Abstract
Economic experiments reveal that humans value cooperation and fairness. Punishing unfair behavior is therefore common, and according to the theory of strong reciprocity, it is also directly related to rewarding cooperative behavior. However, empirical data fail to confirm that positive and negative reciprocity are correlated. Inspired by this disagreement, we determine whether the combined application of reward and punishment is evolutionary advantageous. We study a spatial public goods game, where in addition to the three elementary strategies of defection, rewarding and punishment, a fourth strategy combining the later two competes for space. We find rich dynamical behavior that gives rise to intricate phase diagrams where continuous and discontinuous phase transitions occur in succession. Indirect territorial competition, spontaneous emergence of cyclic dominance, as well as divergent fluctuations of oscillations that terminate in an absorbing phase are observed. Yet despite the high complexity of solutions, the combined strategy can survive only in very narrow and unrealistic parameter regions. Elementary strategies, either in pure or mixed phases, are much more common and likely to prevail. Our results highlight the importance of patterns and structure in human cooperation, which should be considered in future experiments.
Highlights
Humans have mastered the art of cooperation like no other species [1,2]
There exist narrow and rather unrealistic parameter regions where the correlation of positive and negative reciprocity can outperform a particular elementary strategy, these advantages are highly unlikely to play a role in human experiments, and they frequently come second to the evolutionary success that is warranted by punishment alone under the same conditions
The studied four-strategy spatial public goods game gives rise to fascinating evolutionary outcomes that are separated by continuous and discontinuous phase transitions
Summary
Humans have mastered the art of cooperation like no other species [1,2]. Regardless of kinship and individual loss, we work together to achieve feats that are impossible to achieve alone. The second example is of direct relevance for the present work and concerns the strong reciprocity model [23,24,25,26] The latter model postulates that positive and negative reciprocity are directly correlated. While the elementary strategies of rewarding and punishment have received ample attention in the recent past [40,41,42,43,44,45], little is known about their combined effectiveness To amend this knowledge gap, we propose and study a modified spatial public goods game [46,47], where defectors compete with cooperators that punish defectors, reward other cooperators, as well as do both. III, while we first describe the studied spatial public goods game and the methods in more detail
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