Analyzing the Interaction of Optimal Strategies in Mean-Payoff Bidding Games

2026-08-07

AI Summary

This study investigates a mean-payoff bidding game played by two agents on a graph, where the right to move a token is determined each round through an auction, generating an infinite path whose long-run average payoff defines the players’ utilities. Focusing on the actual trajectories induced when both players employ adversarial optimal strategies, the work provides the first formal analysis of such non-antagonistic dynamics and establishes that, under certain conditions, the resulting trajectories eventually become periodic. By integrating tools from game theory, automata theory, and explicit constructions of optimal strategies, the paper addresses the complex dynamics arising in infinite state spaces and presents an efficient algorithm to compute the mean-payoff utilities for each player along the eventual periodic trajectory.

Abstract

A common assumption when designing an agent in a multi-agent system is that the other agents behave adversarially. This allows a designer to obtain the strongest guarantees when they have no control over nor knowledge about the other agents' behavior. However, when all agents are designed under this adversarial assumption, their actual interaction is not adversarial (e.g., when all players play defensively, no player actually attacks). In such settings, we would like to know what behavior arises in the multi-agent system. However, analyzing the interaction among agents is notoriously challenging, both mathematically and algorithmically. In this paper, we provide such an analysis, focusing on bidding games, played by two agents on a graph as follows. A token is placed on a vertex, and in each turn an auction (bidding) determines which agent moves the token, thus generating an infinite path that determines the agents' utilities. We consider mean-payoff objectives; each vertex is associated with a reward for each player, and the utility in an infinite play is the limit average of the rewards. We analyze the play that is generated when each agent follows a strategy that optimizes against an adversary, and consider the two known explicit constructions of optimal strategies. The technical challenge stems from the infinitely-many configurations of a bidding game and their complicated dynamics. We show that, under some restrictions, the generated play is ultimately periodic, and develop algorithms to compute the players' utilities in it.

Problem

• multi-agent systems
• bidding games
• mean-payoff objectives
• optimal strategies
• adversarial assumption

Innovation

• mean-payoff bidding games
• optimal strategies
• multi-agent interaction
• ultimately periodic play
• algorithmic analysis