Simon, Robert Samuel and Tomkowicz, Grzegorz
(2018)
A Bayesian game without ϵ-equilibria.
Israel Journal of Mathematics, 227 (1).
pp. 215-231.
ISSN 0021-2172
Abstract
We present a three player Bayesian game for which there are no ϵ-equilibria in Borel measurable strategies for small enough positive ϵ, however there are non-measurable equilibria. The structure of the game employs a non- amenable semi-group action corresponding to the knowledge of the players. The equilibrium property is related to the proper colouring of graphs and the Borel chromatic number; but rather than keeping adjacent vertices coloured differently there are algebraic conditions relating to the topology of the space and some ergodic operators.
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