We provide easily-verifiable sufficient conditions on the primitives of a Bayesian game to guarantee the existence of a behavioral-strategy Bayes–Nash equilibrium. We allow players' payoff functions to be discontinuous in actions, and illustrate the usefulness of our results via an example of an all-pay auction with general tie-breaking rules which cannot be handled by extant results.
- Discontinuous Bayesian game
- Behavioral strategy
- Random disjoint payoff matching
- Equilibrium existence
- All-pay auction