In class, we've recently been talking about game theory and zero-sum games. When playing the Prisoner's Dilemma, I wondered what the best strategy was, so I'm going to solve it with expected values. First, some explanations: zero-sum games are games in which there is one winner. The Prisoner's Dilemma is one such game. In this game, there are two players, who are the prisoners. Each must decide whether to keep quiet or confess (that the other player is guilty). If both keep quiet, each gets a year of jail time. If both confess, both get five years. If one confesses and the other keeps quiet, the quiet one gets ten years and the confessor gets off free. The goal is to have the least amount of time. While the true odds of the opponent's choice depend on the individual opponent, it's fairly safe to say none of us are mind readers, so we can't truly tell what they'll do. So, for simplicity's sake, I'll say there's an equal chance of the other player confessing or keeping quiet. Now, to calculate the expected value, I'll multiply the probability of each possible result by the number of years it will result in, then add those values together. The expected value of keeping quiet is 5.5, because: If the other player keeps quiet: 0.5 (chance) x 1 (years) = 0.5 If they confess: 0.5x 10= 5 5+0.5=5.5 The expected value of confessing is 2.5, because: If they keep quiet: 0.5x0=0 If they confess: 0.5x5=2.5 2.5+0=2.5 Based on expected value, the player is much better off confessing. As I said before, the chances of what the other player will do depend on who the other player is, and must be estimated. However, it's still better to confess, and here's why. The goal of the game is to have the least jail time. If both players keep quiet every round, they'll tie every time. In order for one to get ahead, someone has to confess. Whoever doesn't confess will lose unless the other player decides to keep quiet in a later round, and the losing player confesses. Since there's no good reason to risk keeping quiet, the winning player probably won't do it. So, in the end, the best strategy is to throw the other player under the bus–and hope they don't do the same to you! So, to summarize:
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AuthorI'm moving on to my 4th (and final) year as a Game Art & Design student at Durham School of the Arts. I'd like to call myself an artist, but I'm a programmer at heart. Archives
February 2020
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