The effect of network topology on optimal exploration strategies and the evolution of cooperation in a mobile population

We model a mobile population interacting over an underlying spatial structure using a Markov movement model. Interactions take the form of public goods games, and can feature an arbitrary group size. Individuals choose strategically to remain at their current location or to move to a neighbouring location, depending upon their exploration strategy and the current composition of their group. This builds upon previous work where the underlying structure was a complete graph (i.e. there was effectively no structure). Here, we consider alternative network structures and a wider variety of, mainly larger, populations. Previously, we had found when cooperation could evolve, depending upon the values of a range of population parameters. In our current work, we see that the complete graph considered before promotes stability, with populations of cooperators or defectors being relatively hard to replace. By contrast, the star graph promotes instability, and often neither type of population can resist replacement. We discuss potential reasons for this in terms of network topology

Predicting Human Cooperation

The Prisoner's Dilemma has been a subject of extensive research due to its importance in understanding the ever-present tension between individual self-interest and social benefit. A strictly dominant strategy in a Prisoner's Dilemma (defection), when played by both players, is mutually harmful. Repetition of the Prisoner's Dilemma can give rise to cooperation as an equilibrium, but defection is as well, and this ambiguity is difficult to resolve. The numerous behavioral experiments investigating the Prisoner's Dilemma highlight that players often cooperate, but the level of cooperation varies significantly with the specifics of the experimental predicament. We present the first computational model of human behavior in repeated Prisoner's Dilemma games that unifies the diversity of experimental observations in a systematic and quantitatively reliable manner. Our model relies on data we integrated from many experiments, comprising 168,386 individual decisions. The computational model is composed of two pieces: the first predicts the first-period action using solely the structural game parameters, while the second predicts dynamic actions using both game parameters and history of play. Our model is extremely successful not merely at fitting the data, but in predicting behavior at multiple scales in experimental designs not used for calibration, using only information about the game structure. We demonstrate the power of our approach through a simulation analysis revealing how to best promote human cooperation.Comment: Added references. New inline citation style. Added small portions of text. Re-compiled Rmarkdown file with updated ggplot2 so small aesthetic changes to plot

Fashion, Cooperation, and Social Interactions

Fashion plays such a crucial rule in the evolution of culture and society that it is regarded as a second nature to the human being. Also, its impact on economy is quite nontrivial. On what is fashionable, interestingly, there are two viewpoints that are both extremely widespread but almost opposite: conformists think that what is popular is fashionable, while rebels believe that being different is the essence. Fashion color is fashionable in the first sense, and Lady Gaga in the second. We investigate a model where the population consists of the afore-mentioned two groups of people that are located on social networks (a spatial cellular automata network and small-world networks). This model captures two fundamental kinds of social interactions (coordination and anti-coordination) simultaneously, and also has its own interest to game theory: it is a hybrid model of pure competition and pure cooperation. This is true because when a conformist meets a rebel, they play the zero sum matching pennies game, which is pure competition. When two conformists (rebels) meet, they play the (anti-) coordination game, which is pure cooperation. Simulation shows that simple social interactions greatly promote cooperation: in most cases people can reach an extraordinarily high level of cooperation, through a selfish, myopic, naive, and local interacting dynamic (the best response dynamic). We find that degree of synchronization also plays a critical role, but mostly on the negative side. Four indices, namely cooperation degree, average satisfaction degree, equilibrium ratio and complete ratio, are defined and applied to measure people's cooperation levels from various angles. Phase transition, as well as emergence of many interesting geographic patterns in the cellular automata network, is also observed.Comment: 21 pages, 12 figure

Evolutionary games on graphs

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first three sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fourth section surveys the topological complications implied by non-mean-field-type social network structures in general. The last three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.Comment: Review, final version, 133 pages, 65 figure

Coalition Formation Game for Cooperative Cognitive Radio Using Gibbs Sampling

This paper considers a cognitive radio network in which each secondary user selects a primary user to assist in order to get a chance of accessing the primary user channel. Thus, each group of secondary users assisting the same primary user forms a coaltion. Within each coalition, sequential relaying is employed, and a relay ordering algorithm is used to make use of the relays in an efficient manner. It is required then to find the optimal sets of secondary users assisting each primary user such that the sum of their rates is maximized. The problem is formulated as a coalition formation game, and a Gibbs Sampling based algorithm is used to find the optimal coalition structure.Comment: 7 pages, 2 figure

Coevolutionary games - a mini review

Prevalence of cooperation within groups of selfish individuals is puzzling in that it contradicts with the basic premise of natural selection. Favoring players with higher fitness, the latter is key for understanding the challenges faced by cooperators when competing with defectors. Evolutionary game theory provides a competent theoretical framework for addressing the subtleties of cooperation in such situations, which are known as social dilemmas. Recent advances point towards the fact that the evolution of strategies alone may be insufficient to fully exploit the benefits offered by cooperative behavior. Indeed, while spatial structure and heterogeneity, for example, have been recognized as potent promoters of cooperation, coevolutionary rules can extend the potentials of such entities further, and even more importantly, lead to the understanding of their emergence. The introduction of coevolutionary rules to evolutionary games implies, that besides the evolution of strategies, another property may simultaneously be subject to evolution as well. Coevolutionary rules may affect the interaction network, the reproduction capability of players, their reputation, mobility or age. Here we review recent works on evolutionary games incorporating coevolutionary rules, as well as give a didactic description of potential pitfalls and misconceptions associated with the subject. In addition, we briefly outline directions for future research that we feel are promising, thereby particularly focusing on dynamical effects of coevolutionary rules on the evolution of cooperation, which are still widely open to research and thus hold promise of exciting new discoveries.Comment: 24 two-column pages, 10 figures; accepted for publication in BioSystem

Heterogeneity in evolutionary games: an analysis of the risk perception

In this work, we analyse the relationship between heterogeneity and cooperation. Previous investigations suggest that this relation is nontrivial, as some authors found that heterogeneity sustains cooperation, while others obtained different results. Among the possible forms of heterogeneity, we focus on the individual perception of risks and rewards related to a generic event, that can show up in a number of social and biological systems. The modelling approach is based on the framework of Evolutionary Game Theory. To represent this kind of heterogeneity, we implement small and local perturbations on the payoff matrix of simple 2-strategy games, as the Prisoner's Dilemma. So, while usually the payoff is considered as a global and time-invariant structure, i.e. it is the same for all individuals of a population at any time, in our model its value is continuously affected by small variations, both in time and space (i.e. position on a lattice). We found that such perturbations can be beneficial or detrimental to cooperation, depending on their setting. Notably, cooperation is strongly supported when perturbations act on the main diagonal of the payoff matrix, whereas when they act on the off-diagonal the resulting effect is more difficult to quantify. To conclude, the proposed model shows a rich spectrum of possible equilibria, whose interpretation might offer insights and enrich the description of several systems.Comment: 7 pages, 5 figure

Antisocial pool rewarding does not deter public cooperation

Rewarding cooperation is in many ways expected behaviour from social players. However, strategies that promote antisocial behaviour are also surprisingly common, not just in human societies, but also among eusocial insects and bacteria. Examples include sanctioning of individuals who behave prosocially, or rewarding of freeriders who do not contribute to collective enterprises. We therefore study the public goods game with antisocial and prosocial pool rewarding in order to determine the potential negative consequences on the effectiveness of positive incentives to promote cooperation. Contrary to a naive expectation, we show that the ability of defectors to distribute rewards to their like does not deter public cooperation as long as cooperators are able to do the same. Even in the presence of antisocial rewarding the spatial selection for cooperation in evolutionary social dilemmas is enhanced. Since the administration of rewards to either strategy requires a considerable degree of aggregation, cooperators can enjoy the benefits of their prosocial contributions as well as the corresponding rewards. Defectors when aggregated, on the other hand, can enjoy antisocial rewards, but due to their lack of contributions to the public good they ultimately succumb to their inherent inability to secure a sustainable future. Strategies that facilitate the aggregation of akin players, even if they seek to promote antisocial behaviour, thus always enhance the long-term benefits of cooperation.Comment: 9 two-column pages, 5 figures; accepted for publication in Proceedings of the Royal Society