### Effect of Variable-Threshold Strategies in Demographic Donor-Recipient and Prisoner's Dilemma Games

*Tsuneyuki Namekata, Yoko Namekata*

Building: Law Building

Room: Breakout 3 - Law Building, Room 104

Date: 2012-07-12 03:30 PM – 05:00 PM

Last modified: 2012-04-02

#### Abstract

We consider effect of variable-threshold strategies on emergence of cooperation in Demographic dilemma game, Donor-Recipient or Prisoner's Dilemma game.

Tit for Tat changes his move at each period depending on the previous opponentâ€™s move. In real life, people further change their tendency toward cooperation or defection. We want to incorporate this change into our model. We introduce variable-threshold strategies which are extended forms of TFT. We interpret that TFT uses Defect if the state is 0, Cooperate if it is 1 and the smallest state number that prescribes using Cooperate as a threshold. AllC has zero threshold in this interpretation. We allow up to three states. Variable-threshold strategy changes its threshold by at most one at some age (once in his lifetime) depending on its experience until then. Thus variable-threshold TFT who was born as TFT may change to AllC or AllD. Also variable-threshold AllC who was born as AllC may change to TFT.

Players are initially randomly distributed in square lattice of cells. In each period, players move locally to random cell in von Neumann neighbors if unoccupied or globally to random unoccupied cell in the whole lattice, and play dilemma game against local neighboring player or against randomly selected player from the whole lattice. If wealth (accumulated payoff) of player becomes negative or his age becomes greater than his lifetime, he dies. If his wealth becomes greater than some amount and there is unoccupied cell in neighbors, he has an offspring.

A stage game is Donor-Recipient or Prisoner's Dilemma game. Donor-Recipient game is a two-person game where one player is randomly selected as Donor and the other as Recipient. Donor has two moves, Cooperate and Defect. Cooperate means Donor pays cost c in order for Recipient to receive benefit b (b>c>0). Defect means Donor does nothing. Note that Recipient has no move. Prisoner's Dilemma game which we use here is a two-person simultaneous move game where both players have two moves, Cooperate and Defect, whose meanings are the same as in Donor-Recipient game. For convenience sake we shift the original payoffs in order the new payoffs of player to be positive if the opponent uses Cooperate and negative if Defect.

We investigate, by Agent-Based Simulation, emergence of cooperation where there are variable-threshold strategies and the difference between Donor-Recipient and Prisoner's Dilemma game, and show some cases where cooperation emerges more frequently with variable-threshold strategies than without them.

Tit for Tat changes his move at each period depending on the previous opponentâ€™s move. In real life, people further change their tendency toward cooperation or defection. We want to incorporate this change into our model. We introduce variable-threshold strategies which are extended forms of TFT. We interpret that TFT uses Defect if the state is 0, Cooperate if it is 1 and the smallest state number that prescribes using Cooperate as a threshold. AllC has zero threshold in this interpretation. We allow up to three states. Variable-threshold strategy changes its threshold by at most one at some age (once in his lifetime) depending on its experience until then. Thus variable-threshold TFT who was born as TFT may change to AllC or AllD. Also variable-threshold AllC who was born as AllC may change to TFT.

Players are initially randomly distributed in square lattice of cells. In each period, players move locally to random cell in von Neumann neighbors if unoccupied or globally to random unoccupied cell in the whole lattice, and play dilemma game against local neighboring player or against randomly selected player from the whole lattice. If wealth (accumulated payoff) of player becomes negative or his age becomes greater than his lifetime, he dies. If his wealth becomes greater than some amount and there is unoccupied cell in neighbors, he has an offspring.

A stage game is Donor-Recipient or Prisoner's Dilemma game. Donor-Recipient game is a two-person game where one player is randomly selected as Donor and the other as Recipient. Donor has two moves, Cooperate and Defect. Cooperate means Donor pays cost c in order for Recipient to receive benefit b (b>c>0). Defect means Donor does nothing. Note that Recipient has no move. Prisoner's Dilemma game which we use here is a two-person simultaneous move game where both players have two moves, Cooperate and Defect, whose meanings are the same as in Donor-Recipient game. For convenience sake we shift the original payoffs in order the new payoffs of player to be positive if the opponent uses Cooperate and negative if Defect.

We investigate, by Agent-Based Simulation, emergence of cooperation where there are variable-threshold strategies and the difference between Donor-Recipient and Prisoner's Dilemma game, and show some cases where cooperation emerges more frequently with variable-threshold strategies than without them.

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