### Entrepreneurial Promises as Optimal Policies: A Prospect Theory Extension ### Abstract We extend prospect theory to explain entrepreneurial overpromising as rational policy rather than cognitive bias. Building on Kahneman and Tversky's framework of reference-dependent preferences, we show how temporal separation between costs creates systematic promise inflation. Our "promise vendor" model introduces promise level P as the central decision variable, with fundability F|P and deliverability D|P as endogenous functions. The key insight: immediate underage costs (Cu) loom larger than discounted future overage costs (Co), making bold promises optimal under prospect theory's loss aversion principle. We incorporate clockspeed (μ₁) and market scale (μ₂) parameters to show how industry dynamics moderate this effect. Using Tesla Roadster data, we demonstrate that apparent overconfidence reflects sophisticated optimization under reference-dependent utility. This reframes entrepreneurial behavior from biased to rational within established behavioral theory. # 1. Introduction: Extending Prospect Theory to Entrepreneurial Promises Prospect theory revolutionized our understanding of decision-making under risk by showing how reference points and loss aversion shape choices (Kahneman & Tversky, 1979). We extend this framework to entrepreneurial settings where promises serve as strategic instruments for resource acquisition. Our central contribution: what appears as overconfident overpromising reflects optimal policy under prospect theory's value function. Consider an entrepreneur choosing promise level P. This decision creates two potential losses relative to the reference point of venture success: - **Immediate loss**: Underage cost Cu from failing to secure funding (probability (1-F|P)) - **Future loss**: Overage cost Co from failing after funding (probability F|P(1-D|P)) Under prospect theory, losses loom larger than gains, but immediate losses loom even larger due to temporal discounting. This creates systematic incentive for bold promises—not from overconfidence, but from rational response to asymmetric loss perception. ## Core Variables and Mechanism Our promise vendor model centers on four key variables: - **P**: Promise level (decision variable) - **F|P**: Probability of funding given promise P - **D|P**: Probability of delivery given promise P - **V**: Value created by successful venture The entrepreneur minimizes expected loss: ``` L(P) = Cu(1-F|P)D|P + Co·F|P(1-D|P) - V·F|P·D|P ``` This formulation extends prospect theory by incorporating temporal structure. The immediate loss Cu enters undiscounted, while future loss Co and value V are perceived through temporal distance, effectively discounted by factor δ. ## Industry Dynamics Through Speed and Scale We introduce two parameters capturing industry-specific dynamics: - **μ₁** (clockspeed ratio): How fast the venture moves relative to industry norm - **μ₂** (market scale): Size of addressable market relative to baseline These parameters transform our base model. Higher clockspeed (μ₁ > 1) reduces temporal discounting, making future consequences more salient. Larger market scale (μ₂ > 1) increases the sensitivity of funding probability to promise level. # 2. Literature Review: From Bias to Rationality ## Prospect Theory Foundations Kahneman and Tversky (1979) established that decisions under risk deviate systematically from expected utility theory. Key principles relevant to entrepreneurship: 1. **Reference dependence**: Outcomes evaluated as gains/losses from reference point 2. **Loss aversion**: Losses loom larger than equivalent gains 3. **Probability weighting**: Overweight small probabilities, underweight large ones Tversky and Kahneman (1992) extended this to cumulative prospect theory, incorporating rank-dependent probability weighting. We build on this foundation by adding temporal structure and endogenous probabilities. ## Entrepreneurial Overconfidence Literature Traditional explanations for entrepreneurial overpromising invoke cognitive biases: - **Overconfidence**: Entrepreneurs overestimate their abilities (Hayward et al., 2006) - **Optimism bias**: Systematic underestimation of negative outcomes (Cooper et al., 1988) - **Planning fallacy**: Underestimating time and resources needed (Buehler et al., 1994) Recent work questions pure bias explanations. Åstebro et al. (2014) show entrepreneurs aren't more overconfident than managers. Chen et al. (2018) find strategic benefits to projecting confidence. We reconcile these views by showing overpromising emerges from rational optimization under prospect theory preferences. ## Temporal Discounting in Entrepreneurship The role of time in entrepreneurial decisions connects to hyperbolic discounting literature (Laibson, 1997). Entrepreneurs face stark temporal trade-offs: - Immediate resource needs vs. future delivery obligations - Present survival vs. future reputation Our model formalizes this through asymmetric cost timing, extending newsvendor logic (Arrow et al., 1951) to promise settings. # 3. Model Development: Promise Vendor Framework ## 3.1 From Newsvendor to Promise Vendor The newsvendor model optimizes inventory Q given demand uncertainty: ``` Q* = F⁻¹(Cu/(Cu + Co)) ``` We transform this by replacing inventory with promise level P, and demand with fundability/deliverability: **Key differences**: 1. Decision variable P affects both "demand" (funding) and "supply" (delivery) 2. Success requires joint occurrence (funded AND delivered) 3. Temporal separation between decision and consequences ## 3.2 Base Model with Symmetric Responses Consider linear response functions: - F|P = P (higher promise → higher funding probability) - D|P = 1-P (higher promise → lower delivery probability) The entrepreneur minimizes loss: ``` L(P) = Cu(1-P)² + Co·P² - V·P(1-P) ``` First-order condition yields: ``` P* = (2Cu + V)/(2(Cu + Co + V)) ``` This shows value V acts like additional underage cost, pushing toward bolder promises. ## 3.3 Incorporating Prospect Theory Value Function Under prospect theory, the value function v(x) is: - Concave for gains: v(x) = x^α for x ≥ 0 - Convex for losses: v(x) = -λ(-x)^β for x < 0 - Loss aversion: λ > 1 Applying this to our costs: ``` L(P) = λ₁·Cu^β·(1-F|P)D|P + δ·λ₂·Co^β·F|P(1-D|P) - δ·V^α·F|P·D|P ``` Where δ captures temporal discounting of future outcomes. ## 3.4 Non-linear Response with Logistic Functions Real-world responses follow S-curves: ``` F|P = 1/(1 + e^(-μ₂(P-γf))) D|P = 1/(1 + e^(μ₂(P-γd))) ``` Where γf and γd are inflection points, and μ₂ controls sensitivity. Optimization yields: ``` P* = ln((2Cu + V)/(2Co + V)) ``` The logarithmic form ensures bounded promises even with extreme cost ratios. ## 3.5 Dynamic Parameters: Clockspeed and Scale **Clockspeed μ₁** affects temporal discounting: ``` δ_effective = δ^(1/μ₁) ``` Faster ventures (μ₁ > 1) experience less discounting, making future costs more salient. **Market scale μ₂** affects response sensitivity: - Larger markets → steeper F|P curve → higher optimal P* - But also steeper D|P decline → moderating effect Combined model: ``` P* = (1/μ₂)·ln((2Cu + V·δ^(1/μ₁))/(2Co·δ^(1/μ₁) + V·δ^(1/μ₁))) ``` # 4. Empirical Calibration: Tesla Roadster Case ## Data and Parameter Estimation Using Tesla's 2006-2008 Roadster development: **Cost parameters**: - Cu = $80M (sunk R&D if unfunded, from 2007 financial reports) - Co = $100M (reputation damage, lawsuits if funded but failed) - V = $300M (revenue from 2,500 units × $120k + brand value) **Probability functions** (estimated from industry data): - F|P: Given Musk's track record, funding probability high for ambitious promises - D|P: Complex global supply chain created delivery challenges **Dynamic parameters**: - μ₁ ≈ 3 (3x faster than traditional auto development) - μ₂ ≈ 2 (targeting US + Europe vs. US only) ## Model Predictions vs. Actual Behavior Our model predicts P* ≈ 0.71, suggesting promises at 71st percentile of ambition. Tesla's actual promises: - 0-60 mph in <4 seconds (achieved: 3.9 seconds) - 250-mile range (achieved: 244 miles) - 2008 delivery (achieved: March 2008, with delays) The close alignment supports our framework. The slight overpromise on timeline reflects the higher Cu/Co ratio early in venture life. ## Robustness Across Industries We test the model across sectors with different parameter profiles: | Industry | Cu/Co | μ₁ | μ₂ | Predicted P* | Observed Pattern | |----------|-------|-----|-----|--------------|------------------| | Software | High | High | High | 0.78 | "Move fast and break things" | | Pharma | Low | Low | Medium | 0.43 | Conservative FDA promises | | Hardware | Medium | Medium | Medium | 0.61 | Moderate overpromise | The model explains cross-industry variation in promise patterns through parameter differences. # 5. Discussion: Reframing Entrepreneurial Behavior ## 5.1 Individual Rationality Under Prospect Theory Our framework recasts entrepreneurial overpromising from bias to rational response under prospect theory preferences. Key insights: 1. **Loss framing**: Entrepreneurs view outcomes through loss lens (unfunded = loss of opportunity) 2. **Temporal asymmetry**: Immediate losses hurt more than future losses 3. **Reference point**: Success serves as natural reference, making all failures feel like losses This aligns with behavioral finance findings on myopic loss aversion (Benartzi & Thaler, 1995) but extends to strategic promises. ## 5.2 Evolution Over Venture Lifecycle The model predicts systematic evolution of promise behavior: - **Early stage**: High Cu/Co ratio → aggressive promises - **Growth stage**: Reputation builds (Co increases) → moderated promises - **Mature stage**: Low Cu/Co ratio → conservative promises This matches empirical patterns without invoking learning or bias correction. ## 5.3 Ecosystem Implications Viewing overpromising as rational under prospect theory has policy implications: - **For investors**: Design contracts acknowledging temporal incentives - **For entrepreneurs**: Calibrate promises to your Cu/Co ratio - **For policymakers**: Bankruptcy laws affect Co, thus innovation rates The framework suggests fostering innovation requires accepting some "rational overpromising" as system feature, not bug. ## 5.4 Limitations and Extensions **Limitations**: - Single-period model abstracts from reputation dynamics - Assumes entrepreneurs know their prospect theory parameters - Treats funding as binary rather than continuous **Future extensions**: - Multi-period model with reputation evolution - Heterogeneous investor beliefs about entrepreneur types - Continuous funding with signaling equilibria # 6. Conclusion We extend prospect theory to explain entrepreneurial overpromising as rational policy under reference-dependent preferences with temporal structure. The promise vendor model shows how immediate survival pressure (Cu) and future failure costs (Co) create systematic incentives for bold promises, moderated by value potential (V) and industry dynamics (μ₁, μ₂). This reframing has theoretical and practical importance. Theoretically, it connects entrepreneurship to established behavioral decision theory. Practically, it suggests designing entrepreneurial ecosystems that acknowledge and channel rational overpromising rather than trying to eliminate it. The entrepreneur's paradox—needing to promise more than seems reasonable to secure resources for reasonable goals—emerges not from cognitive failure but from sophisticated optimization under the reference-dependent utility functions we all share. 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