Stationary Markov Equilibrium Strategies in Asynchronous Stochastic Games: Existence and Computation
We study Asynchronous Dynamic games and show that in games with a finite state space and finite action sets, one can obtain the pure strategy Markov perfect equilibrium by using a simple backward induction method when the time period for the game is finite. The equilibrium strategies for games with...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-11-01
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| Series: | Algorithms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1999-4893/17/11/490 |
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| Summary: | We study Asynchronous Dynamic games and show that in games with a finite state space and finite action sets, one can obtain the pure strategy Markov perfect equilibrium by using a simple backward induction method when the time period for the game is finite. The equilibrium strategies for games with an infinite horizon are then obtained as the point-wise limit of the equilibrium strategies of a sequence of finite horizon games, where the finite horizon games are truncated versions of the original game with successively longer time periods. We also show that if the game has a fixed <i>K</i>-period cycle, then there is a stationary Markov equilibrium. Using these results, we derive an algorithm to compute the equilibrium strategies. We test the algorithm in three experiments. The first is a two-player asynchronous game with three states and three actions. In the second experiment, we compute the equilibrium of a cybersecurity game in which there are two players, an attacker and a defender. In the third experiment, we compute the stationary equilibrium of a duopoly game with two firms that choose an output in alternate periods. |
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| ISSN: | 1999-4893 |