The MaxMin value of stochastic games with imperfect monitoring

In stochastic games, the player’s payoff is a stochastic variable. In most papers, expected payoff is considered as a payoff, which means the risk neutrality of the players. However, there may exist risk-sensitive players who would take into account “risk” measuring their stochastic payoffs. In the paper, we propose a model of stochastic games with mean-variance payoff functions, which is the sum of expectation and standard deviation multiplied by a coefficient characterizing a player’s attention to risk. We construct a cooperative version of a stochastic game with mean-variance preferences by defining characteristic function using a maxmin approach. The imputation in a cooperative stochastic game with mean-variance preferences is supposed to be a random vector. We construct the core of a cooperative stochastic game with mean-variance preferences. The paper extends existing models of discrete-time stochastic games and approaches to find cooperative solutions in these games.

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Analyzing Latency-Aware Self-Adaptation Using Stochastic Games and Simulations

ACM Transactions on Autonomous and Adaptive Systems ◽

10.1145/2774222 ◽

2016 ◽

Vol 10 (4) ◽

pp. 1-28 ◽

Cited By ~ 17

Author(s):

Javier Cámara ◽

Gabriel A. Moreno ◽

David Garlan ◽

Bradley Schmerl

Keyword(s):

Stochastic Games ◽

Self Adaptation ◽

Games And Simulations

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Security investment of interdependent and identical CPSs: Stochastic games with asymmetric information

International Journal of Intelligent Systems ◽

10.1002/int.22555 ◽

2021 ◽

Author(s):

Wei Xing ◽

Congli Mei ◽

Le Liu ◽

Dong Guo ◽

Abdulhameed F. Alkhateeb ◽

...

Keyword(s):

Asymmetric Information ◽

Stochastic Games ◽

Security Investment

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Discrete-Time Constrained Average Stochastic Games with Independent State Processes

Mathematics ◽

10.3390/math7111089 ◽

2019 ◽

Vol 7 (11) ◽

pp. 1089

Author(s):

Wenzhao Zhang

Keyword(s):

Discrete Time ◽

Stochastic Games ◽

Transition Probability ◽

Existence Condition ◽

Linear Program ◽

Global Minimizer ◽

Independent State ◽

Occupation Measures ◽

Best Response ◽

Mathematic Program

In this paper, we consider the discrete-time constrained average stochastic games with independent state processes. The state space of each player is denumerable and one-stage cost functions can be unbounded. In these game models, each player chooses an action each time which influences the transition probability of a Markov chain controlled only by this player. Moreover, each player needs to pay some costs which depend on the actions of all the players. First, we give an existence condition of stationary constrained Nash equilibria based on the technique of average occupation measures and the best response linear program. Then, combining the best response linear program and duality program, we present a non-convex mathematic program and prove that each stationary Nash equilibrium is a global minimizer of this mathematic program. Finally, a controlled wireless network is presented to illustrate our main results.

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