Oct

12

J SogiIn the Prisoner's Dilemma two persons are caught by police. They are interrogated separately. If they both remain silent, both get light sentences. If one rats on the other, he gets off, the other gets life. If they both rat, they both get heavy sentences. Game theory predicts in a quantitative manner they will both rat on each other. The markets present a similar situation.

Model the market with negative drift and two people. If both buy and hold, they retain some money but due to negative drift, it is eroded. If one sells before the other, the market will go down, he wins, the other loses. If both sell, both lose even more money. Though there are added variables, a differential equation from game theory can be used to quantify the process. According to Overcast and Tullock a repeated prisoner's dilemma game can be converted into a differential game by assuming that the players, instead of making decisions individually for each repetition of the prisoner's dilemma game, make decisions on the ratio of cooperative and noncooperative games that they wish to play over the next few moves, and that the actual plays are then determined using this ratio and a randomizing procedure.


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3 Comments so far

  1. Matt Johnson on October 14, 2009 6:24 pm

    This theory is way too simplistic to compare to the financial markets. First off, to model the market with two people, is ridiculous. Second, the differential equation is excellent at quantifying the process of game theory – not the markets. Third, game theory attempts to use math in strategic situations, where the choice of one person depends on the choice of another – you have to know the other person’s position in order to play, again, totally unrealistic in trading. You’ve offered a modeling idea for everyone to see but you won’t do it yourself and post the results – partly I believe because it would be an academic exercise, that would prove to be totally useless in improving one’s P&L.

  2. Craig Bowles on October 15, 2009 8:49 am

    I used to work with a guy who now is teaching philosophy at NC I think. He used to say the easiest way to view complicated problems is to take them to the extremes and it becomes clear. Each trade has two sides no matter the number of trades. Austrian economic theory is seems based on this as it works from the individual up rather than macro down. Economists used to say there are no more Austrians in Austria, they are all here. Doesn’t seem so these days though. If you missed Steve Wynn’s interview, it’s a pretty good. http://www.zerohedge.com/article/steve-wynn-if-good-government-then-i-am-mary-poppins

  3. Anonymous on April 5, 2012 9:39 am

    I guess he doesn’t mean deterministic differential equations, they would be stochastic and why not who says differential equations can’t be used for markets? but apart from that, I know nothing about game theory to comment further.

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