Consequences of fluctuating group size for the evolution of cooperation

Studies of cooperation have traditionally focused on discrete games such as the well-known prisoner's dilemma, in which players choose between two pure strategies: cooperation and defection. Increasingly, however, cooperation is being studied in continuous games that feature a continuum of strategies determining the level of cooperative investment. For the continuous snowdrift game, it has been shown that a gradually evolving monomorphic population may undergo evolutionary branching, resulting in the emergence of a defector strategy that coexists with a cooperator strategy. This phenomenon has been dubbed the 'tragedy of the commune'. Here we study the effects of fluctuating group size on the tragedy of the commune and derive analytical conditions for evolutionary branching. Our results show that the effects of fluctuating group size on evolutionary dynamics critically depend on the structure of payoff functions. For games with additively separable benefits and costs, fluctuations in group size make evolutionary branching less likely, and sufficiently large fluctuations in group size can always turn an evolutionary branching point into a locally evolutionarily stable strategy. For games with multiplicatively separable benefits and costs, fluctuations in group size can either prevent or induce the tragedy of the commune. For games with general interactions between benefits and costs, we derive a general classification scheme based on second derivatives of the payoff function, to elucidate when fluctuations in group size help or hinder cooperation.Comment: 22 pages, 5 figure

Chris Cannings: A Life in Games

Chris Cannings was one of the pioneers of evolutionary game theory. His early work was inspired by the formulations of John Maynard Smith, Geoff Parker and Geoff Price; Chris recognized the need for a strong mathematical foundation both to validate stated results and to give a basis for extensions of the models. He was responsible for fundamental results on matrix games, as well as much of the theory of the important war of attrition game, patterns of evolutionarily stable strategies, multiplayer games and games on networks. In this paper we describe his work, key insights and their influence on research by others in this increasingly important field. Chris made substantial contributions to other areas such as population genetics and segregation analysis, but it was to games that he always returned. This review is written by three of his students from different stages of his career

Interaction and imitation in a world of Quixotes and Sanchos

Producción CientíficaThis paper studies a two-population evolutionary game in a new setting in between a symmetric and an asymmetric evolutionary model. It distinguishes two types of agents: Sanchos, whose payoffs are defined by a prisoner’s dilemma game, and Quixotes, whose payoffs are defined by a snowdrift game. Considering an imitative revision protocol, a revising agent is paired with someone from his own population or the other population. When matched, they observe payoffs, but not identities. Thus, agents in one population interact and imitate agents from their own population and from the other population. In this setting we prove that a unique mixed-strategy asymptotically stable fixed point of the evolutionary dynamics exists. Taking as an example the compliance with social norms, and depending on the parameters, two type of equilibrium are possible, one with full compliance among Quixotes and partial compliance among Sanchos, or another with partial compliance among Quixotes and defection among Sanchos. In the former type, Sanchos comply above their Nash equilibrium (as they imitate compliant Quixotes). In the latter type, Quixotes comply below their Nash equilibrium (as they imitate defecting Sanchos)

Landscape and flux for quantifying global stability and dynamics of game theory

Game theory has been widely applied to many areas including economics, biology and social sciences. However, it is still challenging to quantify the global stability and global dynamics of the game theory. We developed a landscape and flux framework to quantify the global stability and global dynamics of the game theory. As an example, we investigated the models of three-strategy games: a special replicator-mutator game, the repeated prison dilemma model. In this model, one stable state, two stable states and limit cycle can emerge under different parameters. The repeated Prisoner's Dilemma system has Hopf bifurcation transitions from one stable state to limit cycle state, and then to another one stable state or two stable states, or vice versa. We explored the global stability of the repeated Prisoner's Dilemma system and the kinetic paths between the basins of attractor. The paths are irreversible due to the non-zero flux. One can explain the game for $Peace$ and $War$.Comment: 25 pages, 15 figure

Eco-evolutionary dynamics of social dilemmas

Social dilemmas are an integral part of social interactions. Cooperative actions, ranging from secreting extra-cellular products in microbial populations to donating blood in humans, are costly to the actor and hence create an incentive to shirk and avoid the costs. Nevertheless, cooperation is ubiquitous in nature. Both costs and benefits often depend non-linearly on the number and types of individuals involved -- as captured by idioms such as `too many cooks spoil the broth' where additional contributions are discounted, or `two heads are better than one' where cooperators synergistically enhance the group benefit. Interaction group sizes may depend on the size of the population and hence on ecological processes. This results in feedback mechanisms between ecological and evolutionary processes, which jointly affect and determine the evolutionary trajectory. Only recently combined eco-evolutionary processes became experimentally tractable in microbial social dilemmas. Here we analyse the evolutionary dynamics of non-linear social dilemmas in settings where the population fluctuates in size and the environment changes over time. In particular, cooperation is often supported and maintained at high densities through ecological fluctuations. Moreover, we find that the combination of the two processes routinely reveals highly complex dynamics, which suggests common occurrence in nature.Comment: 26 pages, 11 figure

Ecological theatre and the evolutionary game: how environmental and demographic factors determine payoffs in evolutionary games

In the standard approach to evolutionary games and replicator dynamics, differences in fitness can be interpreted as an excess from the mean Malthusian growth rate in the population. In the underlying reasoning, related to an analysis of "costs" and "benefits", there is a silent assumption that fitness can be described in some type of units. However, in most cases these units of measure are not explicitly specified. Then the question arises: are these theories testable? How can we measure "benefit" or "cost"? A natural language, useful for describing and justifying comparisons of strategic "cost" versus "benefits", is the terminology of demography, because the basic events that shape the outcome of natural selection are births and deaths. In this paper, we present the consequences of an explicit analysis of births and deaths in an evolutionary game theoretic framework. We will investigate different types of mortality pressures, their combinations and the possibility of trade-offs between mortality and fertility. We will show that within this new approach it is possible to model how strictly ecological factors such as density dependence and additive background fitness, which seem neutral in classical theory, can affect the outcomes of the game. We consider the example of the Hawk-Dove game, and show that when reformulated in terms of our new approach new details and new biological predictions are produced