The modified stochastic game

We present a new tool for the study of multiplayer stochastic games, namely the modified game, which is a normal-form game that depends on the discount factor, the initial state, and for every player a partition of the set of states and a vector that assigns a real number to each element of the partition. We study properties of the modified game, like its equilibria, min–max value, and max–min value. We then show how this tool can be used to prove the existence of a uniform equilibrium in a certain class of multiplayer stochastic games.