2015/05/23 by Stéphane Le Roux, Roux, Stephane Le
Decision Sciences · Economics, Econometrics and Finance · #91A18 #91A44 #Computer Science and Game Theory (cs.GT) #Economic theories and models #F.4.1 #FOS: Computer and information sciences #FOS: Mathematics #Game Theory and Applications #Game Theory and Voting Systems #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.1505.06320
openalex publication_date 2015/05/23 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
Subgame perfect equilibria are specific Nash equilibria in perfect information games in extensive form. They are important because they relate to the rationality of the players. They always exist in infinite games with continuous real-valued payoffs, but may fail to exist even in simple games with slightly discontinuous payoffs. This article considers only games whose outcome functions are measurable in the Hausdorff difference hierarchy of the open sets (i.e. Δ02 when in the Baire space), and it characterizes the families of linear preferences such that every game using these preferences has a subgame perfect equilibrium: the preferences without infinite ascending chains (of course), and such that for all players a and b and outcomes x,y,z we have ¬(z