Evolutionarily Stable Stackelberg Equilibrium

2026-03-18

AI Summary

This study addresses the challenge posed by mutant invasions to equilibrium stability in leader–follower games by proposing the evolutionarily stable Stackelberg equilibrium (SESS). In this framework, the leader commits to a mixed strategy while anticipating that a symmetric population of followers will adopt an evolutionarily stable strategy (ESS) in the subgame, subject to ecological constraints. This work is the first to explicitly incorporate evolutionary stability into the Stackelberg setting, distinguishing between the ESS choices of leaders and followers and thereby overcoming a key limitation of existing approaches that neglect resistance to mutations. Integrating game theory, ESS theory, and optimization algorithms, the authors develop an efficient computational method for SESS applicable to both discrete and continuous games, demonstrating its efficacy in biological contexts such as cancer therapy—where the physician acts as the leader and cancer cell phenotypes constitute the follower population.

Technology Category

Game Theory and Economic Paradigms: EquilibriumMultiagent Systems: Mechanism DesignSearch and Optimization: Evolutionary Computation

Application Category

Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystemsWeb Mining and Content Analysis: Models for Web evolutionSecurity and Privacy: Large-scale security measurements

Abstract

We present a new solution concept called evolutionarily stable Stackelberg equilibrium (SESS). We study the Stackelberg evolutionary game setting in which there is a single leading player and a symmetric population of followers. The leader selects an optimal mixed strategy, anticipating that the follower population plays an evolutionarily stable strategy (ESS) in the induced subgame and may satisfy additional ecological conditions. We consider both leader-optimal and follower-optimal selection among ESSs, which arise as special cases of our framework. Prior approaches to Stackelberg evolutionary games either define the follower response via evolutionary dynamics or assume rational best-response behavior, without explicitly enforcing stability against invasion by mutations. We present algorithms for computing SESS in discrete and continuous games, and validate the latter empirically. Our model applies naturally to biological settings; for example, in cancer treatment the leader represents the physician and the followers correspond to competing cancer cell phenotypes.

Problem

• Stackelberg equilibrium
• evolutionarily stable strategy
• evolutionary game theory
• mutation stability
• leader-follower dynamics

Innovation

• Stackelberg equilibrium
• evolutionarily stable strategy
• evolutionary game theory
• leader-follower dynamics
• mutation stability