2021/05/29 by Włodzimierz Fechner, Fechner, Włodzimierz, Maria Słomian +1
Business, Management and Accounting · Economics, Econometrics and Finance · Mathematics · #91A06 #91A10 #91A60 #Benford’s Law and Fraud Detection #Consumer Market Behavior and Pricing #FOS: Mathematics #Game Theory and Voting Systems #Primary: 91A15. Secondary: 39B62 #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2105.14263
openalex publication_date 2021/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 introduced and discussed in the present paper. It allows us to avoid rather restrictive assumptions of super-multiplicativity and super-additivity, which appear in Pontiggia's and other authors' works. We terminate the paper with some examples which in particular show that our approach leads to a larger class of probability functions than existed in the literature so far.