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Learning through reinforcement for N-person repeated constrained games.

A S Poznyak¹, K Najim

¹Dept. of Control Autom., CINVESTAV-IPN, Mexico City, Mexico.

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society

|February 5, 2008

Summary

This study introduces an adaptive strategy for N-person averaged constrained stochastic repeated games, using a novel reinforcement learning approach. Simulation results demonstrate the strategy

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Area of Science:

Game Theory
Reinforcement Learning
Stochastic Processes

Background:

N-person averaged constrained stochastic repeated games present complex strategic interactions.
Players learn and adapt strategies without prior knowledge of game parameters.
Constraints on action probabilities add complexity to equilibrium analysis.

Purpose of the Study:

To design and analyze an adaptive strategy for N-person averaged constrained stochastic repeated games.
To ensure the existence and uniqueness of a Nash equilibrium under diagonal concavity conditions.
To develop a learning automaton-based strategy using current game outcomes and constraints.

Main Methods:

Modeling players as stochastic variable-structure learning automata.
Employing the Bush-Mosteller reinforcement scheme with a normalization procedure.
Utilizing the Lagrange multipliers approach with regularization for constraint handling.

Main Results:

The proposed adaptive strategy effectively utilizes current game realizations (outcomes and constraints).
Asymptotic properties of the algorithm are rigorously analyzed.
Simulation results confirm the feasibility and performance of the adaptive strategy.

Conclusions:

The developed adaptive strategy offers a viable solution for constrained stochastic repeated games.
The approach guarantees Nash equilibrium under specific conditions.
This method provides a practical tool for analyzing and playing complex dynamic games.