Julián García

Direct reciprocity in structured populations

Reciprocity and repeated games have been at the center of attention when studying the evolution of human cooperation. Direct reciprocity is considered to be a powerful mechanism for the evolution of cooperation, and it is generally assumed that it can lead to high levels of cooperation. Here we explore an open-ended, infinite strategy space, where every strategy that can be encoded by a finite state automaton is a possible mutant. Surprisingly, we find that direct reciprocity alone does not lead to high levels of cooperation. Instead we observe perpetual oscillations between cooperation and defection, with defection being substantially more frequent than cooperation. The reason for this is that “indirect invasions” remove equilibrium strategies: every strategy has neutral mutants, which in turn can be invaded by other strategies. However, reciprocity is not the only way to promote cooperation. Another mechanism for the evolution of cooperation, which has received as much attention, is assortment because of population structure. Here we develop a theory that allows us to study the synergistic interaction between direct reciprocity and assortment. This framework is particularly well suited for understanding human interactions, which are typically repeated and occur in relatively fluid but not unstructured populations. We show that if repeated games are combined with only a small amount of assortment, then natural selection favors the behavior typically observed among humans: high levels of cooperation implemented using conditional strategies.

Extrapolating Weak Selection in Evolutionary Games

In evolutionary games, reproductive success is determined by payoffs. Weak selection means that even large differences in game outcomes translate into small fitness differences. Many results have been derived using weak selection approximations, in which perturbation analysis facilitates the derivation of analytical results. Here, we ask whether results derived under weak selection are also qualitatively valid for intermediate and strong selection. By “qualitatively valid” we mean that the ranking of strategies induced by an evolutionary process does not change when the intensity of selection increases. For two-strategy games, we show that the ranking obtained under weak selection cannot be carried over to higher selection intensity if the number of players exceeds two. For games with three (or more) strategies, previous examples for multiplayer games have shown that the ranking of strategies can change with the intensity of selection. In particular, rank changes imply that the most abundant strategy at one intensity of selection can become the least abundant for another. We show that this applies already to pairwise interactions for a broad class of evolutionary processes. Even when both weak and strong selection limits lead to consistent predictions, rank changes can occur for intermediate intensities of selection. To analyze how common such games are, we show numerically that for randomly drawn two-player games with three or more strategies, rank changes frequently occur and their likelihood increases rapidly with the number of strategies . In particular, rank changes are almost certain for , which jeopardizes the predictive power of results derived for weak selection.

Leaving the loners alone: Evolution of cooperation in the presence of antisocial punishment

The idea that voluntary participation may promote the evolution of cooperation and punishment in public good games has been recently called into question based on the study of the complete strategy set in which anyone can punish anyone else. If punishment actions are detached from contribution and participation in the game, the combination of punishment and voluntary participation no longer leads to high levels of cooperation. We show that this result crucially depends on specific details of the role of those who abstain from the collective endeavour, and only holds for a small subset of assumptions. If these loners are truly alone, cooperators who punish only defectors prevail, even when antisocial punishment is available.

The Structure of Mutations and the Evolution of Cooperation

Evolutionary game dynamics in finite populations assumes that all mutations are equally likely, i.e., if there are strategies a single mutation can result in any strategy with probability . However, in biological systems it seems natural that not all mutations can arise from a given state. Certain mutations may be far away, or even be unreachable given the current composition of an evolving population. These distances between strategies (or genotypes) define a topology of mutations that so far has been neglected in evolutionary game theory. In this paper we re-evaluate classic results in the evolution of cooperation departing from the assumption of uniform mutations. We examine two cases: the evolution of reciprocal strategies in a repeated prisoners dilemma, and the evolution of altruistic punishment in a public goods game. In both cases, alternative but reasonable mutation kernels shift known results in the direction of less cooperation. We therefore show that assuming uniform mutations has a substantial impact on the fate of an evolving population. Our results call for a reassessment of the “model-less” approach to mutations in evolutionary dynamics.

Evil green beards: Tag recognition can also be used to withhold cooperation in structured populations

Natural selection works against cooperation unless a specific mechanism is at work. These mechanisms are typically studied in isolation. Here we look at the interaction between two such mechanisms: tag recognition and population structure. If cooperators can recognize each other, and only cooperate among themselves, then they can invade defectors. This is known as the green beard effect. Another mechanism is assortment caused by population structure. If interactions occur predominantly between alike individuals, then indiscriminate cooperation can evolve. Here we show that these two mechanisms interact in a non-trivial way. When assortment is low, tags lead to conventional green beard cycles with periods of tag based cooperation and periods of defection. However, if assortment is high, evil green beard cycles emerge. In those cycles, tags are not used to build up cooperation with others that share the tag, but to undermine cooperation with others that do not share the tag. High levels of assortment therefore do not lead to indiscriminate cooperation if tags are available. This shows that mechanisms that are known to promote cooperation in isolation can interact in counterintuitive ways.

Towards a self-stopping evolutionary algorithm using coupling from the past

In this paper a stopping criterion for a particular class of evolutionary algorithms is devised. First, a model of a generic evolutionary algorithm using iterated random maps is presented. The model allows the exploration of a connection between coupling from the past, and a stopping criterion for evolutionary algorithms. Accordingly, a method to stop a generic evolutionary algorithm is proposed. Some computational experiments are carried out to test the stopping criterion, using a modified version of coupling from the past. Empirical evidence is shown to support the suitability of the criterion.

On geometric and statistical properties of the attractors of a generic evolutionary algorithm

In this work, evolutionary algorithms are modeled as random dynamical systems. The combined action of selection and variation is expressed as a stochastic operator acting on the space of populations. The long term behavior of selection and variation is studied separately. Then the combined effect is analyzed by characterizing the attractor and stationary measure of the dynamics. As a main result it is proved that the stationary measure is supported on populations made up of optimizers. Also, some experiments are carried out in order to visualize the evolvable populations, the attractor sets and the stationary measure. Some geometric properties of such sets are discussed.

Chromodynamics of accents? [Commentary on: Emma Cohen: The Evolution of Tag-Based Cooperation in Humans: The Case for Accent.]

Recent game-theoretic simulation and analytical models have demonstrated that cooperative strategies mediated by indicators of cooperative potential, or “tags,” can invade, spread, and resist invasion by noncooperators across a range of population-structure and cost-benefit scenarios. The plausibility of these models is potentially relevant for human evolutionary accounts insofar as humans possess some phenotypic trait that could serve as a reliable tag. Linguistic markers, such as accent and dialect, have frequently been either cursorily defended or promptly dismissed as satisfying the criteria of a reliable and evolutionarily viable tag. This paper integrates evidence from a range of disciplines to develop and assess the claim that speech accent mediated the evolution of tag-based cooperation in humans. Existing evidence warrants the preliminary conclusion that accent markers meet the demands of an evolutionarily viable tag and potentially afforded a cost-effective solution to the challenges of maintaining viable cooperative relationships in diffuse, regional social networks.

Cooperation, Solution Concepts and Long-term Dynamics in the Iterated Prisoner’s Dilemma

Solution concepts help designing co-evolutionary algorithms by interfacing search mechanisms and problems. This work analyses co-evolutionary dynamics by coupling the notion of solution concept with a Markov chain model of co-evolution. It is shown that once stationarity has been reached by the Markov chain, and given a particular solution concept of interest, the dynamics can be seen as a Bernoulli process describing how the algorithm visits solution and non-solution sets. A particular analysis is presented using the iterated prisoners dilemma. By numerically computing the Markov chain transition matrices and stationary distributions, a complex and strong relation between variation and selection is observed.