Brian Skyrms, author of the successful Evolution of the Social Contract (which won the prestigious Lakatos Award) has written a sequel. The book is a study of ideas of cooperation and collective action. The point of departure is a prototypical story found in Rousseau's A Discourse on Inequality. Rousseau contrasts the pay-off of hunting hare where the risk of non-cooperation is small but the reward is equally small, against the pay-off of hunting the stag where maximum cooperation is required but where the reward is so much greater. Thus, rational agents are pulled in one direction by considerations of risk and in another by considerations of mutual benefit. Written with Skyrms's characteristic clarity and verve, this intriguing book will be eagerly sought out by students and professionals in philosophy, political science, economics, sociology and evolutionary biology.

In the animal world, collective action to shelter, protect and nourish requires the cooperation of group members. Among humans, many situations require the cooperation of more than two individuals simultaneously. Most of the relevant literature has focused on an extreme case, the N-person Prisoner's Dilemma. Here we introduce a model in which a threshold less than the total group is required to produce benefits, with increasing participation leading to increasing productivity. This model constitutes a generalization of the two-person stag hunt game to an N-person game. Both finite and infinite population models are studied. In infinite populations this leads to a rich dynamics that admits multiple equilibria. Scenarios of defector dominance, pure coordination or coexistence may arise simultaneously. On the other hand, whenever one takes into account that populations are finite and when their size is of the same order of magnitude as the group size, the evolutionary dynamics is profoundly affected: it may ultimately invert the direction of natural selection, compared with the infinite population limit.

In this pithy and highly readable book, Brian Skyrms, a recognised authority on game and decision theory, investigates traditional problems of the social contract in terms of evolutionary dynamics. Game theory is skilfully employed to offer new interpretations of a wide variety of social phenomena, including justice, mutual aid, commitment, convention and meaning. The author eschews any grand, unified theory. Rather, he presents the reader with tools drawn from evolutionary game theory for the purpose of analysing and coming to understand the social contract. The book is not technical and requires no special background knowledge. As such, it could be enjoyed by students and professionals in a wide range of disciplines: political science, philosophy, decision theory, economics and biology.

We consider a dynamic social network model in which agents play repeated games in pairings determined by a stochastically evolving social network. Individual agents begin to interact at random, with the interactions modeled as games. The game payoffs determine which interactions are reinforced, and the network structure emerges as a consequence of the dynamics of the agents' learning behavior. We study this in a variety of game-theoretic conditions and show that the behavior is complex and sometimes dissimilar to behavior in the absence of structural dynamics. We argue that modeling network structure as dynamic increases realism without rendering the problem of analysis intractable. P airs from among a population of 10 individuals interact repeatedly. Perhaps they are cooperating to hunt stags and rabbits, or coordinating on which concert to attend together; perhaps they are involved in the somewhat more antagonistic situation of bargaining to split a fixed payoff, or attempting to escape the undesirable but compelling equilibrium of a Prisoner's Dilemma. As time progresses, the players adapt their strategies, perhaps incorporating randomness in their decision rules, to suit their environment. But they may also exert control over their environment. The players may have choice over the pairings but not perfect information about the other players. They may improve their lot in two different ways. A child who is being bullied learns either to fight better or to run away. Similarly, a player who obtains unsatisfactory results may choose either to change strategies or to change associates. Regardless of whether the interactions are mostly cooperative or mostly antagonistic, it is natural and desirable to allow evolution of the social network (the propensity for each pair to interact) as well as the individuals' strategies.We build a model that incorporates both of these modes of evolution. The idea is simple.(*) Individual agents begin to interact at random. The interactions are modeled as games. The game payoffs determine which interactions are reinforced, and the social network structure emerges as a consequence of the dynamics of the agents' learning behavior.As the details of the specific game and the reinforcement dynamics vary, we then obtain a class of models. In this paper, we treat some simple reinforcement dynamics, which may serve as a base for future investigation.The idea of simultaneous evolution of strategy and social network appears to be almost completely unexplored. Indeed, the most thoroughly studied models of evolutionary game theory assume mean-field interactions, where each individual is always equally likely to interact with each other. Standard treatments of evolutionary game dynamics 1 2 operate entirely in this paradigm. This is due, to a large extent, to considerations of theoretical tractability of the model. Models have been introduced that allow the agents some control over their choice of partner (3), but the control is still exerted in a mean-field setting: one chooses between the pres...

We consider a dynamic social network model in which agents play repeated games in pairings determined by a stochastically evolving social network. Individual agents begin to interact at random, with the interactions modeled as games. The game payoffs determine which interactions are reinforced, and the network structure emerges as a consequence of the dynamics of the agents' learning behavior. We study this in a variety of game-theoretic conditions and show that the behavior is complex and sometimes dissimilar to behavior in the absence of structural dynamics. We argue that modeling network structure as dynamic increases realism without rendering the problem of analysis intractable. P airs from among a population of 10 individuals interact repeatedly. Perhaps they are cooperating to hunt stags and rabbits, or coordinating on which concert to attend together; perhaps they are involved in the somewhat more antagonistic situation of bargaining to split a fixed payoff, or attempting to escape the undesirable but compelling equilibrium of a Prisoner's Dilemma. As time progresses, the players adapt their strategies, perhaps incorporating randomness in their decision rules, to suit their environment. But they may also exert control over their environment. The players may have choice over the pairings but not perfect information about the other players. They may improve their lot in two different ways. A child who is being bullied learns either to fight better or to run away. Similarly, a player who obtains unsatisfactory results may choose either to change strategies or to change associates. Regardless of whether the interactions are mostly cooperative or mostly antagonistic, it is natural and desirable to allow evolution of the social network (the propensity for each pair to interact) as well as the individuals' strategies.We build a model that incorporates both of these modes of evolution. The idea is simple.(*) Individual agents begin to interact at random. The interactions are modeled as games. The game payoffs determine which interactions are reinforced, and the social network structure emerges as a consequence of the dynamics of the agents' learning behavior.As the details of the specific game and the reinforcement dynamics vary, we then obtain a class of models. In this paper, we treat some simple reinforcement dynamics, which may serve as a base for future investigation.The idea of simultaneous evolution of strategy and social network appears to be almost completely unexplored. Indeed, the most thoroughly studied models of evolutionary game theory assume mean-field interactions, where each individual is always equally likely to interact with each other. Standard treatments of evolutionary game dynamics 1 2 operate entirely in this paradigm. This is due, to a large extent, to considerations of theoretical tractability of the model. Models have been introduced that allow the agents some control over their choice of partner (3), but the control is still exerted in a mean-field setting: one chooses between the pres...