Borel Games with Lower-Semi-Continuous Payoffs

TL;DR

This paper proves that in two-player non-zero-sum Borel games with lower-semi-continuous payoffs, a subgame-perfect epsilon-equilibrium always exists, highlighting the importance of payoff continuity conditions.

Contribution

It establishes the existence of subgame-perfect epsilon-equilibria in Borel games under lower-semi-continuous payoffs, extending prior results and clarifying conditions for equilibrium existence.

Findings

Existence of subgame-perfect epsilon-equilibrium under lower-semi-continuous payoffs

Counterexample showing non-existence without lower-semi-continuity

Complements previous work by Solan and Vieille (2003)

Abstract

We prove that every two-player non-zero-sum Borel game with lower-semi-continuous payoffs admits a subgame-perfect $\ep$-equilibrium. This result complements Example 3 in Solan and Vieille (2003), which shows that a subgame-perfect $\ep$-equilibrium need not exists when the payoffs are not lower-semi-continuous.