Correlated Equilibria and Fairness in Concurrent Stochastic Games

TL;DR

This paper explores correlated equilibria in concurrent stochastic games, demonstrating they are easier to compute, more equitable, and can enhance joint outcomes compared to traditional Nash equilibria, with applications in automated verification.

Contribution

It introduces an alternative optimality criterion of social fairness for correlated equilibria and develops algorithms for their computation in complex stochastic games.

Findings

Correlated equilibria are computationally easier to obtain.

Correlated equilibria lead to more equitable outcomes.

They can improve joint payoffs in multi-agent stochastic games.

Abstract

Game-theoretic techniques and equilibria analysis facilitate the design and verification of competitive systems. While algorithmic complexity of equilibria computation has been extensively studied, practical implementation and application of game-theoretic methods is more recent. Tools such as PRISM-games support automated verification and synthesis of zero-sum and (epsilon-optimal subgame-perfect) social welfare Nash equilibria properties for concurrent stochastic games. However, these methods become inefficient as the number of agents grows and may also generate equilibria that yield significant variations in the outcomes for individual agents. Instead, we consider correlated equilibria, in which players can coordinate through public signals, and introduce an alternative optimality criterion of social fairness, which can be applied to both Nash and correlated equilibria. We show that correlated equilibria are easier to compute, are more equitable, and can also improve joint outcomes. We implement algorithms for both normal form games and the more complex case of multi-player concurrent stochastic games with temporal logic specifications.