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Biology 4415 Evolution LABORATORY EXERCISE 5 : THE PRISONER’S DILEMMA The Prisoner’s Dilemma originally was a classic problem in the mathematical field of game theory. In the original version of the Prisoner’s Dilemma problem, there are two criminals who are in prison for a relatively minor crime, serving, say, a three-year sentence. The prosecutor thinks that both are guilty of a much more serious crime— perhaps a murder—but can’t prove it with the evidence he has. So he meets with each prisoner individually, without the other one knowing of the meeting, and he makes the prisoners a deal: If one of them confesses to the serious crime, and rats on the other one, the one who confesses will go free and the one who doesn’t will get twenty-five years in prison. However, if they both confess, both will get ten-year sentences. If neither one does, of course, the prosecutor won’t be able to make a case, and both will end up serving three years for their more minor offense. We can draw up a matrix of payoffs for the four possible outcomes. Each prisoner has to choose whether to cooperate (that is, cooperate with his fellow prisoner, and refuse to snitch) or defect (tattle to the authorities). If we call the prisoners A and B, then the outcomes are: A Cooperates A Defects B Cooperates A: - 3 B: - 3
A: 0
B: - 25
B Defects A: - 25 B: 0
A: - 10
B: - 10
(The outcomes are written as negative numbers because they’re penalties. If they were bonuses—say, if a defector got not only freedom but a $25,000 reward—then we’d write positive numbers.) As the rules stand, the best thing to do is to defect— if the Dilemma is presented only once. Why? Briefly: the worst that can happen to a defector (ten years in prison) is better than the worst that can happen to a cooperator (25 years in prison), and the best that can happen to a defector (freedom) is better than the best that could happen to a cooperator (three years in prison). This applies whether the payoffs are negative, as in the example above using prison time, or positive, as it would be if winning money were the aim of the game. And if the game is played only once, neither A nor B can retaliate if he thinks he’s been suckered.
Another way to look at it is this: Suppose that A knew that B would decide what to do by flipping a coin. Then if A defected, he’d have a 50% chance of going free, a 50% chance of serving ten years—for an expectation of (0.5)(0) + (0.5)(-10) = - 5. If A cooperated, his expectation would be (0.5)(-3) + (0.5)(-25) = - 14. A’s best move is to defect. For the same reason, so is B’s. A single Prisoner’s Dilemma isn’t very interesting, and isn’t all that biologically realistic. However... what would happen if, after both were out of prison, A and B were caught again and put in the same situation? What should a prisoner choose if he knows that his buddy has cooperated with him before? Or ratted on him before? What if the Dilemma is presented to both criminals, each with different partners? What if the goal isn’t to minimize a single penalty (here, a term in jail) but to minimize the total penalty over a long lifetime? If both players in a Prisoner’s Dilemma know that the game will be repeated a finite number of times, and know how many times the game will be repeated, defection is still the best option. But tn a game like this that’s repeated indefinitely, in which neither player knows how many times the game will be repeated, the “winning strategy” is not so simple. In fact, it turns out that cooperation works better than defection over the long term. This indefinite game is called an Iterated Prisoner’s Dilemma , and it has applications in everything from economics and political science to evolutionary biology. In evolution, the Iterated Prisoner’s Dilemma can be used to look at the question: How can cooperation evolve? Does natural selection shape organisms in ways that benefit them at the expense of others? The answer, surprisingly, turns out to be “no”. In computer simulations in which “virtual organisms” interact, either in random pairings or in “round-robin tournaments”, limited cooperation is the most successful strategy over the long term. Many organisms interact in ways that can be modeled as Iterative Prisoner’s Dilemmas. MATERIALS: strategy cards (three types, labeled AC, AD, TT) encounter cards (two types, labeled Cooperate and Defect) “life energy” tokens (beans, beads, marbles, pennies, etc.)
1. Each player starts with twenty-five tokens, representing some sort of life resource (energy, food, etc.) Each player also starts with two cards labeled “Cooperate” and “Defect”. 2. Each player randomly draws a card that gives him or her a strategy to play. DO NOT SHOW YOUR CARD TO ANYONE, OR TELL ANYONE WHAT YOUR STRATEGY IS! There are three options: - Always Cooperate (AC). A player playing the AC strategy always cooperates, no matter what has gone before.
7. Turn in a full lab writeup that includes: - the class data - graphs of the average gain vs. frequency of each strategy - a general discussion of the results - a discussion of how this simulation would apply to evolution
