Optimally Installing Strict Equilibria
This provides a framework for reward design in game theory and multi-agent systems, applicable to bounded rational agents, though it appears incremental as it builds on existing equilibrium concepts.
The paper tackles the problem of designing rewards to make a desired behavior a strict equilibrium across multiple solution concepts (dominant strategy, Nash, correlated, coarse correlated) and their Markov-perfect equivalents, developing a mathematical characterization and efficient iterative algorithms that generalize to optimization via linear programming.
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.