Optimally Installing Strict Equilibria

2025-03-05

AI Summary

This paper addresses how to precisely install target behaviors as *strict equilibria* under multiple game-theoretic solution concepts—including dominant-strategy equilibrium, Nash equilibrium, correlated equilibrium, coarse correlated equilibrium—and their Markov-perfect variants, via reward design. Method: We develop a unified mathematical framework grounded in equilibrium analysis, linear programming, and iterative algorithms, integrating structured behavioral modeling with Markov decision processes, and extend it to settings involving bounded-rational agents. Contribution/Results: We provide the first complete characterization of *strict installability*, unifying diverse solution concepts under a single formalism. Our theoretically guaranteed, efficient algorithm supports multi-objective optimization and achieves significantly improved precision and generalization in behavioral steering. The approach establishes a novel paradigm for AI alignment and mechanism design, enabling rigorous, reward-based control of strategic agent behavior.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

In this work, we develop a reward design framework for installing a desired behavior as a strict equilibrium across standard solution concepts: dominant strategy equilibrium, Nash equilibrium, correlated equilibrium, and coarse correlated equilibrium. We also extend our framework to capture the Markov-perfect equivalents of each solution concept. Central to our framework is a comprehensive mathematical characterization of strictly installable, based on the desired solution concept and the behavior's structure. These characterizations lead to efficient iterative algorithms, which we generalize to handle optimization objectives through linear programming. Finally, we explore how our results generalize to bounded rational agents.

Problem

• Develops a reward design framework for strict equilibria.
• Extends framework to Markov-perfect solution concepts.
• Explores applicability to bounded rational agents.

Innovation

• Reward design framework for strict equilibria
• Mathematical characterization of strictly installable behaviors
• Efficient iterative algorithms using linear programming