Mobility, fitness collection, and the breakdown of cooperation

The spatial arrangement of individuals is thought to overcome the dilemma of cooperation: When cooperators engage in clusters, they might share the benefit of cooperation while being more protected against noncooperating individuals, who benefit from cooperation but save the cost of cooperation. This is paradigmatically shown by the spatial prisoner's dilemma model. Here, we study this model in one and two spatial dimensions, but explicitly take into account that in biological setups, fitness collection and selection are separated processes occurring mostly on vastly different time scales. This separation is particularly important to understand the impact of mobility on the evolution of cooperation. We find that even small diffusive mobility strongly restricts cooperation since it enables noncooperative individuals to invade cooperative clusters. Thus, in most biological scenarios, where the mobility of competing individuals is an irrefutable fact, the spatial prisoner's dilemma alone cannot explain stable cooperation, but additional mechanisms are necessary for spatial structure to promote the evolution of cooperation. The breakdown of cooperation is analyzed in detail. We confirm the existence of a phase transition, here controlled by mobility and costs, which distinguishes between purely cooperative and noncooperative absorbing states. While in one dimension the model is in the class of the voter model, it belongs to the directed percolation universality class in two dimensions. DOI: 10.1103/PhysRevE.87.04271

How Evolutionary Dynamics Affects Network Reciprocity in Prisoner's Dilemma

Cooperation lies at the foundations of human societies, yet why people cooperate remains a conundrum. The issue, known as network reciprocity, of whether population structure can foster cooperative behavior in social dilemmas has been addressed by many, but theoretical studies have yielded contradictory results so far—as the problem is very sensitive to how players adapt their strategy. However, recent experiments with the prisoner's dilemma game played on different networks and in a specific range of payoffs suggest that humans, at least for those experimental setups, do not consider neighbors' payoffs when making their decisions, and that the network structure does not influence the final outcome. In this work we carry out an extensive analysis of different evolutionary dynamics, taking into account most of the alternatives that have been proposed so far to implement players' strategy updating process. In this manner we show that the absence of network reciprocity is a general feature of the dynamics (among those we consider) that do not take neighbors' payoffs into account. Our results, together with experimental evidence, hint at how to properly model real people's behaviorThis work was supported by the Swiss Natural Science Foundation through grant PBFRP2_145872 and by Ministerio de Economía y Competitividad (Spain) through grant PRODIEVO.Publicad

Evolutionary graph theory: Breaking the symmetry between interaction and replacement

We study evolutionary dynamics in a population whose structure is given by two graphs: the interaction graph determines who plays with whom in an evolutionary game; the replacement graph specifies the geometry of evolutionary competition and updating. First, we calculate the fixation probabilities of frequency dependent selection between two strategies or phenotypes. We consider three different update mechanisms: birth-death, death-birth and imitation. Then, as a particular example, we explore the evolution of cooperation. Suppose the interaction graph is a regular graph of degree h, the replacement graph is a regular graph of degree g and the overlap between the two graphs is a regular graph of degree l. We show that cooperation is favored by natural selection if b/c > hg/l. Here, b and c denote the benefit and cost of the altruistic act. This result holds for death-birth updating, weak selection and large population size. Note that the optimum population structure for cooperators is given by maximum overlap between the interaction and the replacement graph (g = h = l), which means that the two graphs are identical. We also prove that a modified replicator equation can describe how the expected values of the frequencies of an arbitrary number of strategies change on replacement and interaction graphs: the two graphs induce a transformation of the payoff matrix

A spatial econometric model for transboundary air pollution control treaties: an analysis of noncooperative international behavior

This dissertation develops a theoretical model that explains differences in emission reductions of transboundary air pollutants among nations based on national income, political freedom, the cost of emission reductions, emissions from other countries, the type of pollutant, and the pollutant\u27s dispersion characteristics. The model is based on the theory of the private provision of impure public goods. This theoretical model is then used to derive a reduced form demand equation for emission reductions that can be econometrically estimated using spatial autoregressive techniques for time-series cross-section data;The econometric model is applied to 25 European nations and covers the period from 1980 to 1990. These nations were signatories to the 1985 Helsinki Protocol, which mandated reductions in sulfur dioxide (SO2), and the 1988 Sofia Protocol, which limited emissions of nitrogen oxides (NO x). The signing of these treaties indicated a recognition of the problems caused by acid rain and ozone pollution, yet the two treaties had very different requirements regarding emission reductions. By taking into account the differences between nations and the different characteristics of the pollutants, my model allows a closer examination of the reasons for the differences in treaty requirements and treaty adherence;The results indicate that nations follow a Nash-subscription model in choosing their emission reductions. In other words, nations tend to free ride on the emission reductions of other nations. The spatial autoregressive model performs convincingly for SO2, but the model for NO x is less satisfying. While nations continue to exhibit Nash behavior, other variables fail to be significant or have the wrong sign. However, these results may be explained as resulting from the characteristic nature of NO x as compared with SO2. Since it originates from a larger number of sources, it is harder to control than SO2 emissions;A better understanding of the factors that influence a nation\u27s decision to reduce its emissions may provide a foundation for the negotiation of future transboundary pollution control treaties. New treaties could require some nations to make greater (or smaller) cuts in emissions, but by taking into account differences among the nations, larger total reductions and greater compliance might result

The appropriation of endogenously provided common-pool resources

Because game theory suggests that the origin of a common-pool resource should not affect appropriation behavior, experimental studies of appropriation from common-pool resources generally presume resources are exogenously provided. However, behavioral economic research indicates that the origin of a resource may affect the use of that resource. We investigate the potential role of resource origin by considering the appropriation of a common-pool resource after users have determined its productive capacity through contributions. Results indicate that resource origin does not significantly influence aggregate appropriation levels but that endogenous resource provision leads to individual strategic behavior

Appointing Federal Judges: The President, the Senate, and the Prisoner\u27s Dilemma

This paper argues that the expansion of the White House\u27s role in judicial appointments since the late 1970s, at the expense of the Senate, has contributed to heightened levels of ideological conflict and gridlock over the appointment of federal appeals court judges, by making a cooperative equilibrium difficult to sustain. Presidents have greater electoral incentive to behave ideologically, and less incentive to cooperate with other players in the appointments process, than do senators, who are disciplined to a greater extent in their dealings with each other by the prospect of retaliation over repeat play. The possibility of divided government exacerbates the difficulty of achieving cooperative equilibrium by making both the benefits of cooperative behavior and the costs of retaliation highly uncertain