## 1. probabilsitic program 1. Probabilistic inference provides a robust methodology for dealing with dynamic and multi-stakeholder complexities in entrepreneurial decisions. Traditional optimization methods (e.g., integer programming, branch-and-bound) lack flexibility under rapidly changing entrepreneurial conditions, whereas probabilistic models handle adaptive learning more naturally, allowing entrepreneurs to dynamically adjust their decisions based on real-time feedback ## 2. group prior [[tan_zhixuan]]'s recommendation on social prior from [[session7_social planner]] + (Inverse) planning coordination systems - [[📜planning with theory of mind for few shot adaptation in sequential social dilemmas]] ## 3.pomdp - lp - POMDP literature on information gathering, myopic policies, LP approximations for MDPs # 4. 📦multiple hypothesis testing + inventory management **Markovian Prompt: Supply Chain Math for Startup Testing Decisions** **Main Mathematical Framework:** 1. **Basic Testing Decision Equation**: - <span style="color: blue">ΔEU(n)</span> = <span style="color: green">[nα/(α+n)]</span><span style="color: red">(μ-φ_true)</span> - <span style="color: orange">nc^y</span> + <span style="color: purple">c^φ</span> - Where: - n = number of tests (e.g., cars to test) - α = prior confidence - μ = belief about market success - φ_true = actual market reality - c^y = cost per test - c^φ = fixed cost of alternative research 2. **Multi-Stakeholder Decision Rule**: Test stakeholder j if: <span style="color: green">w_j·InfoGain_j</span> + <span style="color: blue">Σ_{i≠j} w_i·Spillover_{j→i}</span> > <span style="color: red">γc_j</span> **Testing Errors Meet Inventory Theory Table:** |Testing Concept|Inventory Theory Equivalent|Startup Application|TAXIE Example| |---|---|---|---| |**Type I Error (False Positive)**|**Overage Cost**|Launching bad product|Building a large EV fleet when market isn't ready| |• Probability: α|• Excess inventory risk|• Wrongly entering market|• Risk of unsold car capacity| |• Cost: C₁|• Cost of unsold goods|• Wasted investment|• Cost of idle EVs| |**Type II Error (False Negative)**|**Underage Cost**|Missing good opportunity|Abandoning EV rideshare too early| |• Probability: β|• Stockout risk|• Skipping winning idea|• Missing first-mover advantage| |• Cost: C₂|• Lost sales cost|• Competitor wins market|• Tesla/others capture market| |**Prior Belief (μ)**|**Demand Forecast**|Market size belief|TAXIE believed high demand for EV rideshare| |**Prior Strength (α)**|**Forecast Confidence**|How certain you are|Low confidence (needed testing)| |**Optimal Sample Size**|**Economic Order Quantity**|How many to test|n* = 2-3 cars was optimal| |**Total Cost Minimization**|**Total Inventory Cost**|Balance all error costs|Minimize false launches + missed opportunities| **Easy Explanation:** Think of testing like ordering inventory: - Order too much (Type I error) = Launch product nobody wants - Order too little (Type II error) = Miss a great opportunity - The goal: Find the sweet spot that minimizes total mistakes **TAXIE Case Study:** TAXIE tested with 2 cars and learned: 1. **Range hypothesis**: ✓ Confirmed (260 miles sufficient) 2. **Driver earnings**: ✓ Validated initially 3. **Willingness to pay**: ✓ $400/week seemed viable 4. **Infrastructure**: ? Needed larger test (>50 cars) 5. **Scalability**: ? Systems untested at scale 6. **Profitability**: ✗ Not viable at current scale **Optimal Sample Size Calculation:** Using the formula n* = √[α²(μ-φ_true)/c^y] - α For TAXIE: - Prior belief (μ): 0.5 (moderate optimism) - True reality (φ_true): 0.2 (market was actually weak) - Prior confidence (α): 2 (low confidence) - Cost per car test (c^y): 0.15 - Spillover factor: 1.5 (testing reveals multiple insights) n* = √[4 × 0.3 × 2.5 / 0.15] - 2 = √[20] - 2 = 2.47 ≈ 2-3 cars **Key Insights from TAXIE:** 1. Testing 2 cars was mathematically optimal given their constraints 2. They correctly learned about range, driver economics, and pricing 3. They couldn't test infrastructure and scalability with just 2 cars 4. The spillover effect (one test reveals multiple insights) justified the investment **Visual Requirements:** 1. **Decision Flowchart**: Show how TAXIE moved through hypothesis testing 2. **Learning Curve**: Plot information gained vs. number of cars tested 3. **Error Cost Diagram**: Visualize Type I vs Type II error tradeoffs 4. **Spillover Network**: Show how testing drivers revealed insights about infrastructure, pricing, and operations **Main Takeaway:** Supply chain math helps startups test efficiently. Just as inventory managers balance overstocking vs. stockouts, entrepreneurs must balance over-investing in bad ideas vs. missing good opportunities. The optimal testing strategy minimizes total error costs while maximizing learning through spillover effects. --- # relevant papers from [[📝moon24_csv_ai_cofounder]] | Paper Title | Reason for Classification (Hypothesis Testing & Stakeholder Complexity) | Optimization Component (3.1 Theoretical) | | ------------------------------------------------------------------------------------------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | **Adaptive Entrepreneurship: A Preliminary Framework Using Exaptation and Exchangeability** | Uses exaptation and cross-context hypothesis testing to proactively explore and validate stakeholder opportunities, strategically reducing uncertainty across markets and stakeholders . | Formulates stakeholder uncertainty reduction via exchangeable decises, systematically structuring state-action hypotheses for proactive testing ($U_d$) . | | **Zero to One and Done** | Systematically classifies and tests uncertainties across contexts (epistemic and aleatoric) to proactively generalize validated insightsple stakeholder opportunities, thus strategically reducing complexity . | Clarifies how proactive hypothesis testing accelerates uncertainty reduction through validation of exchangeability across contexts, refining stakeholder-focused state-action-utility relationships ($U_d$) . | | **Equity Proposal as Action: Optimal Term Sheets via Conversational Inference** | Implements iterative hypothesis-probing proposals during negotiations, reducing stakeholder complexity through structured conversational inference about investor intentions and founder-investor alignments . | Defines proactive hypothesis-driven negotiation strategies as structured sequences of proposals, explicitly mapping stakeholder state-action-utility interactions ($U_i$) . |