This chapter discusses two types of stochastic policy for extensive form game representation as well as the existence and computation of saddle-point equilibrium. For games in extensive form, a mixed policy corresponds to selecting a pure policy in random based on a previously selected probability distribution before the game starts, and then playing that policy throughout the game. It is assumed that the random selections by both players are done statistically independently and the players will try to optimize the expected outcome of the game. After providing an overview of mixed policies and saddle-point equilibria, the chapter considers the behavioral policy for games in extensive form. It also explores behavioral saddle-point equilibrium, behavioral vs. mixed policy, recursive computation of equilibria for feedback games, mixed vs. behavioral order interchangeability, and non-feedback games. It concludes with practice exercises and their corresponding solutions, along with additional exercises.
Monotonicity of solutions converging to a saddle point equilibrium
