Saddle point equilibrium under uncertain environment

2018 ◽  
Vol 41 (5) ◽  
pp. 2063-2073 ◽  
Author(s):  
Yun Sun ◽  
Chunxiao Ding ◽  
Yuanguo Zhu
Keyword(s):  
Saddle Point ◽  
Uncertain Environment ◽  
Saddle Point Equilibrium

Mixed Policies

2017 ◽  
Author(s):  
João P. Hespanha
Keyword(s):  
Probability Distribution ◽  
Saddle Point ◽  
Security Policy ◽  
General Type ◽  
Zero Sum Games ◽  
Security Levels ◽  
Mixed Action ◽  
Zero Sum ◽  
Saddle Point Equilibrium ◽  
Action Spaces

This chapter explores the concept of mixed policies and how the notions for pure policies can be adapted to this more general type of policies. A pure policy consists of choices of particular actions (perhaps based on some observation), whereas a mixed policy involves choosing a probability distribution to select actions (perhaps as a function of observations). The idea behind mixed policies is that the players select their actions randomly according to a previously selected probability distribution. The chapter first considers the rock-paper-scissors game as an example of mixed policy before discussing mixed action spaces, mixed security policy and saddle-point equilibrium, mixed saddle-point equilibrium vs. average security levels, and general zero-sum games. It concludes with practice exercises with corresponding solutions and an additional exercise.

Stochastic Policies for Games in Extensive Form

2017 ◽  
Author(s):  
João P. Hespanha
Keyword(s):  
Probability Distribution ◽  
Saddle Point ◽  
Extensive Form ◽  
Form Game ◽  
Expected Outcome ◽  
Recursive Computation ◽  
Extensive Form Game ◽  
Saddle Point Equilibrium ◽  
Computation Of Equilibria ◽  
Game Representation

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.

scholarly journals Game Approach for H∞ Robust Control Strategy to Follow the Production in the Singularly Perturbed Bilinear Dynamic Input-Output Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Ning Bin ◽  
Chengke Zhang ◽  
Huainian Zhu ◽  
Qiyou Liu
Keyword(s):  
Robust Control ◽  
Saddle Point ◽  
Control Model ◽  
Singularly Perturbed ◽  
Input Output ◽  
Social Production ◽  
Numerical Result ◽  
Production Development ◽  
Differential Game Theory ◽  
Saddle Point Equilibrium

For simulating and analyzing the input and output problem of national economy more accurately, this paper considers the fast and slow production processes during the course of social production development, takes stochastic economic risks into consideration, and constructs a H∞ robust control model to follow the production in the singularly perturbed dynamic input-output systems. Further introducing ideas of noncooperative differential game theory, the H∞ robust control model is transformed into a saddle-point equilibrium game model, and a new method for solving dynamic input-output problem by using saddle-point equilibrium strategies is obtained. A numerical result is presented in the end to illustrate the effectiveness of the method.

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