Game Theory
Max Jacobson
Morgan Kinsinger
ECN 338
B. Ferguson
8 May 2013
Dish Duty Keeping the kitchen clean while living in a house with ten people is a frustrating day-to-day challenge. Ideally, everyone in the house cleans up each mess they make immediately after they make it. Instead, housemates often leave their dirty dishes in the sink or on the counter for hours waiting to wash them later. Even more frustrating, housemates may wait for someone else to get fed up with the pile of dirty dishes and proceed to wash them. The kitchen constantly accumulates dirty dishes. Irresponsible housemates continue to shirk on their responsibility to clean up their messes because their actions are unobservable, or they believe another housemate will need a clean kitchen and be forced to clean it. The tolerance level of the kitchen’s cleanliness differs between all ten of the housemates. Because of the different preferences, some are more inclined to wash the dirty dishes whenever, but others prefer to wait until there are literally no more clean dishes left leaving them no choice but to wash a dish. In creating a game theoretical model to try and better understand the quandary in our kitchen, we will use repeated prisoners’ dilemma games, collective action analysis, and finally, a two species evolutionary game. We begin by applying a Repeated Prisoners’ Dilemma I (PDI) model to our situation. The rules for a PDI game are simple; the two players can either cooperate (wash) or defect (not wash). The players can fully observe each other’s move to wash their dish or to not wash. They will move in sequential order where player one moves first and the second player observes the move (see fig. 1). Then the second player carries out a move. The strategy called tit-for-tat (t-f-t), where player one cooperates on the first play and then does what the other player did the previous period, will be used to model the behavior of our players. The probability of continuing the
Morgan Kinsinger
ECN 338
B. Ferguson
8 May 2013
Dish Duty Keeping the kitchen clean while living in a house with ten people is a frustrating day-to-day challenge. Ideally, everyone in the house cleans up each mess they make immediately after they make it. Instead, housemates often leave their dirty dishes in the sink or on the counter for hours waiting to wash them later. Even more frustrating, housemates may wait for someone else to get fed up with the pile of dirty dishes and proceed to wash them. The kitchen constantly accumulates dirty dishes. Irresponsible housemates continue to shirk on their responsibility to clean up their messes because their actions are unobservable, or they believe another housemate will need a clean kitchen and be forced to clean it. The tolerance level of the kitchen’s cleanliness differs between all ten of the housemates. Because of the different preferences, some are more inclined to wash the dirty dishes whenever, but others prefer to wait until there are literally no more clean dishes left leaving them no choice but to wash a dish. In creating a game theoretical model to try and better understand the quandary in our kitchen, we will use repeated prisoners’ dilemma games, collective action analysis, and finally, a two species evolutionary game. We begin by applying a Repeated Prisoners’ Dilemma I (PDI) model to our situation. The rules for a PDI game are simple; the two players can either cooperate (wash) or defect (not wash). The players can fully observe each other’s move to wash their dish or to not wash. They will move in sequential order where player one moves first and the second player observes the move (see fig. 1). Then the second player carries out a move. The strategy called tit-for-tat (t-f-t), where player one cooperates on the first play and then does what the other player did the previous period, will be used to model the behavior of our players. The probability of continuing the