Game Theory with Simulation in the Presence of Unpredictable Randomisation

TL;DR

This paper investigates how AI agents' predictability can be exploited through simulation to improve social welfare in game-theoretic settings, revealing both limitations and conditions for positive outcomes.

Contribution

It introduces the concept of mixed-strategy simulation in game theory, showing its potential benefits and computational complexity in enhancing social welfare.

Findings

Mixed-strategy simulation may not improve outcomes in all trust games.

Deciding Pareto-improving equilibria via simulation is NP-hard.

Simulation can enhance social welfare under trust scaling, coordination challenges, or privacy needs.

Abstract

AI agents will be predictable in certain ways that traditional agents are not. Where and how can we leverage this predictability in order to improve social welfare? We study this question in a game-theoretic setting where one agent can pay a fixed cost to simulate the other in order to learn its mixed strategy. As a negative result, we prove that, in contrast to prior work on pure-strategy simulation, enabling mixed-strategy simulation may no longer lead to improved outcomes for both players in all so-called "generalised trust games". In fact, mixed-strategy simulation does not help in any game where the simulatee's action can depend on that of the simulator. We also show that, in general, deciding whether simulation introduces Pareto-improving Nash equilibria in a given game is NP-hard. As positive results, we establish that mixed-strategy simulation can improve social welfare if the simulator has the option to scale their level of trust, if the players face challenges with both trust and coordination, or if maintaining some level of privacy is essential for enabling cooperation.