However, there is something odd about this game. It seems as though the two players would benefit by choosing to cooperate. Instead of winning only one point each, they could win three points each. So the"rational"choice of mutual defection has a puzzlin self-destructive flavor The second matrix is an example of a prisoner's dilemma game situation. Just to formalize the situation, let CC be the number of points won by each player when they both cooperate; let dd be the number of points won when both defect; let D be the number of points won by the cooperating party when the other defects; and let dC be the number of points won by the defecting party when the other cooperates. Then the prisoner's dilemma situation is characterized by the following conditions DC>CC>DD>CD DC+ CD In the second game matrix, we have dc=5. Cc=3. DD=1 CD=0 so both conditions are met. In the bunny and clod story, by the way, you can verify that DC=0, 1,DD=-10,CD=-20 Again, these values satisfy the prisoner's dilemma conditions Axelrod's tournament In the late 1970 s political scientist robert Axelrod held a computer tournament designed to investigate the prisoner's dilemma situation(Actually, there were two tournaments Their rules and results are described in Axelrod's book: The Evolution of Cooperation. Contestants in the tournament submitted computer programs that would compete in an iterated prisoner's dilemma game of approximately two hundred rounds, using the second matrix above. Each contestant's program played five iterated games against each of the other programs submitted, and after all games had been played the scores were tallied The contestants in Axelrod's tournament included professors of political science mathematics, computer science, and economics. The winning program-the program the highest average score- was submitted by Anatol Rapoport, a professor of psychole make up our own Scheme programs to play the iterated prisoner's dilemma game s and at the University of Toronto. In this project, we will pursue Axelrod's investigatio As part of this project, we will be running a similar tournament, but now involving a hree-person prisoner,s dilemmaHowever, there is something odd about this game. It seems as though the two players would benefit by choosing to cooperate. Instead of winning only one point each, they could win three points each. So the “rational” choice of mutual defection has a puzzling self-destructive flavor. The second matrix is an example of a prisoner's dilemma game situation. Just to formalize the situation, let CC be the number of points won by each player when they both cooperate; let DD be the number of points won when both defect; let CD be the number of points won by the cooperating party when the other defects; and let DC be the number of points won by the defecting party when the other cooperates. Then the prisoner's dilemma situation is characterized by the following conditions: In the second game matrix, we have so both conditions are met. In the Bunny and Clod story, by the way, you can verify that: Again, these values satisfy the prisoner's dilemma conditions. Axelrod's Tournament In the late 1970's, political scientist Robert Axelrod held a computer tournament designed to investigate the prisoner's dilemma situation (Actually, there were two tournaments. Their rules and results are described in Axelrod's book: The Evolution of Cooperation.). Contestants in the tournament submitted computer programs that would compete in an iterated prisoner's dilemma game of approximately two hundred rounds, using the second matrix above. Each contestant's program played five iterated games against each of the other programs submitted, and after all games had been played the scores were tallied. The contestants in Axelrod's tournament included professors of political science, mathematics, computer science, and economics. The winning program - the program with the highest average score - was submitted by Anatol Rapoport, a professor of psychology at the University of Toronto. In this project, we will pursue Axelrod's investigations and make up our own Scheme programs to play the iterated prisoner's dilemma game. As part of this project, we will be running a similar tournament, but now involving a three-person prisoner's dilemma