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Practice paper

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

Richard Wise
Journal of Risk Management in Financial Institutions, 1 (2), 146-155 (2008)
https://doi.org/10.69554/BHWI5941

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.

Keywords: non-cooperative game theory; fixed point equilibrium; strategy responses; Nash equilibrium; volatility; illiquidity traps; speculative market

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Author's Biography

Richard Wise was educated at Cambridge University, graduating with a double first in mathematics in 1990. He worked at the regulatory forbearer of the UK Financial Services Authority, the Securities and Futures Authority, as a risk analyst before joining JP Morgan Chase in 1995. He has worked in various roles at JP Morgan including being an interest rate derivative trader in the London office prior to relocating to Japan. He has spent the last seven years in Japan building the market risk management function for Asia-Pacific. He is now in a global role heading risk management for the institutional equities business of JP Morgan.

Citation

Wise, Richard (2008, March 1). Technical note: Application of non-cooperative game theory to market disequilibria. In the Journal of Risk Management in Financial Institutions, Volume 1, Issue 2. https://doi.org/10.69554/BHWI5941.

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cover image, Journal of Risk Management in Financial Institutions
Journal of Risk Management in Financial Institutions
Volume 1 / Issue 2
© Henry Stewart
Publications LLP

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