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 repea ted game with random pay-offs. The suggested study is based on the learning automata paradigm and a limiting average reward criterion is tackled to an alyse the arising Nash equilibrium. No information concerning the distribut ion of the pay-off is a priori available. The novelty of the suggested adap tive strategy is related to the incorporation of a 'normalization procedure ' into the standard Bush-Mosteller scheme to provide a possibility to opera te not only with binary but also with any bounded rewards of a stochastic n ature. The analysis of the convergence (adaptation) as well as the converge nce rate (rate of adaptation) are presented and the optimal design paramete rs of this adaptive procedure are derived. The obtained adaptation rate tur ns out to be of o(n(-1/3)).