Max-Min Control Problems and Solving Zero-Sum Games on Networks
The mathematical tool we develop in this chapter allows us to derive methods and algorithms for solving max-min discrete control problems and to determine optimal stationary strategies of the players in dynamic zero-sum games on networks. We propose polynomial-time algorithms for finding max-min paths on networks and determining optimal strategies of players in antagonistic positional games. These algorithms are applied for studying and solving cyclic games. The computational complexity of the proposed algorithms is analyzed.
KeywordsNash Equilibrium Optimal Strategy Directed Path Polynomial Time Algorithm Directed Cycle
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