Otman Javier Gordillo To what extent game theory is a helpful approach to the financial markets Game theory is the science that mathematically captures the behaviour of agents (humans, nations or animals) in strategic situations (when the individual success depends on the choices of others players). Before it, election choice was framed in the idea of individual election without interaction among agents, situation that biased social sciences’ analysis because in many cases, one agents’ response reflects not only his or her preferences, but also preferences of other agents in the “game” (Owen, 2008). In this sense, game theory brought to social sciences tools to realistically analyse interactions among individuals. It was initially introduced by von Neumann and Morgenstern in 1944 and Nash in 1950, and since then, it has been increasingly used not only in economics, but also in computer science, engineering, biology, political science, international relations and even philosophy. Financial markets have been not isolated of the influence of game theory: it has affected theory foundations, market analysis and trading methods. Indeed, its influence has been so important that The Economist (1996) said that “managers have much to learn from game theory — provided they use it to clarify their thinking”; in a similar vein The Wall Street Journal (1995), the most influential business newspaper said “game theory is hot”. The purpose of this essay is to unveil the revolutionary applications of game theory not only in finance theory, but also in trading, pricing and agents’ competition (every day finance or real finance). This document will focus on three foremost aspects: first, the analysis of the financial market as a game to point out the capability of game theory to analyse markets. Afterwards I will focus on the contributions of game theory to the development of modern finances mentioning asset pricing’s approach, invertors’ unusual behaviour and analysis of interaction complex models. Finally I am going to indicate some limitations of game theory related to markets study. My target is to point out that the analysis of markets of any kind of assets including not only Wall Street’s (stock exchange), but also Main Street’s (industrial production); is now more
accurate because game theory gave adequate tools that reflect genuine agent’s behaviour.
To begin with, financial markets (for instance, Dow Jones Industrial Index, S&P500 or FTSE,) can be depicted as a strategic game with N players: individual, institutional investors, pension fund managers and investment bank traders, playing in the market. The payoffs of each player are clearly determined: win or lose money according to the amount invested. Even though it seems that there are big differences among agents, the target of each player is to maximize their wealth (Engle, 2008). To maximise profits, agents can choose among three options: buy, sell or hold (Shelton, 1997). In the case of prisoner’s dilemma, election is limited to confess and not confess. Agents share the same background, because financial information is public: pricing techniques, corporative results, earnings reports, economic indicators, and even rumours are confirmed or denied by specialized business diaries. However, despite the information is nearly perfect, and agents share the same inputs, players do not know the intentions, opinions and potential strategies of opponents: nobody knows neither how the portfolio of the opponent is conformed, non what risk level is acceptable to the opponent. This “asymmetric information” gives the conditions to price volatility (Engle, 2008) and agent’s optimal responses reflect decisions of others players. The same characterization can be applied to any kind of markets: commodities, bonds, equities, currencies and derivatives.
Once established the analogy between financial markets and strategic games to verify the validity of this approach, it is...