource scarcity price $\gamma$ (violet for Sublime, red for Segway) over successive funding rounds (Seed through Series C). The right side shows the venture state transition matrices $D(S,A)$ at Early Stage and Growth Stage for each venture (Segway in red hues, Sublime in blue/violet hues). Each matrix illustrates the probabilities of moving from a given current state (rows: combinations of stakeholder expectations high/low) to a next state (columns) after one action. Higher values (darker color) along a single row indicate more deterministic transitions._ **Parameter trajectories:** I observe stark differences in the $\lambda$ and $\gamma$ trajectories between the two ventures. For **Sublime (STRAP-guided)**, all stakeholder uncertainty penalties $\lambda_j$ start moderately high but **decline steadily and significantly at each stage**. By the Growth stage, $\lambda$ values approach zero for all three stakeholder types (orange, green, and blue solid lines falling to the bottom of the left plot), indicating that stakeholders have been essentially convinced – their residual uncertainties are minimal. This reflects how STRAP systematically reduced each stakeholder’s major doubts through targeted experiments. In contrast, **Segway’s $\lambda$ values (dashed lines)** also decline with time but **remain substantially higher throughout**. Notably, Segway’s **demand-side $\lambda$ (blue dashed)** stays elevated even into the Launch stage, meaning a core uncertainty (customer adoption) was never fully resolved. The **investor $\lambda$ (orange dashed)** for Segway drops after large investments (they put money in), but because that investment wasn’t predicated on corresponding customer validation, the investor’s uncertainty later crept back in when sales disappointed – effectively, their confidence was premature. These trends underscore Insight 1 in practice: Sublime’s concerted uncertainty minimization translated into a high probability of stakeholder satisfaction, whereas Segway’s remaining uncertainty meant success likelihood never peaked as high. The **resource shadow price $\gamma$** further differentiates the strategies. Sublime’s $\gamma$ (violet line) starts around 5 (high during Seed stage, indicating each dollar is precious) but then **peaks and declines** to about 2 by Growth. This implies that after the critical early experiments, additional funding had diminishing marginal value – a sign that the venture became more efficient in its learning; money was no longer the bottleneck by Growth. Segway’s $\gamma$ (red dashed line), however, **stays high (~6-7) for longer and declines only slightly** by later stages. In fact, $\gamma$ spikes during the Prototype/Validation stage when Segway poured in resources – meaning even with a lot spent, the venture still had a high marginal value of money (they could have used even more to answer unresolved questions, but they had actually used it ineffectively). A persistently high $\gamma$ reflects resource inefficiency: Segway was throwing cash at problems without significantly reducing uncertainty, so every new dollar was almost as needed as the last. This aligns with **Insight 4** (efficiency of capital use outweighs total capital) – Sublime’s lower $\gamma$ by Growth shows they made each dollar count (each funding round significantly de-risked the venture), whereas Segway’s war chest didn’t buy clarity (high $\gamma$ indicated money was still limiting venture progress because of unresolved unknowns). **State transition matrices:** The right panel of Figure 1 visualizes how each venture’s **decision-state dynamics** changed from early to later stages. Each matrix is effectively a heatmap of $P(S_{next} | S_{current}, \text{action})$ for the possible aggregate states (here simplified to high/low expectation for each stakeholder). **Segway’s early-stage matrix** (top-right, left side) is quite **diffuse** – for a given current state (row), the probabilities are spread among multiple next states (values 0.4, 0.6, 0.5, etc., with no single dominant outcome). This indicates a highly stochastic evolution: early on, if Segway took an action, the outcome in terms of stakeholder reactions was unpredictable; the venture could land in various states (e.g., maybe customers like it but regulators push back, or vice versa) with no clear certainty. **Sublime’s early matrix** (bottom-right, left side) is also stochastic (as all ventures are at the start), but one can already see slightly more concentration (one outcome per row is a bit darker), suggesting that even initial actions were chosen to target likely desired outcomes (e.g., by focusing on the key bottleneck, Sublime had a higher chance to move into a specifically better state, rather than random directions). By the **growth stage**, the difference is pronounced: **Sublime’s state transition matrix (bottom-right, right)** becomes almost **diagonal with very dark cells** at the desired “all-high” state – effectively an **absorbing state** where if stakeholders are mostly convinced, the next state stays convinced (the venture stays on track with >90% probability of remaining in the success region). This indicates the system has become **nearly deterministic**: given the venture reached a critical mass of buy-in, further actions lead to predictable positive outcomes (e.g., scaling just leads to growth in a straightforward way). On the other hand, **Segway’s later-stage matrix** (top-right, right) still shows significant off-diagonal elements – there are multiple possible next states with considerable probability. For example, even in what they thought was a “high” state, there remained a chance to fall to a lower state (stakeholders backtracking or being disappointed). Segway never achieved a truly absorbing success state; the process remained **path-dependent and uncertain**, reflecting how they never fully aligned all stakeholders (Insight 5: without sufficient uncertainty reduction, the venture’s trajectory stays stochastic rather than locking into a win). **Venture outcomes:** As expected, the STRAP-guided trajectory (Sublime) achieved a successful outcome (all stakeholders committed and venture scaled) in the simulation with high probability, whereas the Segway-like trajectory had a much lower success probability and higher variability. Beyond success/failure, STRAP provides interpretability: looking at these metrics, an entrepreneur can diagnose _why_ things are going wrong. For instance, if $\lambda_{\text{customer}}$ remains high late in the game, it’s a red flag that customer concerns were never fully addressed; if $\gamma$ is still high after a big spend, it warns that resources were not used effectively to buy down risk; if the state transitions remain unpredictable, it means some stakeholder’s expectations are not aligned or some uncertainty is still lurking. By quantifying these, STRAP turns nebulous entrepreneurial wisdom (“de-risk the venture”, “get everyone on the same page”) into trackable metrics and decision criteria. Finally, My analysis underscores several **key insights** that connect the mathematics of STRAP to tangible venture outcomes: - **Insight 1 – Uncertainty vs. Likelihood:** The primal-dual transformation in STRAP shows that minimizing stakeholder uncertainty (entropy/variance) directly **maximizes the likelihood** of satisfying those stakeholders. In practice, ventures that relentlessly drive down uncertainty for each stakeholder dramatically increase their overall chance of success (as seen with Sublime vs. Segway’s stakeholder confidence levels). - **Insight 2 – Confirmation to Break Deadlocks:** **Stakeholder expectations must be coordinated** to avoid “waiting for others” deadlocks. The analysis revealed that aligning stakeholders’ belief updates (e.g., via shared pilots or synchronized communication) was critical to Sublime’s tipping point, whereas Segway suffered from fragmented stakeholder buy-in. - **Insight 3 – Bottleneck-First Action:** The **highest ROI experiments (uncertainty reduced per dollar)** should be done first. STRAP’s bottleneck sequencing embodies this, and the case comparison showed how addressing the biggest unknown (demand for Segway, technical viability for Sublime) before anything else yields far better outcomes. A focused experiment can eliminate a whole branch of risk, enabling all subsequent efforts to build on a solid base. - **Insight 4 – Resource Efficiency over Quantity:** **Using resources efficiently matters more than amassing resources.** Sublime succeeded with relatively limited funding by optimally allocating it to learning, reflected in declining $\gamma$ and rapid knowledge gain. Segway, despite ample capital, failed to convert money into equivalent progress (high $\gamma$ persisted) and illustrates that simply having funds is not enough – it’s the _information value_ extracted per dollar that counts. - **Insight 5 – From Stochastic to Deterministic:** Successful venture development is marked by a shift from a high-variance, stochastic process to a low-variance, predictable one. By the later stages, STRAP-guided ventures like Sublime **achieved near-deterministic state transitions** (everyone is on board, so outcomes of actions are certain within normal business variation), whereas Segway remained probabilistic (key players still not fully convinced, so any move had risk of unexpected fallout). This insight captures the essence of “de-risking”: eventually, if you solve enough uncertainties, the rest of the journey is straightforward execution. These insights, borne out in both the mathematical model and the case comparisons, demonstrate how STRAP not only improves the odds of venture success but also provides a **clear explanatory framework**. Entrepreneurs can pinpoint why a strategy is or isn’t working and course-correct with principled decisions. In essence, STRAP offers a way to **navigate uncertainty with strategy** – perceiving the road ahead, acting on the biggest obstacles, and confirming that all travel companions (stakeholders) are moving forward together. ### 4.3 Uncertainty Assessment and Limitations Despite its contributions, the STRAP framework has several important limitations driven by modeling simplifications and tractability-oriented design choices. First, it collapses a venture’s multi-dimensional uncertainty into a weighted linear combination of stakeholder-specific uncertainties. This additive objective (summing $U_d, U_s, U_i$ with fixed weights) assumes independent contributions from each stakeholder domain, potentially overlooking interaction effects or nonlinearities in how uncertainties jointly impact outcomes. Similarly, stakeholders are represented in a coarse way: the model considers only a few homogeneous stakeholder groups (e.g. investor, supplier, customer), with fixed importance weights $W$ and an initial uncertainty state $S_0$ for each. This approach cannot capture heterogeneity within a stakeholder group – in practice, different investors or customers may perceive and evaluate the venture very differently – nor can it reflect dynamic shifts in stakeholder influence over time. Another limitation is how interdependent stakeholder decisions are handled. The current framework acknowledges cross-stakeholder dependencies (e.g. an investor’s commitment might hinge on prior customer adoption) but addresses them only indirectly, by sequentially “leveling” uncertainties across stakeholders rather than modeling their decisions simultaneously. In other words, STRAP coordinates stakeholders by first equalizing their confidence levels and then proceeding, instead of explicitly capturing circular wait-and-see dynamics – a simplification that aids analysis but may reduce realism in scenarios where stakeholder actions truly coincide. Furthermore, to preserve computational tractability the STRAP rule employs a greedy, one-step optimal policy: at each iteration the entrepreneur pursues the action with the highest uncertainty-reduction-per-cost benefit (the steepest “information gain” per resource spent). While this heuristic efficiently breaks the current biggest bottleneck, it might sacrifice long-term optimality if certain actions yield synergistic benefits only in combination or if an initially suboptimal step unlocks better opportunities later. Finally, the framework relies on model parameters that may be challenging to calibrate in practice – such as quantifying each stakeholder’s uncertainty and weighting them (W), or estimating the impact of each possible action ($\mu_j$, $\beta_j$) on those uncertainties. Misestimation of these inputs or changes in the external environment could limit the framework’s generalizability beyond the contexts tested. These assumptions and simplifications could be relaxed in future work (for example, allowing richer stakeholder heterogeneity or a concurrent game-theoretic decision model at the cost of higher complexity), and exploring such extensions would help assess how robust STRAP’s recommendations remain when its more restrictive constraints are lifted. # 5. Discussion ### Entrepreneurial Operations Perspective (Fine et al., 2022) My framework’s emphasis on systematically reducing uncertainty aligns with recent insights in entrepreneurial operations. Fine et al. (2022) argue that startups require domain-specific operations management tools and stage-specific tactics as they scale. They document how ventures that attempt “naked scaling” (growing without tailored operational processes) often become chaotic, and they propose a catalog of ten scaling tools (e.g. **processification**, **segmentation**) to introduce needed structure. While My approach focuses on decision-making under uncertainty, it complements Fine’s operational lens by providing a quantitative method to decide _which_ process or experiment to implement first. Moreover, Fine et al. highlight that startups adopt different modes – some are **capability-first** (operations-centric) while others are **customer-first** – depending on context. My personalized STRAP model captures this contingency: by adjusting the initial state S0S_0 and weights WW, an entrepreneur can calibrate the framework to a capability-driven mode (emphasizing supply-side experiments) or a customer-driven mode (prioritizing demand-side tests). This ability to **personalize the decision model** makes My results more realistic, echoing Fine’s call for context-contingent guidance. In essence, STRAP provides a flexible decision engine that works in tandem with the operational “toolkit” approach – helping to determine when to apply tools like processification or segmentation based on which uncertainty is most critical in the venture’s current stage. ### Entrepreneurial Strategy Perspective (Gans et al., 2019) My findings also resonate with the entrepreneurial strategy literature, particularly the framework of Gans et al. (2019). Gans and colleagues confront the paradox that even with rigorous analysis, founders often face **multiple, equally plausible strategic paths** and must eventually commit to one. To navigate this, they derive the heuristic “**Test Two, Choose One**,” which advises entrepreneurs to experiment with at least two strategic alternatives before selecting the best path forward. This stopping rule underscores the “shadow cost” of experimentation – additional tests provide information but delay commitment. My STRAP framework generalizes this idea by formally quantifying the trade-off between learning and moving ahead. Instead of a fixed “test two then stop” rule, STRAP’s **Sequential Threshold Reduction for Actionable Perceptions (STRAP)** adaptively signals when to move from testing to action. In particular, the **dual formulation** in My model yields a clear threshold for action: when the expected gain from reducing uncertainty falls below the resource “price” of further experiments, the entrepreneur should choose a path (analogous to Gans’s stopping rule). Notably, Gans et al. encourage entrepreneurs to actively **choose their strategic environment** rather than passively accept it. STRAP operationalizes this by allowing founders to simulate outcomes under different stakeholder scenarios (different S0,WS_0, W settings) and then _select_ the scenario in which to commit. Thus, My results reinforce Gans et al.’s emphasis on entrepreneurial choice while providing a more fine-grained, quantitative decision criterion that accounts for resource constraints and the nuanced value of information. ### Real Options Theory and Staged Experimentation The sequential decision process enabled by My framework is grounded in principles akin to **Real Options Theory** in strategy. Real options reasoning posits that when facing high uncertainty, managers should make staged, low-commitment investments to “keep upside potential open while truncating downside losses”. This logic is evident in many entrepreneurial practices such as phased product trials or pilot programs. My uncertainty-minimization approach formalizes such staging: each experiment can be seen as purchasing an “option” to continue the venture under improved knowledge, while the **dual variable** (My resource shadow price) represents the option’s exercise threshold. Early in a venture, when uncertainty is greatest and resources are scarce, My model sets a high threshold (high γ\gamma) for pursuing an experiment – effectively only allowing actions with a large information yield per dollar (a high “real option” value). This mirrors real options advice to invest in only the most uncertainty-resolving projects first. Conversely, as uncertainty diminishes (e.g. after some successful tests) and resources expand, the threshold γ\gamma lowers, permitting smaller or riskier bets – analogous to exercising options and expanding commitment as confidence grows. By mathematically linking uncertainty reduction to the probability of venture success (My dual interpretation), I address a classic challenge in real options models: providing a concrete trigger for action. In essence, STRAP provides a computationally tractable way to apply real-options style thinking to entrepreneurial strategy, whereas prior real options approaches often remained qualitative (encouraging a mindset of flexibility) or were too complex to apply for day-to-day startup decisions. My results demonstrate that it is possible to **quantify the value of experimentation** in entrepreneurship and determine an optimal stopping point for learning, which bridges the gap between abstract real-options reasoning (e.g. “stage yMy investments” per McGrath, 1999) and practical decision-making guidance. ### Stakeholder-Centric Strategy Lens A core premise of My work is that a startup’s strategic direction can be defined by **which stakeholder uncertainties it tackles first**. This offers a novel lens on strategy that is complementary to traditional product-market definitions. Prior studies hint at this perspective: Fine et al. observed that some ventures focused on building internal capabilities (operations partners, supply chain) before courting customers, whereas others did the opposite. I generalize this idea by identifying three stakeholder categories—customer (demand-side), operational partner (supply-side), and investor (resource-side)—and allowing the entrepreneur to prioritize among them through action selection. The combination of which two stakeholder groups are addressed early effectively shapes the venture’s path. For example, a **customer–investor focus** (testing market demand while pitching to investors) yields a different trajectory than a **customer–partner focus** (working closely with early adopters and a supply partner before seeking outside capital). My case analysis (e.g. the Segway scenario) illustrates that pursuing any single category to the exclusion of others is rarely viable; instead, successful entrepreneurs sequence their focus, often temporarily satisfying two stakeholder constituencies while deferring the third. This aligns with the notion that a startup must achieve a minimum viable alignment among stakeholders to progress. Strategy, in this view, is the art of choosing _which_ stakeholders to align first and which to keep in flux until later. Gans et al.’s advice that entrepreneurs surface multiple alternatives and “choose which strategic environment to situate their idea in” can be interpreted as choosing which stakeholder context to bet on initially. My framework makes this explicit: by tuning the weights WW on each uncertainty type, founders can simulate different “stakeholder-first” strategies and see how the likely outcomes change. The results show that this stakeholder-centric approach yields a coherent strategy definition – one that is especially useful in multi-sided or platform ventures where deciding whether to acquire customers, partners, or funding first is the quintessential strategic decision. ### Addressing Technical Challenges and Broader Applications Beyond theoretical comparisons, My work explicitly tackles key technical questions raised in the introduction and methods, paving the way for long-term applications: - **Personalization and Realism:** By incorporating the initial state S0S_0 (prior beliefs about stakeholder metrics) and customizable weight vectors WW for uncertainties, the framework adapts to each venture’s unique context. This personalization dramatically enhances realism. For instance, a biotech startup with assured demand but high technical risk can start with S0S_0 reflecting low customer uncertainty but high technical uncertainty, and assign weights that prioritize R&D experiments. In contrast, a consumer app might weight market experiments more. Such tailoring means My model’s recommendations mirror the _actual_ challenges a founder faces, avoiding the one-size-fits-all bias that plagues generic startup advice. In effect, the STRAP framework serves as a decision GPS, adjusting its route based on the terrain (industry norms, founder background, macro-economic climate) to remain relevant and valid for that specific venture. This addresses the need for context-aware decision support and answers the question of long-term applicability: a personalized model remains applicable as the venture evolves or as it is deployed across different domains. - **Tractability and Interpretability of the Dual Formulation:** A major contribution of My approach is demonstrating that one can achieve computational tractability _and_ intuitive interpretability in entrepreneurial decision models. Traditional formulations that consider multiple stakeholders and sequential decisions (e.g. full POMDP models or dynamic programs) become intractable very quickly. I overcame this by adopting a primal-dual optimization framework. The **primal** side focuses on uncertainty reduction under resource constraints, while the **dual** side provides economic intuition – each stakeholder’s uncertainty has an implicit “price”, and the resource budget has a “shadow price” γ\gamma that sets a **threshold** for worthwhile actions. This dual variable γ\gamma yields a simple rule: _only pursue experiments that offer an expected likelihood improvement per cost above γ\gamma_. Such a rule is not only easy to compute (since γ\gamma adjusts until an optimal balance is found) but also easy to explain to practitioners as “bang-for-buck.” The dual formulation thereby translates complex math into the familiar language of trade-offs (e.g. “Is this test worth it given My burn rate?”). This clarity sets My framework apart from prior models and ensures it can be used for **long-term planning**: entrepreneurs can update their γ\gamma as budgets change or as earlier experiments reduce uncertainty, maintaining a clear decision criterion at each step. - **Generality across Domains (Uncertainty–Environment Fit):** The principles of My decision framework are designed to generalize beyond the specific mobility case used for illustration. I explicitly structured the model around categories of uncertainty and stakeholder interactions that are present in virtually all entrepreneurial domains (customers, operating partners/suppliers, investors/backers). This abstraction means that the same STRAP process — Perception → Action → Confirmation guided by uncertainty reduction value — can be applied whether the venture is in clean energy, software, healthcare, or any other field. What changes is the “uncertainty-environment fit,” i.e. the profile of uncertainties characteristic of that industry or business model. My approach readily accommodates these differences: for a given domain, one can initialize S0S_0 to represent the typical unknowns (e.g. in pharma, regulatory approval probability might be a key state; in a two-sided marketplace, getting a critical mass of one user side is a key uncertainty) and set resource constraints according to that environment’s norms. I have essentially **factorized entrepreneurial decisions** from the domain specifics – the model doesn’t hard-code any mobility-specific parameter, which is why it can generalize. In comparative studies, I expect that applying My framework to different industries will yield strategies that “fit” those environments (for example, more sequential testing in highly regulated industries, more parallel experimentation in fast-changing consumer tech), confirming that the model’s logic adapts to the context. This generality is a strong indicator of long-term usefulness: the framework could serve as a backbone for decision-support tools or pedagogical simulations across a wide range of entrepreneurial scenarios, with only the need to plug in industry-specific uncertainty data. ### Implications for Future Work The encouraging alignment of My framework with diverse strands of research and its adaptability across contexts opens up several avenues for future work. One immediate implication is the opportunity to **empirically validate** the STRAP rule in real startup settings: researchers could track ventures as they apply My uncertainty-driven experiments and compare their performance or pivot frequency against those following more ad-hoc decision processes. Another promising direction is to extend the model’s multi-stakeholder aspect – future research might incorporate additional stakeholder groups (e.g. regulators or community stakeholders in social enterprises) to test the limits of tractability and see how the decision rules adjust. There is also room to refine the personalization aspect by developing a library of domain-specific S0S_0 and WW presets (a “playbook library”) that new founders could choose from, which would effectively operationalize the contingency insights of Fine et al. and others. In the long term, integrating My framework with rich data (e.g. using machine learning to better estimate uncertainty reduction from various actions) could make the recommendations even more precise and dynamic. I see the STRAP approach as a starting point for a new class of entrepreneurship strategy tools – ones that blend rigorous optimization with the flexibility of real options and stakeholder theory. By anchoring strategic choices in quantitative uncertainty reduction, future work can build on this foundation to help entrepreneurs not only make better decisions in their ventures, but also contribute to a more scientific understanding of entrepreneurship as a process of iterative learning and commitment. The result would be a deeper unification of entrepreneurship research and practice, ensuring that theoretical advances directly inform actionable guidance for the founders of tomorrow. - todo: connecting the code of 📽️Perception Modeling and ⚡️bottleneck sequencing