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Noncooperative Game TheoryAn Introduction for Engineers and Computer Scientists$
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João P. Hespanha

Print publication date: 2017

Print ISBN-13: 9780691175218

Published to Princeton Scholarship Online: May 2018

DOI: 10.23943/princeton/9780691175218.001.0001

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Stochastic Policies for Games in Extensive Form

Stochastic Policies for Games in Extensive Form

(p.87) Lecture 8 Stochastic Policies for Games in Extensive Form
Noncooperative Game Theory

João P. Hespanha

Princeton University Press

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.

Keywords:   stochastic policy, extensive form game representation, saddle-point equilibrium, mixed policy, pure policy, behavioral policy, behavioral saddle-point equilibrium, recursive computation, feedback game, non-feedback game

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