Abstract
In the framework of evolutionary games with institutional reciprocity, limited incentives are at disposal for rewarding cooperators and punishing defectors. In the simplest case, it can be assumed that, depending on their strategies, all players receive equal incentives from the common pool. The question arises, however, what is the optimal distribution of institutional incentives? How should we best reward and punish individuals for cooperation to thrive? We study this problem for the public goods game on a scale-free network. We show that if the synergetic effects of group interactions are weak, the level of cooperation in the population can be maximized simply by adopting the simplest “equal distribution” scheme. If synergetic effects are strong, however, it is best to reward high-degree nodes more than low-degree nodes. These distribution schemes for institutional rewards are independent of payoff normalization. For institutional punishment, however, the same optimization problem is more complex, and its solution depends on whether absolute or degree-normalized payoffs are used. We find that degree-normalized payoffs require high-degree nodes be punished more lenient than low-degree nodes. Conversely, if absolute payoffs count, then high-degree nodes should be punished stronger than low-degree nodes.
Highlights
In human societies, cooperation is essential for the maintenance of public goods
Institutionalized punishment appears to be more common than institutionalized reward, both concepts are in use throughout the world
We perform Monte Carlo simulations of the public goods game described in the Methods section, whereby we consider separately institutional rewarding with absolute payoffs and institutional punishment with absolute payoffs, as well as institutional rewarding with degree-normalized payoffs and institutional punishment with degree-normalized payoffs
Summary
Cooperation is essential for the maintenance of public goods. the collapse of cooperation happens often in many public goods dilemmas which we nowadays face, like protecting the global climate or avoiding overfishing of our oceans (Hardin, 1968; O’Neill and Oppenheimer, 2002). Ample research efforts have been devoted to the study of the emergence of institutions and their effectiveness in promoting prosocial behavior (Yamagishi, 1986; Ostrom, 1990; Gurerk et al, 2006; Henrich, 2006; Cuesta et al, 2008; Sigmund et al, 2010; Baldassarri and Grossman, 2011; Sasaki and Unemi, 2011; Szolnoki et al, 2011a,b; Cressman et al, 2012; Isakov and Rand, 2012; Sasaki et al, 2012; Bechtel and Scheve, 2013; Cressman et al, 2013; Vasconcelos et al, 2013; Vukov et al, 2013) It has been shown, for example, that institutional rewarding promotes the evolution of cooperation in the liner public goods game (Cuesta et al, 2008), the nonlinear public goods games (Chen et al, 2013), and in structured populations in general (Jiménez et al, 2008, 2009; Szolnoki et al, 2011a,b). Institutional punishment is less costly and more effective to warrant a given level of public cooperation, especially if participation in the public goods game is optional (Sasaki et al, 2012; Sasaki, 2013)
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