Evolutionary stable strategies and game dynamics for n-person games

This note contains a generalization of the definition of an evolutionary stable strategy and of the corresponding game dynamics from 2-person to n-person games. This broader framework also allows modelling of several interacting populations or of populations containing different types of individuals, for example males and females.     

Personal experience and reputation interact in human decisions to help reciprocally

There is ample evidence that human cooperative behaviour towards other individuals is often conditioned on information about previous interactions. This information derives both from personal experience (direct reciprocity) and from experience of others (i.e. reputation; indirect reciprocity). Direct and indirect reciprocity have been studied separately, but humans often have access to both types of information. Here, we experimentally investigate information use in a repeated helping game. When acting as donor, subjects can condition their decisions to help recipients with both types of information at a small cost to access such information. We find that information from direct interactions weighs more heavily in decisions to help, and participants tend to react less forgivingly to negative personal experience than to negative reputation. Moreover, effects of personal experience and reputation interact in decisions to help. If a recipient''s reputation is positive, the personal experience of the donor has a weak effect on the decision to help, and vice versa. Yet if the two types of information indicate conflicting signatures of helpfulness, most decisions to help follow personal experience. To understand the roles of direct and indirect reciprocity in human cooperation, they should be studied in concert, not in isolation.     

Female sperm use and storage between fertilization events drive sperm competition and male ejaculate allocation

Sperm competition theory has traditionally focused on how male allocation responds to female promiscuity, when males compete to fertilize a single clutch of eggs. Here, we develop a model to ask how female sperm use and storage across consecutive reproductive events affect male ejaculate allocation and patterns of mating and paternity. In our model, sperm use (a single parameter under female control) is the main determinant of sperm competition, which alters the effect of female promiscuity on male success and, ultimately, male reproductive allocation. Our theory reproduces the general pattern predicted by existing theory that increased sperm competition favors increased allocation to ejaculates. However, our model predicts a negative correlation between male ejaculate allocation and female promiscuity, challenging the generality of a prevailing expectation of sperm competition theory. Early models assumed that the energetic costs of precopulatory competition and the level of sperm competition are both determined by female promiscuity, which leads to an assumed covariation between these two processes. By modeling precopulatory costs and sperm competition independently, our theoretical framework allows us to examine how male allocation should respond independently to variation in sperm competition and energetic trade‐offs in mating systems that have been overlooked in the past.     

Video game play and lucid dreams: Implications for the development of consciousness.

The improvement of various cognitive skills associated with video game play has been well documented; however, the development of consciousness implications have not been considered. In the present study several potential indicators of consciousness development, including and especially lucid dreaming frequency, were examined as a function of video game play. In the first study, high video game players were more likely to report lucid dreams, observer dreams, and dream control when dream recall frequency and motion disorientation during play were controlled. There were no similar differences in other consciousness development indices. In the second study, a slightly different pattern of results occurred because of respondents all being frequent players. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Superparasitism as a differential game

Superparasitism refers to a female parasitoid laying an egg in a host already parasitized by a conspecific. In solitary species, only one offspring per host is expected to complete development, hence the game. Hosts are often clumped in patches and several females exploiting such an aggregate of resource make its state change over time, hence the dynamical character of the game. Two coupled questions arise: (i) Is it worth accepting a parasitized host? (ii) When to leave the host patch? Through these decisions (i) the competition for healthy hosts and (ii) the trade-off between leaving in quest of a better patch and staying to make the patch less profitable for other parasitoids (this is a way to lower superparasitism likely to occur after having left the patch) are addressed. The aim of this work is to characterize a strategy that would be evolutionarily relevant in such a situation, as it directly concerns females' reproductive success. Investigating a (synchronous) nonzero-sum two-player differential game allows us to characterize candidate dynamic evolutionarily stable policies in terms of both oviposition and patch-leaving decisions. For that matter, the game is (in the most part of the parameter space) completely solved if the probability that superparasitism succeeds is assumed to be close to one-half, a fair value under direct competition. The strategic equilibrium consists, for each females, in (i) superparasitizing consistently upon arrival on the patch, and (ii) leaving when the loss of fitness due to superparasitism likely to occur after its departure is reduced to zero. The competing females are thus expected to leave the patch as they arrived: synchronously. Superparasitism does not necessarily lead to a war of attrition.     

How reinforcer type affects choice in economic games

Behavioral economists stress that experiments on judgment and decision-making using economic games should be played with real money if the results are to have generality. Behavior analysts have sometimes disputed this contention and have reported results in which hypothetical rewards and real money have produced comparable outcomes. We review studies that have compared hypothetical and real money and discuss the results of two relevant experiments. In the first, using the Sharing Game developed in our laboratory, subjects' choices differed markedly depending on whether the rewards were real or hypothetical. In the second, using the Ultimatum and Dictator Games, we again found sharp differences between real and hypothetical rewards. However, this study also showed that time off from a tedious task could serve as a reinforcer every bit as potent as money. In addition to their empirical and theoretical contributions, these studies make the methodological point that meaningful studies may be conducted with economic games without spending money: time off from a tedious task can serve as a powerful reward.     

The 'spiteful' origins of human cooperation

We analyse generosity, second-party ('spiteful') punishment (2PP), and third-party ('altruistic') punishment (3PP) in a cross-cultural experimental economics project. We show that smaller societies are less generous in the Dictator Game but no less prone to 2PP in the Ultimatum Game. We might assume people everywhere would be more willing to punish someone who hurt them directly (2PP) than someone who hurt an anonymous third person (3PP). While this is true of small societies, people in large societies are actually more likely to engage in 3PP than 2PP. Strong reciprocity, including generous offers and 3PP, exists mostly in large, complex societies that face numerous challenging collective action problems. We argue that 'spiteful' 2PP, motivated by the basic emotion of anger, is more universal than 3PP and sufficient to explain the origins of human cooperation.     

Evolutionary dynamics in structured populations

Evolutionary dynamics shape the living world around us. At the centre of every evolutionary process is a population of reproducing individuals. The structure of that population affects evolutionary dynamics. The individuals can be molecules, cells, viruses, multicellular organisms or humans. Whenever the fitness of individuals depends on the relative abundance of phenotypes in the population, we are in the realm of evolutionary game theory. Evolutionary game theory is a general approach that can describe the competition of species in an ecosystem, the interaction between hosts and parasites, between viruses and cells, and also the spread of ideas and behaviours in the human population. In this perspective, we review the recent advances in evolutionary game dynamics with a particular emphasis on stochastic approaches in finite sized and structured populations. We give simple, fundamental laws that determine how natural selection chooses between competing strategies. We study the well-mixed population, evolutionary graph theory, games in phenotype space and evolutionary set theory. We apply these results to the evolution of cooperation. The mechanism that leads to the evolution of cooperation in these settings could be called ‘spatial selection’: cooperators prevail against defectors by clustering in physical or other spaces.     

One-third rules with equality: Second-order evolutionary stability conditions in finite populations

The one-third law of evolutionary dynamics [Nowak et al. 2004. Emergence of cooperation and evolutionary stability in finite populations. Nature 428, 246-650] describes a robustness criterion for evolution in a finite population: If at an A-frequency of 1/3, the fitness of an A player is greater (smaller) than the fitness of a B player, then a single A mutant that appears in a population of otherwise all B has a fixation probability greater (smaller) than the neutral threshold 1/N, the inverse population size. We examine the case where at an A-frequency of 1/3, the fitness of an A player is exactly equal to the fitness of a B player. We find that in this case the relative magnitude of the cross payoffs matters: If the payoff of A against B is larger (smaller) than the payoff of B against A, then a single A mutant has a fixation probability larger (smaller) than 1/N. If the cross payoffs coincide, we are in the special case of a partnership game, where the deviation cost from an inefficient equilibrium is exactly balanced by the potential gain of switching to the payoff dominant equilibrium. We show that in this case the fixation probability of A is lower than 1/N. Finally, we illustrate our findings by a language game with differentiated costs of signals.