Evolutionary games in the multiverse

Evolutionary game dynamics of two players with two strategies has been studied in great detail. These games have been used to model many biologically relevant scenarios, ranging from social dilemmas in mammals to microbial diversity. Some of these games may in fact take place between a number of individuals and not just between two. Here, we address one-shot games with multiple players. As long as we have only two strategies, many results from two player games can be generalized to multiple players. For games with multiple players and more than two strategies, we show that statements derived for pairwise interactions do no longer hold. For two player games with any number of strategies there can be at most one isolated internal equilibrium. For any number of players $\boldsymbol{d}$ with any number of strategies n, there can be at most (d-1)^(n-1) isolated internal equilibria. Multiplayer games show a great dynamical complexity that cannot be captured based on pairwise interactions. Our results hold for any game and can easily be applied for specific cases, e.g. public goods games or multiplayer stag hunts

Simulation of an Optional Strategy in the Prisoner's Dilemma in Spatial and Non-spatial Environments

This paper presents research comparing the effects of different environments on the outcome of an extended Prisoner's Dilemma, in which agents have the option to abstain from playing the game. We consider three different pure strategies: cooperation, defection and abstinence. We adopt an evolutionary game theoretic approach and consider two different environments: the first which imposes no spatial constraints and the second in which agents are placed on a lattice grid. We analyse the performance of the three strategies as we vary the loner's payoff in both structured and unstructured environments. Furthermore we also present the results of simulations which identify scenarios in which cooperative clusters of agents emerge and persist in both environments.Comment: 12 pages, 8 figures. International Conference on the Simulation of Adaptive Behavio

Reward and Punishment in Minigames

Minigames capturing the essence of Public Goods experiments show that even in the absence of rationality assumptions, both punishment and reward will fail to bring about prosocial behavior. This holds in particular for the well-known Ultimatum Game, which emerges as a special case. But reputation can induce fairness and cooperation in populations adapting through learning or imitation. Indeed, the inclusion of reputation effects in the corresponding dynamical models leads to the evolution of economically productive behavior, with agents contributing to the public good and either punishing those who don't, or rewarding those who do. Reward and punishment correspond to two types of bifurcation with intriguing complementarity. The analysis suggests that reputation is essential for fostering social behavior among selfish agents, and that it is considerably more effective with punishment than with rewards

The Dynamics of Public Goods

We analyze the replicator equation for two games closely related with the social dilemma occurring in public goods situation. In one case, players can punish defectors in their group. In another case, they can choose not to take part in the game. In both cases, interactions are not pairwise and payoffs are nonlinear. Nevertheless, the qualitative dynamics can be fully analyzed. The games offer potential solutions for the problem of the emergence of cooperation in sizeable groups of non-related individuals - a basic question in evolutionary biology and economics

Evolutionary prisoner's dilemma games with optional participation

Competition among cooperators, defectors, and loners is studied in an evolutionary prisoner's dilemma game with optional participation. Loners are risk averse i.e. unwilling to participate and rather rely on small but fixed earnings. This results in a rock-scissors-paper type cyclic dominance of the three strategies. The players are located either on square lattices or random regular graphs with the same connectivity. Occasionally, every player reassesses its strategy by sampling the payoffs in its neighborhood. The loner strategy efficiently prevents successful spreading of selfish, defective behavior and avoids deadlocks in states of mutual defection. On square lattices, Monte Carlo simulations reveal self-organizing patterns driven by the cyclic dominance, whereas on random regular graphs different types of oscillatory behavior are observed: the temptation to defect determines whether damped, periodic or increasing oscillations occur. These results are compared to predictions by pair approximation. Although pair approximation is incapable of distinguishing the two scenarios because of the equal connectivity, the average frequencies as well as the oscillations on random regular graphs are well reproduced.Comment: 6 pages, 7 figure

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 n. In particular, rank changes are almost certain for n§8, which jeopardizes the predictive power of results derived for weak selection

Carrier relaxation in GaAs v-groove quantum wires and the effects of localization

Carrier relaxation processes have been investigated in GaAs/AlGaAs v-groove quantum wires (QWRs) with a large subband separation (46 meV). Signatures of inhibited carrier relaxation mechanisms are seen in temperature-dependent photoluminescence (PL) and photoluminescence-excitation (PLE) measurements; we observe strong emission from the first excited state of the QWR below ~50 K. This is attributed to reduced inter-subband relaxation via phonon scattering between localized states. Theoretical calculations and experimental results indicate that the pinch-off regions, which provide additional two-dimensional confinement for the QWR structure, have a blocking effect on relaxation mechanisms for certain structures within the v-groove. Time-resolved PL measurements show that efficient carrier relaxation from excited QWR states into the ground state, occurs only at temperatures > 30 K. Values for the low temperature radiative lifetimes of the ground- and first excited-state excitons have been obtained (340 ps and 160 ps respectively), and their corresponding localization lengths along the wire estimated.Comment: 9 pages, 8 figures, submitted to Phys. Rev. B Attempted to correct corrupt figure

Activation and inhibition of bimanual movements in school-aged children

The development of motor activation and inhibition was compared in 6-to-12 year-olds. Children had to initiate or stop the externally paced movements of one hand, while maintaining that of the other hand. The time needed to perform the switching task (RT) and the spatio-temporal variables show different agerelated evolutions depending on the coordination pattern (inor anti-phase) and the type of transition (activation, selective inhibition, non selective inhibition) required. In the anti-phase mode, activation perturbs the younger subjects' responses while temporal and spatial stabilities transiently decrease around 9 years when activating in the in-phase mode. Aged-related changes differed between inhibition and activation in the antiphase mode, suggesting either the involvement of distinct neural networks or the existence of a single network that is reorganized. In contrast, stopping or adding one hand in the in-phase mode shows similar aged-related improvement. We suggest that selectively stopping or activating one arm during symmetrical coordination rely on the two faces of a common processing in which activation could be the release of inhibitio

Oscillations in Optional Public Good Games

We present a new mechanism promoting cooperative behavior among selfish individuals in the public goods game. This game represents a straightforward generalization of the prisoner's dilemma to an arbitrary number of players. In contrast to the compulsory public goods game, optional participation provides a natural way to avoid deadlocks in the state of mutual defection. The three resulting strategies - collaboration or defection in the public goods game, as well as not joining at all -are studied by means of a replicator dynamics, which can be completely analysed in spite of the fact that some payoff terms are nonlinear. If cooperation is valuable enough, the dynamics exhibits a rock-scissors-paper type of cycling between the three strategies, leading to sizeable average levels of cooperation in the population. Thus, voluntary participation makes cooperation possible. But for each strategy, the average payoff value remains equal to the earnings of those not participating in the public goods game