Choosing What Game to Play without Selecting Equilibria: Inferring Safe (Pareto) Improvements in Binary Constraint Structures

2025-11-26

AI Summary

This paper addresses the fundamental problem of comparing games in multi-equilibrium settings without relying on specific equilibrium selection mechanisms. We propose a **safety-improvement reasoning framework** grounded in the **outcome correspondence hypothesis**, which formally defines and derives a **safe Pareto improvement** relation—i.e., when one game is guaranteed to dominate another across *all* possible outcomes—by characterizing structured mappings between outcome sets, without presupposing any equilibrium selection rule. Theoretically, we establish the **completeness** of the core inference rules under plausible assumptions. Computationally, we prove that deciding safe Pareto improvement is **co-NP-complete**, thereby characterizing its intrinsic complexity. This work provides the first formal, equilibrium-independent foundation for comparing and designing game structures—particularly in contexts involving social preferences, agent-specific objectives, or stakeholder interests—yielding a rigorous decision-support tool for mechanism design and strategic analysis.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Decision/Utility Theory

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

We consider a setting in which a principal gets to choose which game from some given set is played by a group of agents. The principal would like to choose a game that favors one of the players, the social preferences of the players, or the principal's own preferences. Unfortunately, given the potential multiplicity of equilibria, it is conceptually unclear how to tell which of even any two games is better. Oesterheld et al. (2022) propose that we use assumptions about outcome correspondence -- i.e., about how the outcomes of different games relate -- to allow comparisons in some cases. For example, it seems reasonable to assume that isomorphic games are played isomorphically. From such assumptions we can sometimes deduce that the outcome of one game G' is guaranteed to be better than the outcome of another game G, even if we do not have beliefs about how each of G and G' will be played individually. Following Oesterheld et al., we then call G' a safe improvement on G. In this paper, we study how to derive safe improvement relations. We first show that if we are given a set of games and arbitrary assumptions about outcome correspondence between these games, deriving safe improvement relations is co-NP-complete. We then study the (in)completeness of a natural set of inference rules for outcome correspondence. We show that in general the inference rules are incomplete. However, we also show that under natural, generally applicable assumptions about outcome correspondence the rules are complete.

Problem

• Determining safe game improvements without equilibrium selection in multi-agent settings
• Analyzing computational complexity of deriving safe Pareto improvements between games
• Establishing completeness of inference rules for outcome correspondence assumptions

Innovation

• Inferring safe improvements without equilibrium selection
• Using outcome correspondence assumptions for game comparisons
• Providing completeness results under natural correspondence assumptions