Strategically Seeking Service: How Competition Can Generate Poisson Arrivals
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Bibliographic record
Abstract
We consider a simple game in which strategic agents select arrival times to a service facility. Agents find congestion costly and, hence, try to arrive when the system is underutilized. Working in discrete time, we characterize pure-strategy Nash equilibria for the case of ample service capacity. In this case, agents try to spread themselves out as much as possible and their self-interested actions will lead to a socially optimal outcome if all agents have the same well-behaved delay cost function. For even modest sized problems, the set of possible pure-strategy Nash equilibria is quite large, making implementation potentially cumbersome. We consequently examine mixed-strategy Nash equilibria and show that there is a unique symmetric Nash equilibrium. Not only is this equilibrium independent of the number of agents and their individual delay cost functions, the arrival pattern it generates approaches a discrete-time Poisson process as the number of agents and arrival points gets large. Our results extend to the case of time varying preferences. With an appropriate initialization, the results also extend to a system with limited capacity. Our model lends support to the traditional literature on managing service systems. This work has generally ignored customers strategically choosing arrival times. Rather it is commonly assumed that customers seek service according to some well-behaved process (e.g., that interarrival times follow a renewal process). We show that assuming Poisson arrivals is an acceptable assumption even with strategic customers if the population is large and the horizon is long.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it