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A certain class of noncooperative games is considered with two pure strategies for each of the automata players. The nature of the game is such that the pay-off of each player increases if any other participant in the game chooses the same pure strategy as that player, and decreases otherwise. The pay-off from a joint strategy is generally different for each automaton so that a joint strategy which is mutually profitable is not generally a fair play. A learning automaton model is proposed so that, without any prior agreement, as time unfolds a group of automata achieve a situation in mixed strategies which yields a pay-off for each automaton that is a trade-off between `fairness' and `profitability'. A formal mathematical proof of convergence of the collective situation in mixed strategies is given. An example is given to demonstrate the theoretical results.
Systems, Man and Cybernetics, IEEE Transactions on (Volume:SMC-13 , Issue: 2 )
Date of Publication: March-April 1983