On the Complexity of Non-reversible Betting Games on Many-Valued Events

Abstract

A bookmaker is said to be non-reversible if she does not accept negative stakes on the events. A rational criterion to choose stakes on a book Γ arranged by a non-reversible bookmaker, avoids bad bets. A bad bet is a stake δ on an event φ, that gives the bettor a strictly better payoff independently of the truth values of the events involved. In this paper we study the computational complexity for the problem of deciding whether a book arranged on many-valued events, admits bad bets, or it does not. In this short paper we show our problem to be NP-complete. © Springer-Verlag Berlin Heidelberg 2010.