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Register a new userIf cooperation is likely punish mildly: Insights from economic experiments based on the snowdrift game
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Punishment may deter antisocial behavior. Yet to punish is costly, and the costs often do not offset the gains that are due to elevated levels of cooperation. However, the effectiveness of punishment depends not only on how costly it is, but also on the circumstances defining the social dilemma. Using the snowdrift game as the basis, we have conducted a series of economic experiments to determine whether severe punishment is more effective than mild punishment. We have observed that severe punishment is not necessarily more effective, even if the cost of punishment is identical in both cases. The benefits of severe punishment become evident only under extremely adverse conditions, when to cooperate is highly improbable in the absence of sanctions. If cooperation is likely, mild punishment is not less effective and leads to higher average payoffs, and is thus the much preferred alternative. Presented results suggest that the positive effects of punishment stem not only from imposed fines, but may also have a psychological background. Small fines can do wonders in motivating us to chose cooperation over defection, but without the paralyzing effect that may be brought about by large fines. The later should be utilized only when absolutely necessary.
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Spatial structure is known to have an impact on the evolution of cooperation, and so it has been intensively studied during recent years. Previous work has shown the relevance of some features, such as the synchronicity of the updating, the clustering of the network or the influence of the update rule. This has been done, however, for concrete settings with particular games, networks and update rules, with the consequence that some contradictions have arisen and a general understanding of these topics is missing in the broader context of the space of 2x2 games. To address this issue, we have performed a systematic and exhaustive simulation in the different degrees of freedom of the problem. In some cases, we generalize previous knowledge to the broader context of our study and explain the apparent contradictions. In other cases, however, our conclusions refute what seems to be established opinions in the field, as for example the robustness of the effect of spatial structure against changes in the update rule, or offer new insights into the subject, e.g. the relation between the intensity of selection and the asymmetry between the effects on games with mixed equilibria.
We address the issue of the effects of considering a network of contacts on the emergence of cooperation on social dilemmas under myopic best response dynamics. We begin by summarizing the main features observed under less intellectually demanding dynamics, pointing out their most relevant general characteristics. Subsequently we focus on the new framework of best response. By means of an extensive numerical simulation program we show that, contrary to the rest of dynamics considered so far, best response is largely unaffected by the underlying network, which implies that, in most cases, no promotion of cooperation is found with this dynamics. We do find, however, nontrivial results differing from the well-mixed population in the case of coordination games on lattices, which we explain in terms of the formation of spatial clusters and the conditions for their advancement, subsequently discussing their relevance to other networks.
The promotion of cooperation on spatial lattices is an important issue in evolutionary game theory. This effect clearly depends on the update rule: it diminishes with stochastic imitative rules whereas it increases with unconditional imitation. To study the transition between both regimes, we propose a new evolutionary rule, which stochastically combines unconditional imitation with another imitative rule. We find that, surprinsingly, in many social dilemmas this rule yields higher cooperative levels than any of the two original ones. This nontrivial effect occurs because the basic rules induce a separation of timescales in the microscopic processes at cluster interfaces. The result is robust in the space of 2x2 symmetric games, on regular lattices and on scale-free networks.
Evolutionary game dynamics is one of the most fruitful frameworks for studying evolution in different disciplines, from Biology to Economics. Within this context, the approach of choice for many researchers is the so-called replicator equation, that describes mathematically the idea that those individuals performing better have more offspring and thus their frequency in the population grows. While very many interesting results have been obtained with this equation in the three decades elapsed since it was first proposed, it is important to realize the limits of its applicability. One particularly relevant issue in this respect is that of non-mean-field effects, that may arise from temporal fluctuations or from spatial correlations, both neglected in the replicator equation. This review discusses these temporal and spatial effects focusing on the non-trivial modifications they induce when compared to the outcome of replicator dynamics. Alongside this question, the hypothesis of linearity and its relation to the choice of the rule for strategy update is also analyzed. The discussion is presented in terms of the emergence of cooperation, as one of the current key problems in Biology and in other disciplines.
Interactions among individuals in natural populations often occur in a dynamically changing environment. Understanding the role of environmental variation in population dynamics has long been a central topic in theoretical ecology and population biology. However, the key question of how individuals, in the middle of challenging social dilemmas (e.g., the tragedy of the commons), modulate their behaviors to adapt to the fluctuation of the environment has not yet been addressed satisfactorily. Utilizing evolutionary game theory and stochastic games, we develop a game-theoretical framework that incorporates the adaptive mechanism of reinforcement learning to investigate whether cooperative behaviors can evolve in the ever-changing group interaction environment. When the action choices of players are just slightly influenced by past reinforcements, we construct an analytical condition to determine whether cooperation can be favored over defection. Intuitively, this condition reveals why and how the environment can mediate cooperative dilemmas. Under our model architecture, we also compare this learning mechanism with two non-learning decision rules, and we find that learning significantly improves the propensity for cooperation in weak social dilemmas, and, in sharp contrast, hinders cooperation in strong social dilemmas. Our results suggest that in complex social-ecological dilemmas, learning enables the adaptation of individuals to varying environments.
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