### Concept: Evolutionarily stable strategy

#### 172

##### Evolution of cooperation in multiplex networks.

- OPEN
- Scientific reports
- Published over 5 years ago
- Discuss

We study evolutionary game dynamics on structured populations in which individuals take part in several layers of networks of interactions simultaneously. This multiplex of interdependent networks accounts for the different kind of social ties each individual has. By coupling the evolutionary dynamics of a Prisoner’s Dilemma game in each of the networks, we show that the resilience of cooperative behaviors for extremely large values of the temptation to defect is enhanced by the multiplex structure. Furthermore, this resilience is intrinsically related to a non-trivial organization of cooperation across the network layers, thus providing a new way out for cooperation to survive in structured populations.

#### 54

##### Iterated Prisoner’s Dilemma contains strategies that dominate any evolutionary opponent.

- Proceedings of the National Academy of Sciences of the United States of America
- Published almost 6 years ago
- Discuss

The two-player Iterated Prisoner’s Dilemma game is a model for both sentient and evolutionary behaviors, especially including the emergence of cooperation. It is generally assumed that there exists no simple ultimatum strategy whereby one player can enforce a unilateral claim to an unfair share of rewards. Here, we show that such strategies unexpectedly do exist. In particular, a player X who is witting of these strategies can (i) deterministically set her opponent Y’s score, independently of his strategy or response, or (ii) enforce an extortionate linear relation between her and his scores. Against such a player, an evolutionary player’s best response is to accede to the extortion. Only a player with a theory of mind about his opponent can do better, in which case Iterated Prisoner’s Dilemma is an Ultimatum Game.

#### 48

##### Social cycling and conditional responses in the Rock-Paper-Scissors game

- Scientific reports
- Published over 3 years ago
- Discuss

How humans make decisions in non-cooperative strategic interactions is a big question. For the fundamental Rock-Paper-Scissors (RPS) model game system, classic Nash equilibrium (NE) theory predicts that players randomize completely their action choices to avoid being exploited, while evolutionary game theory of bounded rationality in general predicts persistent cyclic motions, especially in finite populations. However as empirical studies have been relatively sparse, it is still a controversial issue as to which theoretical framework is more appropriate to describe decision-making of human subjects. Here we observe population-level persistent cyclic motions in a laboratory experiment of the discrete-time iterated RPS game under the traditional random pairwise-matching protocol. This collective behavior contradicts with the NE theory but is quantitatively explained, without any adjustable parameter, by a microscopic model of win-lose-tie conditional response. Theoretical calculations suggest that if all players adopt the same optimized conditional response strategy, their accumulated payoff will be much higher than the reference value of the NE mixed strategy. Our work demonstrates the feasibility of understanding human competition behaviors from the angle of non-equilibrium statistical physics.

#### 26

It is often assumed that in public goods games, contributors are either strong or weak players and each individual has an equal probability of exhibiting cooperation. It is difficult to explain why the public good is produced by strong individuals in some cooperation systems, and by weak individuals in others. Viewing the asymmetric volunteer’s dilemma game as an evolutionary game, we find that whether the strong or the weak players produce the public good depends on the initial condition (i.e., phenotype or initial strategy of individuals). These different evolutionarily stable strategies (ESS) associated with different initial conditions, can be interpreted as the production modes of public goods of different cooperation systems. A further analysis revealed that the strong player adopts a pure strategy but mixed strategies for the weak players to produce the public good, and that the probability of volunteering by weak players decreases with increasing group size or decreasing cost-benefit ratio. Our model shows that the defection probability of a “strong” player is greater than the “weak” players in the model of Diekmann (1993). This contradicts Selten’s (1980) model that public goods can only be produced by a strong player, is not an evolutionarily stable strategy, and will therefore disappear over evolutionary time. Our public good model with ESS has thus extended previous interpretations that the public good can only be produced by strong players in an asymmetric game.

#### 25

##### An oscillating tragedy of the commons in replicator dynamics with game-environment feedback

- OPEN
- Proceedings of the National Academy of Sciences of the United States of America
- Published over 1 year ago
- Discuss

A tragedy of the commons occurs when individuals take actions to maximize their payoffs even as their combined payoff is less than the global maximum had the players coordinated. The originating example is that of overgrazing of common pasture lands. In game-theoretic treatments of this example, there is rarely consideration of how individual behavior subsequently modifies the commons and associated payoffs. Here, we generalize evolutionary game theory by proposing a class of replicator dynamics with feedback-evolving games in which environment-dependent payoffs and strategies coevolve. We initially apply our formulation to a system in which the payoffs favor unilateral defection and cooperation, given replete and depleted environments, respectively. Using this approach, we identify and characterize a class of dynamics: an oscillatory tragedy of the commons in which the system cycles between deplete and replete environmental states and cooperation and defection behavior states. We generalize the approach to consider outcomes given all possible rational choices of individual behavior in the depleted state when defection is favored in the replete state. In so doing, we find that incentivizing cooperation when others defect in the depleted state is necessary to avert the tragedy of the commons. In closing, we propose directions for the study of control and influence in games in which individual actions exert a substantive effect on the environmental state.

#### 11

##### Navigable networks as Nash equilibria of navigation games

- Nature communications
- Published over 2 years ago
- Discuss

Common sense suggests that networks are not random mazes of purposeless connections, but that these connections are organized so that networks can perform their functions well. One function common to many networks is targeted transport or navigation. Here, using game theory, we show that minimalistic networks designed to maximize the navigation efficiency at minimal cost share basic structural properties with real networks. These idealistic networks are Nash equilibria of a network construction game whose purpose is to find an optimal trade-off between the network cost and navigability. We show that these skeletons are present in the Internet, metabolic, English word, US airport, Hungarian road networks, and in a structural network of the human brain. The knowledge of these skeletons allows one to identify the minimal number of edges, by altering which one can efficiently improve or paralyse navigation in the network.

#### 11

##### Towards a richer evolutionary game theory

- OPEN
- Journal of the Royal Society, Interface / the Royal Society
- Published over 4 years ago
- Discuss

Most examples of the application of evolutionary game theory to problems in biology involve highly simplified models. I contend that it is time to move on and include much more richness in models. In particular, more thought needs to be given to the importance of (i) between-individual variation; (ii) the interaction between individuals, and hence the process by which decisions are reached; (iii) the ecological and life-history context of the situation; (iv) the traits that are under selection, and (v) the underlying psychological mechanisms that lead to behaviour. I give examples where including variation between individuals fundamentally changes predicted outcomes of a game. Variation also selects for real-time responses, again resulting in changed outcomes. Variation can select for other traits, such as choosiness and social sensitivity. More generally, many problems involve coevolution of more than one trait. I identify situations where a reductionist approach, in which a game is isolated from is ecological setting, can be misleading. I also highlight the need to consider flexibility of behaviour, mental states and other issues concerned with the evolution of mechanism.

#### 9

##### Strategic tradeoffs in competitor dynamics on adaptive networks

- OPEN
- Scientific reports
- Published 7 months ago
- Discuss

Recent empirical work highlights the heterogeneity of social competitions such as political campaigns: proponents of some ideologies seek debate and conversation, others create echo chambers. While symmetric and static network structure is typically used as a substrate to study such competitor dynamics, network structure can instead be interpreted as a signature of the competitor strategies, yielding competition dynamics on adaptive networks. Here we demonstrate that tradeoffs between aggressiveness and defensiveness (i.e., targeting adversaries vs. targeting like-minded individuals) creates paradoxical behaviour such as non-transitive dynamics. And while there is an optimal strategy in a two competitor system, three competitor systems have no such solution; the introduction of extreme strategies can easily affect the outcome of a competition, even if the extreme strategies have no chance of winning. Not only are these results reminiscent of classic paradoxical results from evolutionary game theory, but the structure of social networks created by our model can be mapped to particular forms of payoff matrices. Consequently, social structure can act as a measurable metric for social games which in turn allows us to provide a game theoretical perspective on online political debates.

#### 7

##### Cooperate without looking: Why we care what people think and not just what they do

- Proceedings of the National Academy of Sciences of the United States of America
- Published about 3 years ago
- Discuss

Evolutionary game theory typically focuses on actions but ignores motives. Here, we introduce a model that takes into account the motive behind the action. A crucial question is why do we trust people more who cooperate without calculating the costs? We propose a game theory model to explain this phenomenon. One player has the option to “look” at the costs of cooperation, and the other player chooses whether to continue the interaction. If it is occasionally very costly for player 1 to cooperate, but defection is harmful for player 2, then cooperation without looking is a subgame perfect equilibrium. This behavior also emerges in population-based processes of learning or evolution. Our theory illuminates a number of key phenomena of human interactions: authentic altruism, why people cooperate intuitively, one-shot cooperation, why friends do not keep track of favors, why we admire principled people, Kant’s second formulation of the Categorical Imperative, taboos, and love.

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##### Evolutionary dynamics of N-person Hawk-Dove games

- OPEN
- Scientific reports
- Published 8 months ago
- Discuss

In the animal world, the competition between individuals belonging to different species for a resource often requires the cooperation of several individuals in groups. This paper proposes a generalization of the Hawk-Dove Game for an arbitrary number of agents: the N-person Hawk-Dove Game. In this model, doves exemplify the cooperative behavior without intraspecies conflict, while hawks represent the aggressive behavior. In the absence of hawks, doves share the resource equally and avoid conflict, but having hawks around lead to doves escaping without fighting. Conversely, hawks fight for the resource at the cost of getting injured. Nevertheless, if doves are present in sufficient number to expel the hawks, they can aggregate to protect the resource, and thus avoid being plundered by hawks. We derive and numerically solve an exact equation for the evolution of the system in both finite and infinite well-mixed populations, finding the conditions for stable coexistence between both species. Furthermore, by varying the different parameters, we found a scenario of bifurcations that leads the system from dominating hawks and coexistence to bi-stability, multiple interior equilibria and dominating doves.