{"title":"Beyond Nash Equilibrium: Achieving Bayesian Perfect Equilibrium with Belief Update Fictitious Play","authors":"Qi Ju, Zhemei Fang, Yunfeng Luo","doi":"arxiv-2409.02706","DOIUrl":null,"url":null,"abstract":"In the domain of machine learning and game theory, the quest for Nash\nEquilibrium (NE) in extensive-form games with incomplete information is\nchallenging yet crucial for enhancing AI's decision-making support under varied\nscenarios. Traditional Counterfactual Regret Minimization (CFR) techniques\nexcel in navigating towards NE, focusing on scenarios where opponents deploy\noptimal strategies. However, the essence of machine learning in strategic game\nplay extends beyond reacting to optimal moves; it encompasses aiding human\ndecision-making in all circumstances. This includes not only crafting responses\nto optimal strategies but also recovering from suboptimal decisions and\ncapitalizing on opponents' errors. Herein lies the significance of\ntransitioning from NE to Bayesian Perfect Equilibrium (BPE), which accounts for\nevery possible condition, including the irrationality of opponents. To bridge this gap, we propose Belief Update Fictitious Play (BUFP), which\ninnovatively blends fictitious play with belief to target BPE, a more\ncomprehensive equilibrium concept than NE. Specifically, through adjusting\niteration stepsizes, BUFP allows for strategic convergence to both NE and BPE.\nFor instance, in our experiments, BUFP(EF) leverages the stepsize of Extensive\nForm Fictitious Play (EFFP) to achieve BPE, outperforming traditional CFR by\nsecuring a 48.53\\% increase in benefits in scenarios characterized by dominated\nstrategies.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"88 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Computer Science and Game Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.02706","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In the domain of machine learning and game theory, the quest for Nash
Equilibrium (NE) in extensive-form games with incomplete information is
challenging yet crucial for enhancing AI's decision-making support under varied
scenarios. Traditional Counterfactual Regret Minimization (CFR) techniques
excel in navigating towards NE, focusing on scenarios where opponents deploy
optimal strategies. However, the essence of machine learning in strategic game
play extends beyond reacting to optimal moves; it encompasses aiding human
decision-making in all circumstances. This includes not only crafting responses
to optimal strategies but also recovering from suboptimal decisions and
capitalizing on opponents' errors. Herein lies the significance of
transitioning from NE to Bayesian Perfect Equilibrium (BPE), which accounts for
every possible condition, including the irrationality of opponents. To bridge this gap, we propose Belief Update Fictitious Play (BUFP), which
innovatively blends fictitious play with belief to target BPE, a more
comprehensive equilibrium concept than NE. Specifically, through adjusting
iteration stepsizes, BUFP allows for strategic convergence to both NE and BPE.
For instance, in our experiments, BUFP(EF) leverages the stepsize of Extensive
Form Fictitious Play (EFFP) to achieve BPE, outperforming traditional CFR by
securing a 48.53\% increase in benefits in scenarios characterized by dominated
strategies.