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

This paper deals with the design and analysis of a modijied version of the BushMosteller reiqfimement scheme applied by partners in a zero-sum repeuted grme 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 qf the pay-off is a priori available. The noveltjl of the suggested adaptive strategj3 is related to the incorporation qf a 'normalization procedure' into the standard Bu.sh-Mostcller scheme to provide a po.r.sibilitj, to operate not only with binary but also ~ , i t h unj3 hounded rewards of a stochastic nature. The analysis of the convergerre (adaptation) us well as the convergence rate (rute of adaptation) are presented and the optimal design parumetcrs of this adaptive procedure are derived. The obtained adaptation rute turns out to be of o(n-'I3).