# A Bayesian Game without epsilon equilibria

## TL;DR

This paper constructs a three-player Bayesian game demonstrating the non-existence of epsilon equilibria in measurable strategies for small epsilon, while showing that non-measurable equilibria do exist, highlighting limitations of epsilon equilibrium concepts.

## Contribution

It introduces a specific Bayesian game where epsilon equilibria in measurable strategies do not exist, revealing new insights into equilibrium existence in Bayesian games.

## Key findings

- No epsilon equilibria in measurable strategies for small epsilon
- Existence of non-measurable equilibria in the constructed game
- Highlights limitations of epsilon equilibrium concepts in Bayesian games

## Abstract

We present a three player Bayesian game for which there is no epsilon equilibria in Borel measurable strategies for small enough epsilon, however there are non-measurable equilibria.