A new class of probabilities in the n-person red-and-black game

Abstract

We discuss a model of a n-person, non-cooperative stochastic game, inspired by the discrete version of the red-and-black gambling problem introduced by Dubins and Savage in 1965. Our main theorem generalizes a result of Pontiggia from 2007 which provides conditions upon which bold strategies for all players form a Nash equilibrium. Our tool is a functional inequality, which is introduced and discussed in the present paper. It allows us to avoid restrictive assumptions of super-multiplicativity and super-additivity, which appear in Pontiggia' and other author works. We terminate the paper with some examples which in particular show that our approach leads to a essentially larger class of probability functions than existed in the literature so far.