Effect of the presence of empty sites on the evolution of cooperation by costly punishment in spatial games

2009 ◽  
Vol 256 (2) ◽  
pp. 297-304 ◽  
Author(s):  
Takuya Sekiguchi ◽  
Mayuko Nakamaru
2015 ◽  
Author(s):  
Jorge Peña ◽  
Bin Wu ◽  
Arne Traulsen

AbstractSpatial structure greatly affects the evolution of cooperation. While in two-player games the condition for cooperation to evolve depends on a single structure coefficient, in multiplayer games the condition might depend on several structure coefficients, making it difficult to compare different population structures. We propose a solution to this issue by introducing two simple ways of ordering population structures: the containment order and the volume order. If population structure 𝒮1 is greater than population structure 𝒮2 in the containment or the volume order, then 𝒮1 can be considered a stronger promoter of cooperation. We provide conditions for establishing the containment order, give general results on the volume order, and illustrate our theory by comparing different models of spatial games and associated update rules. Our results hold for a large class of population structures and can be easily applied to specific cases once the structure coefficients have been calculated or estimated.


2012 ◽  
Vol 20 (2) ◽  
pp. 301-319 ◽  
Author(s):  
Shade T. Shutters

Altruistic punishment occurs when an agent incurs a cost to punish another but receives no material benefit for doing so. Despite the seeming irrationality of such behavior, humans in laboratory settings routinely pay to punish others even in anonymous, one-shot settings. Costly punishment is ubiquitous among social organisms in general and is increasingly accepted as a mechanism for the evolution of cooperation. Yet if it is true that punishment explains cooperation, the evolution of altruistic punishment remains a mystery. In a series of computer simulations I give agents the ability to punish one another while playing a continuous prisoner's dilemma. In simulations without social structure, expected behavior evolves—agents do not punish and consequently no cooperation evolves. Likewise, in simulations with social structure but no ability to punish, no cooperation evolves. However, in simulations where agents are both embedded in a social structure and have the option to inflict costly punishment, cooperation evolves quite readily. This suggests a simple and broadly applicable explanation of cooperation for social organisms that have nonrandom social structure and a predisposition to punish one another. Results with scale-free networks further suggest that nodal degree distribution plays an important role in determining whether cooperation will evolve in a structured population.


Author(s):  
Robert M. May ◽  
Sebastian Bohoeffer ◽  
Martin A. Nowak

1993 ◽  
Vol 1 (1_2) ◽  
pp. 15-37 ◽  
Author(s):  
Kristian Lindgren ◽  
Mats G. Nordahl

We review results on the evolution of cooperation based on the iterated Prisoner's Dilemma. Coevolution of strategies is discussed both in situations where everyone plays against everyone, and for spatial games. Simple artificial ecologies are constructed by incorporating an explicit resource flow and predatory interactions into models of coevolving strategies. Properties of food webs are reviewed, and we discuss what artificial ecologies can teach us about community structure.


2016 ◽  
Vol 13 (114) ◽  
pp. 20150881 ◽  
Author(s):  
Jorge Peña ◽  
Bin Wu ◽  
Arne Traulsen

Spatial structure greatly affects the evolution of cooperation. While in two-player games the condition for cooperation to evolve depends on a single structure coefficient, in multiplayer games the condition might depend on several structure coefficients, making it difficult to compare different population structures. We propose a solution to this issue by introducing two simple ways of ordering population structures: the containment order and the volume order. If population structure is greater than population structure in the containment or the volume order, then can be considered a stronger promoter of cooperation. We provide conditions for establishing the containment order, give general results on the volume order, and illustrate our theory by comparing different models of spatial games and associated update rules. Our results hold for a large class of population structures and can be easily applied to specific cases once the structure coefficients have been calculated or estimated.


2013 ◽  
Vol 280 (1752) ◽  
pp. 20122498 ◽  
Author(s):  
Tatsuya Sasaki ◽  
Satoshi Uchida

The exclusion of freeriders from common privileges or public acceptance is widely found in the real world. Current models on the evolution of cooperation with incentives mostly assume peer sanctioning, whereby a punisher imposes penalties on freeriders at a cost to itself. It is well known that such costly punishment has two substantial difficulties. First, a rare punishing cooperator barely subverts the asocial society of freeriders, and second, natural selection often eliminates punishing cooperators in the presence of non-punishing cooperators (namely, ‘second-order’ freeriders). We present a game-theoretical model of social exclusion in which a punishing cooperator can exclude freeriders from benefit sharing. We show that such social exclusion can overcome the above-mentioned difficulties even if it is costly and stochastic. The results do not require a genetic relationship, repeated interaction, reputation or group selection. Instead, only a limited number of freeriders are required to prevent the second-order freeriders from eroding the social immune system.


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