Abstract
Fuzzy matrix games, specifically two‐person zero‐sum games with fuzzy payoffs, are considered. In view of the parametric fuzzy max order relation, a fictitious play algorithm for finding the value of the game is presented. A numerical example to demonstrate the presented algorithm is also given.
Highlights
Game theory is a mathematical discipline which studies situations of competition and cooperation between several involved parties, and it has many applications in broad areas, such as strategic warfare, economic or social problems, animal behaviour, and political voting systems.The simplest game is a finite, two-person, zero-sum game
We consider zero-sum games with fuzzy payoffs with two players, and we assume that player I tries to maximize the profit and player II tries to minimize the costs
The two-person zero-sum game with fuzzy payoffs is defined by m×n matrix G whose entries are fuzzy numbers
Summary
Game theory is a mathematical discipline which studies situations of competition and cooperation between several involved parties, and it has many applications in broad areas, such as strategic warfare, economic or social problems, animal behaviour, and political voting systems. 0 , player I receives payoff gij and player II pays gij , where gij is the entry in row i and column j of matrix G. If player I plays strategy x and player II plays strategy y, player I receives the expected payoff g x, y xTGy, 1.3 where xT denotes the transpose of x. Player I can obtain a payoff at least ν by playing a maximin strategy, and player II can guarantee to pay not more than ν by playing a minimax strategy. For these reasons, the number ν is called the value of the game G. If i, j is a saddle point, gij must be the value of the game
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