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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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Computation of Mixed Saddle-Point Equilibrium Policies

Computation of Mixed Saddle-Point Equilibrium Policies

Chapter:
(p.60) Lecture 6 Computation of Mixed Saddle-Point Equilibrium Policies
Source:
Noncooperative Game Theory
Author(s):

João P. Hespanha

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691175218.003.0006

This chapter focuses on the computation of mixed saddle-point equilibrium policies. In view of the Minimax Theorem, the mixed saddle-point equilibria can be determined by computing the mixed security policies for both players. For 2 x 2 games, the mixed security policy can be computed in closed form using the “graphical method.” After providing an overview of the graphical method, the chapter considers a systematic numerical procedure to find the linear program solution for mixed saddle-point equilibria and the use of MATLAB's Optimization Toolbox to numerically solve linear programs. It then describes a strictly dominating policy and a “weakly” dominating policy before concluding with practice exercises and their corresponding solutions, along with an additional exercise.

Keywords:   mixed saddle-point equilibrium, mixed security policy, graphical method, linear program, MATLAB, strictly dominating policy, weakly dominating policy

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