# Stock Trading and Game Theory, from James Sogi

October 12, 2009 |

In 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.