熵风险敏感进化学习与协调博弈中的均衡选择
Entropic Risk-Sensitive Evolutionary Learning and Equilibrium Selection in Coordination Games
- University of Maryland, College Park（马里兰大学帕克分校）
- University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究提出熵风险敏感进化学习模型，证明在协调博弈中，种群风险态度可系统性调控长期均衡选择，风险寻求偏向收益占优均衡，风险规避偏向最大最小均衡。
AI中文摘要：
我们研究协调博弈中的风险敏感进化学习动力学及其长期均衡选择行为。智能体的风险态度通过经典熵风险度量引入，该度量评估对手引起的收益不确定性，并在两种标准修订协议下（带突变的best response和logit选择）纳入噪声最佳响应。我们首先在单种群对称和两种群非对称设置中分析$2\ imes 2$协调博弈。在单种群设置中，与已知动力学偏向风险占优均衡的风险中性情形不同，我们表明风险敏感性可以改变随机稳定结果：更强的风险寻求态度偏向收益占优均衡，而更强的风险规避态度偏向最大最小均衡。因此，种群的风险态度可作为长期均衡选择的控制旋钮。在两种种群设置中，我们还识别出一个稳健机制：任何超占优均衡在所有风险态度下、两种协议下以及跨种群中都是随机稳定的。我们进一步将单种群分析扩展到对称$k$行动博弈（包括对称$k$行动协调博弈作为特例），在风险敏感best response with mutations下。在此设置中，我们表明，对于足够大的种群，足够风险寻求的智能体在强收益占优均衡存在时唯一选择它，而足够风险规避的智能体在强最大最小均衡存在时唯一选择它。这些结果表明，熵风险敏感性可作为超越经典风险中性基准的、引导进化博弈中均衡选择的系统性机制。
英文摘要：
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.
