Brian Skyrms

We study a low-rationality learning dynamics called probe and adjust. Our emphasis is on its properties in games of information transfer such as the Lewis signaling game or the Bala-Goyal network game. These games fall into the class of weakly better reply games, in which, starting from any action profile, there is a weakly better reply path to a strict Nash equilibrium. We prove that probe and adjust will be close to strict Nash equilibria in this class of games with arbitrarily high probability. In addition, we compare these asymptotic properties to short-run behavior

In this article, we aim to illustrate evolutionary explanations for the emergence of framing effects, discussed in detail in Cristina Bicchieri’s The Grammar of Society . We show how framing effects might evolve which coalesce two economically distinct interactions into a single one, leading to apparently irrational behavior in each individual interaction. Here we consider the now well-known example of the ultimatum game, and show how this ‘irrational’ behavior might result from a single norm which governs behavior in multiple games. We also show how framing effects might result in radically different play in strategically identical situations. We consider the Hawk-Dove game (the game of chicken) and also the Nash bargaining game. Here arbitrary tags or signals might result in one party doing better than another

Amodel for inventing newsignals is introduced in the context of sender–receiver games with reinforcement learning. If the invention parameter is set to zero, it reduces to basic Roth–Erev learning applied to acts rather than strategies, as in Argiento et al. (Stoch. Process. Appl. 119:373–390, 2009). If every act is uniformly reinforced in every state it reduces to the Chinese Restaurant Process—also known as the Hoppe–Pólya urn—applied to each act. The dynamics can move players from one signaling game to another during the learning process. Invention helps agents avoid pooling and partial pooling equilibria.

Sender–receiver games are simple, tractable models of information transmission. They provide a basic setting for the study of the evolution of meaning. It is possible to investigate not only the equilibrium structure of these games, but also the dynamics of evolution and learning—with sometimes surprising results. Generalizations of the usual binary game to interactions with multiple senders, multiple receivers, or both, provide the elements of signaling networks. These can be seen as the loci of information processing, of group decisions, and of teamwork.

Pre-play signals that cost nothing are sometimes thought to be of no significance in interactions which are not games of pure common interest. The chapter investigates the effect of pre-play signals in an evolutionary setting for Assurance, or Stag Hunt, games and for a Bargaining game. The evolutionary game with signals is found to have dramatically different dynamics from the same game without signals. Signals change stability properties of equilibria in the base game, create new polymorphic equilibria, and change the basins of attraction of equilibria in the base game. Signals carry information at equilibrium in the case of the new polymorphic equilibria, but transient information is the basis for large changes in the magnitude of basins of attraction of equilibria in the base game. These phenomena exemplify new and important differences between evolutionary game theory and game theory based on rational choice.

The explanatory significance of equilibrium depends on the underlying dynamics. This chapter investigates questions of stability and robustness with respect to some simple evolutionary models from Skyrms’ book, _Evolution of the Social Contract_. These models use the replicator dynamics. In each one the equilibria are identified and their local dynamic stability properties characterized. In two models, one equilibrium is shown to be globally asymptotically stable. The results are then shown to be robust over a large class of adaptive dynamics that might be considered as alternatives to the replicator dynamics, and the structural stability properties of the three models are investigated. The question of the structural stability of a model of bargaining with correlated encounters raised by D'Arms et al. (1998) is answered in the affirmative. The other two models are not structurally stable. Modification of a structurally unstable signaling system to allow for correlated encounters results in a structurally stable model.

An important feature of many conventions is that the agents use an asymmetry to coordinate their behaviour. We call these ‘correlated conventions’. However, a puzzle arises: since any asymmetry works as well as any other, what are the relevant asymmetries on which a given population founds its correlated conventions? In order to gain traction on this question we need an account of both the invention and evolution of correlated conventions. Invention has remained largely unexplored in the literature. In this article we provide a simple model of the origin and subsequent dynamics of correlated conventions. This model can serve as a base for future investigation.

In this new edition of Evolution of the Social Contract, Brian Skyrms uses evolutionary game theory to analyze the genesis of social contracts and investigates social phenomena including justice, communication, altruism, and bargaining. Featuring new material on evolution and information transfer, and including recent developments in game theory and evolution literature, his book introduces and applies appropriate concepts of equilibrium and evolutionary dynamics, showing how key issues can be modelled as games and considering the ways in which evolution sometimes supports, and sometimes does not support, rational choice. He discusses topics including how bargaining with neighbours promotes sharing of resources, the diversity of behavior in ultimatum bargaining in small societies, the Prisoner's Dilemma, and an investigation into signalling games and the spontaneous emergence of meaningful communication. His book will be of great interest to readers in philosophy of science, social science, evolutionary biology, game and decision theory, and political theory.

In the social sciences norms are sometimes taken to play a key explanatory role. Yet norms differ from group to group, from society to society, and from species to species. How are norms formed and how do they change? This 'state-of-the-art' collection of essays presents some of the best contemporary research into the dynamic processes underlying the formation, maintenance, metamorphosis and dissolution of norms. The volume combines formal modelling with more traditional analysis, and considers biological and cultural evolution, individual learning, and rational deliberation. In filling a significant gap in the current literature this volume will be of particular interest to economists, political scientists and sociologists, in addition to philosophers of the social sciences.