Regularity of the minmax value and equilibria in multiplayer Blackwell games

Ashkenazi-Golan, Galit ORCID: 0000-0003-3896-4131, Flesch, János, Predtetchinski, Arkadi and Solan, Eilon (2024) Regularity of the minmax value and equilibria in multiplayer Blackwell games. Israel Journal of Mathematics. ISSN 0021-2172

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Abstract

A real-valued function φ that is defined over all Borel sets of a topological space is regular if for every Borel set W, φ(W) is the supremum of φ(C), over all closed sets C that are contained in W, and the infimum of φ(O), over all open sets O that contain W. We study Blackwell games with finitely many players. We show that when each player has a countable set of actions and the objective of a certain player is represented by a Borel winning set, that player’s minmax value is regular. We then use the regularity of the minmax value to establish the existence of ε-equilibria in two distinct classes of Blackwell games. One is the class of n-player Blackwell games where each player has a finite action space and an analytic winning set, and the sum of the minmax values over the players exceeds n − 1. The other class is that of Blackwell games with bounded upper semi-analytic payoff functions, history-independent finite action spaces, and history-independent minmax values. For the latter class, we obtain a characterization of the set of equilibrium payoffs.

Item Type:	Article
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	17 Oct 2022 14:09
Last Modified:	20 Dec 2024 00:46
URI:	http://eprints.lse.ac.uk/id/eprint/117118

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