On the rationality of arbitrage prices in non-zero sum contingent claimvaluation games

This analysis reveals the restricted scope of approaches which utilise arbitrage based arguments toprice contingent claims whose payoffs are determined by the outcome of non-zero-sum valuationgames between financial market participants. Many examples of such model formulations can befound, for example, in the recent corporate debt valuation literature. This analysis proposes the moregeneral concept of a rational price for valuing such claims, demonstrating how such prices overcomethe inherent limitations of arbitrage pricing methods. Although rational prices are already used in theliterature, we believe this paper is the first to analyze their formal relationship to arbitrage prices. Wedemonstrate that, when it exists, an arbitrage price: (i) is the equivalent of a pure saddle point strategyin game theory, (ii) can be guaranteed to be rational only in strictly competitive games, and (iii) neverlies above the rational price of the contingent claim....