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The Collective Trust Game: An Online Group Adaptation of the Trust Game Based on the HoneyComb Paradigm

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Stationary Anonymous Sequential Games with Undiscounted Rewards.

Piotr Więcek¹, Eitan Altman²

¹Institute of Mathematics and Computer Science, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland.

Journal of Optimization Theory and Applications

|August 25, 2015

Summary

This summary is machine-generated.

This study extends the theory of stationary anonymous sequential games to total and average rewards. Equilibria in these infinite-player games correspond to limits of finite-player game equilibria.

Keywords:

Anonymous sequential game Average reward Population game Stationary policy Stochastic game Total reward

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Area of Science:

Game Theory
Mathematical Economics
Computational Game Theory

Background:

Stationary anonymous sequential games with undiscounted rewards merge infinite-player population games and stochastic games.
Existing theory primarily addresses specific reward structures.

Purpose of the Study:

Extend the theoretical framework for stationary anonymous sequential games.
Analyze both total expected reward and expected average reward scenarios.
Establish the relationship between infinite and finite player game equilibria.

Main Methods:

Theoretical extension of game theory models.
Analysis of limit behavior as player populations approach infinity.
Comparative analysis of finite and infinite player game equilibria.

Main Results:

Demonstrated that equilibria in infinite-player anonymous sequential games are limits of finite-player game equilibria.
Successfully extended the theory to encompass total expected reward and expected average reward.

Conclusions:

The study provides a robust theoretical foundation for analyzing large-scale anonymous sequential games.
Findings offer insights into the convergence of strategies in games with growing player numbers.
The results are illustrated with practical examples.