Replicator dynamics in public goods games with reward funds

Sasaki T & Unemi T (2011). Replicator dynamics in public goods games with reward funds. Journal of Theoretical Biology: 109-114. DOI:10.1016/j.jtbi.2011.07.026.

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Abstract

Which punishment or rewards are most effective at maintaining cooperation in public goods interaction and deterring defectors who are willing to freeload on others' contribution? The sanction system is itself a public good and can cause problematic "second-order free riders" who do not contribute to the provisions of the sanctions and thus may subvert the cooperation supported by sanctioning. Recent studies have shown that public goods games with punishment can lead to a coercion-based regime if participation in the game is optional. Here, we reveal that even with compulsory participation, rewards can maintain cooperation within an infinitely large population. We consider three strategies for players in a standard public goods game to be a cooperator or a defector in a standard public goods game, or to be a rewarder who contributes to the public good and to a fund that rewards players who contribute during the game. Cooperators do not contribute to the reward fund and are therefore classified as second-order free riders. The replicator dynamics for the three strategies exhibit a rock-scissors-paper cycle, and can be analyzed fully, despite the fact that the expected payoffs are nonlinear. The model does not require repeated interaction, spatial structure, group selection, or reputation. We also discuss a simple method for second-order sanctions, which can lead to a globally stable state where 100% of the population are rewarders.

Item Type: Article
Uncontrolled Keywords: Evolutionary game theory; Cooperation; Sanction; Second-order social dilemma; Rock-scissors-paper cycle
Research Programs: Evolution and Ecology (EEP)
Bibliographic Reference: Journal of Theoretical Biology; 287:109-114 (21 October 2011) (Published online 3 August 2011)
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 08:45
Last Modified: 24 Feb 2016 15:15
URI: http://pure.iiasa.ac.at/9541

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