Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32017
Effect of Modification and Expansion on Emergence of Cooperation in Demographic Multi-Level Donor-Recipient Game

Authors: Tsuneyuki Namekata, Yoko Namekata


It is known that the mean investment evolves from a very low initial value to some high level in the Continuous Prisoner's Dilemma. We examine how the cooperation level evolves from a low initial level to a high level in our Demographic Multi-level Donor-Recipient situation. In the Multi-level Donor-Recipient game, one player is selected as a Donor and the other as a Recipient randomly. The Donor has multiple cooperative moves and one defective move. A cooperative move means the Donor pays some cost for the Recipient to receive some benefit. The more cooperative move the Donor takes, the higher cost the Donor pays and the higher benefit the Recipient receives. The defective move has no effect on them. Two consecutive Multi-level Donor-Recipient games, one as a Donor and the other as a Recipient, can be viewed as a discrete version of the Continuous Prisoner's Dilemma. In the Demographic Multi-level Donor-Recipient game, players are initially distributed spatially. In each period, players play multiple Multi-level Donor-Recipient games against other players. He leaves offspring if possible and dies because of negative accumulated payoff of him or his lifespan. Cooperative moves are necessary for the survival of the whole population. There is only a low level of cooperative move besides the defective move initially available in strategies of players. A player may modify and expand his strategy by his recent experiences or practices. We distinguish several types of a player about modification and expansion. We show, by Agent-Based Simulation, that introducing only the modification increases the emergence rate of cooperation and introducing both the modification and the expansion further increases it and a high level of cooperation does emerge in our Demographic Multi-level Donor-Recipient Game.

Keywords: Agent-based simulation, donor-recipient game, emergence of cooperation, spatial structure, TFT, TF2T.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 708


[1] T. Killingback, M. Doebeli, and N. Knowlton, "Variable investment, the Continuous Prisoner's Dilemma, and the origin of cooperation," Proc. R. Soc. Lond. B, vol. 266, September 1999, pp. 1723-1728.
[2] J. M. Epstein, "Zones of Cooperation in Demographic Prisoner's Dilemma," in Generative Social Science. Princeton University Press, 2006, pp. 199-221.
[3] T. Namekata and Y. Namekata, "Effect of Reluctant Players in Demographic Prisoner's Dilemma Game," in R. Bartak (ed.): Proceedings of the 14th Czech-Japan Seminar on Data Analysis and Decision Making under Uncertainty (held in September 18-21, 2011, Hejnice, Czech Republic). Publishing House of the Faculty of Mathematics and Physics, Charles University in Prague, 2011, pp. 102-109.
[4] T. Namekata and Y. Namekata,"Emergence of cooperation and patterns of move-play in demographic donor-recipient game," in Masahiro Inuiguchi, Yoshifumi Kusunoki and Hirosaki Seki (eds.): Proceedings of the 15th Czech-Japan Seminar on Data Analysis and Decision Making under Uncertainty (held in September 24-27, 2012 Osaka, Japan), 2012, pp. 51-58.
[5] T. Namekata and Y. Namekata, "Role Of Optimist On Emergence Of Cooperation In Demographic Multi-Attribute Donor-Recipient Game," in ECMS 2015 Proceedings edited by: Valeri M. Mladenov, Petia Georgieva, Grisha Spasov, Galidiya Petrova European Council for Modeling and Simulation, 2015, pp. 35-41. doi:10.7148/2015-0035
[6] Repast Simphony 2.4.0 is an advanced, free, and open source agent-based modeling and simulation system downloadable in