Bush‐Mosteller learning for a zero-sum repeated game with random pay-offs

This paper deals with the design and analysis of a modified version of the Bush-Mosteller reinforcement scheme applied by partners in a zero-sum repeated game with random pay-offs. The suggested study is based on the learning automata paradigm and a limiting average reward criterion is tackled to analyse the arising Nash equilibrium. No information concerning the distribution of the pay-off is a priori available. The novelty of the suggested adaptive strategy is related to the incorporation of a 'normalization procedure' into the standard Bush-Mosteller scheme to provide a possibility to operate not only with binary but also with any bounded rewards of a stochastic nature. The analysis of the convergence (adaptation) as well as the convergence rate (rate of adaptation) are presented and the optimal design parameters of this adaptive procedure are derived. The obtained adaptation rate turns out to be of o(n 1/3 ).

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