Existence of Value and Randomized Strategies in Zero-Sum Discrete-Time Stochastic Dynamic Games

1981 ◽  
Vol 19 (5) ◽  
pp. 617-634 ◽  
Author(s):  
P. R. Kumar ◽  
T. H. Shiau
Keyword(s):  
Discrete Time ◽  
Dynamic Games ◽  
Stochastic Dynamic ◽  
Randomized Strategies ◽  
Existence Of Value ◽  
Zero Sum ◽  
Stochastic Dynamic Games

SUBGAME CONSISTENT SOLUTION FOR COOPERATIVE STOCHASTIC DYNAMIC GAMES WITH RANDOM HORIZON

2012 ◽  
Vol 14 (02) ◽  
pp. 1250012 ◽  
Author(s):  
DAVID W. K. YEUNG ◽  
LEON A. PETROSYAN
Keyword(s):  
Discrete Time ◽  
Dynamic Games ◽  
Bellman Equation ◽  
Stochastic Dynamic ◽  
Cooperative Solution ◽  
Optimal Behavior ◽  
Random Horizon ◽  
Consistent Solution ◽  
First Time ◽  
Stochastic Dynamic Games

In cooperative stochastic dynamic games a stringent condition — that of subgame consistency — is required for a dynamically stable cooperative solution. In particular, a cooperative solution is subgame consistent if an extension of the solution policy to a subgame starting at a later time with a state brought about by prior optimal behavior would remain optimal. This paper extends subgame consistent solutions to cooperative stochastic dynamic (discrete-time) games with random horizon. In the analysis new forms of the stochastic Bellman equation and the stochastic Isaacs–Bellman equation in discrete time are derived. Subgame consistent cooperative solutions are obtained for stochastic dynamic games. Analytically tractable payoff distribution mechanisms which lead to the realization of these solutions are developed. This is the first time that subgame consistent solutions for cooperative stochastic dynamic games with random horizon are presented.

State-Feedback Zero-Sum Dynamic Games

2017 ◽  
Author(s):  
João P. Hespanha
Keyword(s):  
Discrete Time ◽  
Information Structure ◽  
Dynamic Games ◽  
State Feedback ◽  
Linear Quadratic ◽  
Feedback Information ◽  
Time Dynamic ◽  
Finite State ◽  
Solution Methods ◽  
Zero Sum

This chapter focuses on the computation of the saddle-point equilibrium of a zero-sum discrete time dynamic game in a state-feedback policy. It begins by considering solution methods for two-player zero sum dynamic games in discrete time, assuming a finite horizon stage-additive cost that Player 1 wants to minimize and Player 2 wants to maximize, and taking into account a state feedback information structure. The discussion then turns to discrete time dynamic programming, the use of MATLAB to solve zero-sum games with finite state spaces and finite action spaces, and discrete time linear quadratic dynamic games. The chapter concludes with a practice exercise that requires computing the cost-to-go for each state of the tic-tac-toe game, and the corresponding solution.

scholarly journals Stochastic Dynamic Games in Belief Space

2021 ◽  
pp. 1-16
Author(s):  
Wilko Schwarting ◽  
Alyssa Pierson ◽  
Sertac Karaman ◽  
Daniela Rus
Keyword(s):  
Dynamic Games ◽  
Stochastic Dynamic ◽  
Stochastic Dynamic Games
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