TY - JOUR
T1 - Regularity of the minmax value and equilibria in multiplayer Blackwell games
AU - Ashkenazi-Golan, Galit
AU - Flesch, János
AU - Predtetchinski, Arkadi
AU - Solan, Eilon
N1 - data source: no data used
PY - 2024/1/1
Y1 - 2024/1/1
N2 - 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.
AB - 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.
U2 - 10.1007/s11856-024-2679-9
DO - 10.1007/s11856-024-2679-9
M3 - Article
SN - 0021-2172
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
ER -