Determining the Equilibrium Solution in Two-Player Dynamic Discrete Markovian Games with transition probabilities influenced by competitor strategies

In most applications and scientific articles, for simplicity the games have been done as one shot. Also, in most of the games, the mixed strategies are not used, whereas a mix of two or more strategies can be more helpful for players in future. Therefore, it is quite natural considering a mix of two or more strategies stochastically. This article introduces a series of games called Markovian Dynamic Games that if you consider the strategies of each player as a state, the player can select the same or another state depending on the situation in the next steps. The selecting each state in each step will be done with a specified probability.This probability is depending on the strategies of the competing players. In this study, a two-player discrete game with Markov chain approach is considered that the probability of transfer is well-known, independent and is only influenced by the competitorchr(chr('39')39chr('39'))s previous strategies. In this paper, the equilibrium points in markovian dynamic games are evaluated and analyzed. Numerical examples are also presented for more explanations. In this paper, the difference between single stage and multi-stage games in determining equilibrium points is shown. If a game is played in a multilevel manner, it is possible to design a discrete game as a Markov chain using the probability of transferring and considering the strategies of the game as a mode in each step, and by determining the probabilities of the specified chain, points He gained some balance.For this purpose, dynamic games were considered,