Technical note: Application of non-cooperative game theory to market disequilibria

Abstract

Non-cooperative game theory is the (n-person) generalisation of decision theory which examines the outcomes of rational players pursuing strategies of perceived self-interest in an interactive forum. The financial market is such a forum, where hedge funds and banks’ proprietary trading divisions are increasingly deploying risk capital in like-minded strategies. This paper shows how the forum can be modelled under a game theoretical construct when consensual trading strategies cluster to a point of liquidity impairment. The paper discusses the relevance of noncooperative game theory to the risk management modelling of such behavioural interactions. Commencing with a review of the seminal paradox of the Prisoner’s Dilemma, the paper develops a simple model for an illiquid capital market, and draws on observations from the Prisoner’s Dilemma to examine the conditions under which a capital market may descend into a disorderly collapse. The broader implications for risk management are consequently discussed. The paper assumes a basic familiarity with the axiomatic tenets of game theory as well as the fundamental concept of an equilibrium fixed point, although a review of the Prisoner’s Dilemma and a justification for the attainment of the fixed point equilibrium should suffice to allow an intuitive understanding for the non-expert.