Abstract
AbstractDefection is frequently seen in co-operative systems [1-3]. Game theoretical solutions to stabilize cooperation rely on reciprocity and reputation in iterated games[4-5]. One of the basic requirements for reciprocity or reputation building is that the strategies of players and the resulting payoffs should be open at the end of every interaction. For games in which the strategies and payoffs remain hidden, these stabilizing factors are unlikely to work. We examine the evolution of cooperation for hidden-strategy games using human mating game as an example. Here faithful parenting can be considered as cooperation and extra-pair mating (EPM) or cuckoldry as defection. Cuckoldry may get exposed only occasionally and the genetic benefits of cuckoldry also remain hidden from the players. Along with mate guarding, social policing is enabled in humans by language and gossiping. However, social policing can be invaded by second order free riders. We suggest that opportunistic blackmailing, which is unique to hidden strategy games can act as a keystone strategy in stabilizing co-operation. This can counteract free riding and stabilize policing. A game theoretical model results into a rock - paper – scissor (R-P-S) like situation with no evolutionary stable strategy (ESS). Simulations result into a stable or stably oscillating polymorphism. Obligate monogamy is an essential trait in the co-existence. In a gender difference model too, polymorphism is seen in both genders but with different traits predominating in the two genders. The model explains intra-gender, inter-gender as well as cross cultural variability in mating strategies in humans.
Highlights
Cooperation is commonly accompanied by cheating or defection in a number of naturally occurring social systems [1,2,3]
The payoff matrix (Table 1) shows that if the maximum probabilistic cost of punishment is greater than the advantage of polygamy, there is no evolutionary stable strategy (ESS) possible
This leads to a rock - paper – scissor (R-P-S) like situation [Fig 1]
Summary
Cooperation is commonly accompanied by cheating or defection in a number of naturally occurring social systems [1,2,3]. The problem of evolution and stability of cooperation between individuals is commonly addressed using a game theory model popularly known as Prisoner’s Dilemma (PD). In a one time PD game, cooperation is not stable and defection is the only stable strategy for any player [4]. In iterated games strategies involving reciprocity or reputation can stabilize cooperation [4,5]. One of the basic assumptions behind all suggested solutions to the problem of stability of cooperation is that the strategies of players and the resulting payoffs are open at the end of every interaction. Reciprocity and reputation would fail to work for games in which the strategies and payoffs remain hidden. We model the evolution of cooperation when the strategies and payoffs remain hidden most of the time
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