# Library

### The Prisoner's Dilemma

In the problem of the prisoner's dilemma, two prisoners are interrogated in separate rooms. Each prisoner is given the choice of cooperating with their partner in crime (saying that they are innocent), or defecting (implicating their partner in crime). It is assumed that the base prison sentence that each will receive is five years, and that the payoff that each receives (time off from their prison sentence) is dependent on what decision they make, and what decision their partner makes. The classic payoffs are:

• If they both cooperate, the lack of testimony from the two prisoners weakens the case. There is still enough circumstantial evidence, however, to keep them in prison for two years each (payoff of 3 years off from the base sentence of five). (reward)
• If they both defect, the testimony that each provides against the other is quite damning. But their slightly conflicting stories allows the judge to imprison them for only four years each (payoff of 1 year off from the base sentence of five). (punishment)
• If one player defects and the other cooperates then there is no case against the defector, but a very strong one against the cooperator. The defector gets immunity and receives no prison sentence (payoff of 5 years off from the base sentence of five), while the judge throws the book at the cooperator who gets the full five year sentence (payoff of 0 years off from the base sentence of five). (sucker's payoff)
• This can be summarized in a matrix describing the payoff (in terms of the number of years off from the 5 year sentence that each receives) to one player (vertical axis) when it meets another player (horizontal axis) as shown on the right.

Player 2
Player 1
 Defect Cooperate Defect 1 5 Cooperate 0 3

Which strategy should you play under these conditions? Let's look at the problem from the point of view of player 1. If player 2 decides to defect, which is the better (more points) strategy? It is clearly better to defect (1 point versus 0 points). If player 2 decides to cooperate, which is the better strategy? Again, it is clearly better to defect (5 points versus 3 points). Thus, it is always better to defect.

Consider, however, that player 2 will be faced with the same choices, and consequently player 2 should always defect. Therefore, if each player plays logically they will both always defect and always receive one point. If they could have agreed beforehand to cooperate then instead they could each wind up with three points, a better outcome. Herein lines the dilemma- logically it pays for each player to defect, yet payoffs would be better if each player cooperated. In the face of such a dilemma, how can cooperation evolve?

Several theories have been proposed to explain how such cooperation can evolve. These ideas include different payoff structures that favor cooperation, reciprocal altruism in which individuals repeatedly interact, and the presence of a spatial structure that allows nearby individuals to interact.

How does this relate to the behavior of the halictid bees? As in the Prisoner's Dilemma each bee has the option of cooperating (providing reliable information) or defecting (providing false information). When both bees cooperate they each have access to their old and new resources. Having access to two good resources may be better than a single one because one may eventually run out. When both bees defect, each bee retains only its original resource. If one bee defects and the other cooperates than the cooperator has only one resource while the defector gets both. The exact payoffs for each of these scenarios is one of the subjects of the lab's investigations, and it is possible that other factors may affect the payoffs.

Since Prof. Shimoda's research pertains to the evolution of cooperation it is useful to employ models that incorporate entire populations of cooperators and defectors. This is done by assuming that cooperators and defectors interact randomly (initially) over the course of a generation. The payoff that each receives is translated into offspring in the next generation, remembering that cooperators give birth to cooperators and defectors give birth to defectors.

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