Evolutionarily Stable Stackelberg Equilibrium

We present an algorithm for computing evolutionarily stable strategies (ESSs) in symmetric perfect-recall extensive-form games of imperfect information. Our main algorithm is for two-player games, and we describe how it can be extended to multiplayer games. The algorithm is sound and computes all ESSs in nondegenerate games and a subset of them in degenerate games which contain an infinite continuum of symmetric Nash equilibria. The algorithm is anytime and can be stopped early to find one or more ESSs. We experiment on an imperfect-information cancer signaling game as well as random games to demonstrate scalability.

We present an algorithm for computing all evolutionarily stable strategies in nondegenerate normal-form games with three or more players.

We study risk-sensitive evolutionary learning dynamics and their long-run equilibrium selection behaviors in coordination games. Agents' risk attitudes enter through the classical entropic risk measure, which evaluates opponent-induced payoff uncertainty and feeds into noisy best responses under two standard revision protocols: best response with mutations and logit choice. We first analyze $2\times 2$ coordination games in both single-population symmetric and two-population asymmetric settings. In the single-population setting, unlike the risk-neutral case where the dynamics are known to favor the risk-dominant equilibrium, we show that risk sensitivity can change the stochastically stable outcome: a greater risk-seeking attitude favors the payoff-dominant equilibrium, while a greater risk-averse attitude favors the maximin equilibrium. Thus, the population's risk attitude may act as a control knob for long-run equilibrium selection. In both population settings, we also identify a robust regime: any super-dominant equilibrium is stochastically stable for all risk attitudes, under both protocols, and across populations. We further extend the single-population analysis to symmetric $k$-action games, which include symmetric $k$-action coordination games as a special case, under risk-sensitive best response with mutations. In this setting, we show that, for sufficiently large populations, sufficiently risk-seeking agents uniquely select the strongly payoff-dominant equilibrium when it exists, whereas sufficiently risk-averse agents uniquely select the strongly maximin equilibrium when it exists. These results show that entropic risk sensitivity may serve as a systematic mechanism for steering equilibrium selection in evolutionary games, beyond the classical risk-neutral benchmark.