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Summary

This summary is machine-generated.

This study reveals that simultaneous exits in games are driven by correlated factors, not just direct influences. A new test detects these endogenous effects, confirmed by Civil War desertion data.

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Area of Science:

Game Theory
Econometrics
Sociology

Background:

Agents' decisions to quit activities are often influenced by others' participation.
Understanding these interdependencies is crucial for modeling group behavior and strategic interactions.

Purpose of the Study:

To develop a model for analyzing interdependent decisions in continuous time games.
To establish conditions for the existence, uniqueness, and detection of endogenous effects in stopping strategies.
To introduce a nonparametric test for identifying correlated influences on simultaneous exits.

Main Methods:

Continuous-time game modeling with interdependent durations.
Analysis of equilibrium stopping strategies.
Development of a nonparametric statistical test for endogenous effects.
Application to historical data on military desertion.

Main Results:

Endogenous effects (correlated factors) are a necessary and sufficient condition for simultaneous exits.
A robust nonparametric test for detecting these effects is established.
Conditions for parameter identification in the game are provided.
Empirical evidence of endogenous influences on Union Army desertion is found.

Conclusions:

Interdependent decisions significantly shape outcomes in continuous-time games.
The developed test effectively identifies correlated influences, robust to multiple equilibria.
The model provides a framework for analyzing strategic behavior in various contexts, as demonstrated by the historical case study.