# Summary Comparison Entrepreneurs face a fundamental speed–accuracy trade-off across these three strategies: **learn-only (🟩D1.1)** updates beliefs on responsiveness ($\beta_c,\beta_r$) to achieve high prediction accuracy but issues a slow, perished prescription based on lagged cost parameters; **act-only (🟩D1.2)** delivers an immediate $q^*$ under fresh cost inputs but relies on stale responsiveness estimates, sacrificing accuracy; **integrated approach (🟥C1)** fuses real-time Bayesian updates of both $q$ and $(\beta_c,\beta_r)$ to balance rapid action with ongoing learning, at the expense of solving a higher-dimensional inference problem—which can, however, be made tractable by leveraging partial orderings (e.g. $\beta_{r} \ll \beta_{c}$) to shrink search space. | Approach | Information Flow | Speed of Action | Prediction Accuracy around New Opportunity | Limitation | |:---------|:----------------|:----------------|:-------------------------------------------|:-----------| | **Learn-only (🟩D1.1)** | Update prior on responsiveness $\beta_c,\beta_rlt;br>→ Predict commitment probability $P_{r}, P_{c}$ | Slow | High | Prediction on $\beta$ is fresh but prescription $q(\beta_{r}^t, \beta_{r}^t, C_{u}^{t-\tau}, C_{o}^{t-\tau}, V^{t-\tau})$ is perished. | | **Act-only (🟩D1.2)** | Prior assumption on responsiveness $\beta_c,\beta_r$ <br>→ Prescribe quality $q^*(0)$ | Fast | Poor | Prescription $q(\beta_{r}^{t-\tau}, \beta_{r}^{t-\tau}, C_{u}^{t}, C_{o}^{t}, V^{t})$ is fresh but prediction $\beta$ is perished. | | **Learn & Act (🟥C1)** | Update prior on $q,\beta_c,\beta_r$ | Fast | Moderate | Balance freshness of prediction and prescription through integrated optimization $q(\beta_{r}^{t}, \beta_{r}^{t}, C_{u}^{t}, C_{o}^{t}, V^{t})$ is computationally intense but shrinking search space via partial ordering helps. | [[push_pull()]]