Markov recurrent method

This paper proposes a new application of the stochastic game model to solve the problem of self- organization of the Hamiltonian cycle of a graph. To do this, at the vertices of the undirected graph are placed game agents, whose pure strategies are options for choosing one of the incident edges. A random selection of strategies by all agents forms a set of local paths that begin at each vertex of the graph. Current player payments are defined as loss functions that depend on the strategies of neighboring players that control adjacent vertices of the graph.

In this paper, a stochastic game model of self-organization of strategies of stochastic game of mobile agents in the form of cyclic behavioral patterns, which consist of coordinated strategies for moving agents in a limited discrete space, is developed. The behavioral pattern of a multi-agent system is a visualized form of orderly movement of agents that arises from their initial chaotic movement during the learning of a stochastic game.