Perfect-Information Games with Lower-Semicontinuous Payoffs
Published Online:1 Nov 2010https://doi.org/10.1287/moor.1100.0469
Abstract
We prove that every multiplayer perfect-information game with bounded and lower-semicontinuous payoffs admits a subgame-perfect ε-equilibrium in pure strategies. This result complements Example 3 in Solan and Vieille [Solan, E., N. Vieille. 2003. Deterministic multi-player Dynkin games. J. Math. Econom.39 911–929], which shows that a subgame-perfect ε-equilibrium in pure strategies need not exist when the payoffs are not lower-semicontinuous. In addition, if the range of payoffs is finite, we characterize in the form of a Folk Theorem the set of all plays and payoffs that are induced by subgame-perfect 0-equilibria in pure strategies.
