Brian Skyrms

Game theory based on rational choice is compared with game theory based on evolutionary, or other adaptive, dynamics. The Nash equilibrium concept has a central role to play in both theories, even though one makes extremely strong assumptions about cognitive capacities and common knowledge of the players, and the other does not. Nevertheless, there are also important differences between the two theories. These differences are illustrated in a number of games that model types of interaction that are key ingredients for any theory of the social contract

Italian writers of the fifteenth and sixteenth centuries, notably Pacioli (1494), Tartaglia (1556), and Cardan (1545), had discussed the problem of the division of a stake between two players whose game was interrupted before its close. The problem was proposed to Pascal and Fermat, probably in 1654, by the Chevalier de M´er´e, a gambler who is said to have had unusual ability “even for the mathematics.” The correspondence which ensued between Fermat and Pascal, was fundamental in the development of modern concepts of probability, and it is unfortunate that the introductory letter from Pascal to Fermat is no longer extant. The one here translated, written in 1654, appears in the Œuvres de Fermat (ed. Tannery and Henry, Vol. II, pp. 288–314, Paris 1894) and serves to show the nature of the problem

Pt. I. Zeno and the metaphysics of quantity. Zeno's paradox of measure -- Tractarian nominalism -- Logical atoms and combinatorial possibility -- Strict coherence, sigma coherence, and the metaphysics of quantity -- pt. II. Coherent degrees of belief. Higher-order degrees of belief -- A mistake in dynamic coherence arguments? -- Dynamic coherence and probability kinematics -- Updating, supposing, and MAXENT -- The structure of radical probabilism -- Diachronic coherence and radical probabilism -- pt. III. Induction. Carnapian inductive logic for Markov chains -- Carnapian inductive logic and Bayesian statistics -- Bayesian projectability.

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.

Moral norms are the rules of morality, those that people actually follow, and those that we feel people ought to follow, even when they don’t. Historically, the social sciences have been primarily concerned with describing the many forms that moral norms take in various cultures, with the emerging implication that moral norms are mere arbitrary products of culture. Philosophers, on the other hand, have been more concerned with trying to understand the nature and source of rules that all cultures ought to follow, with relatively little regard for what people actually do. The tension between the two approaches has to do with whether there are any standards higher than the whims of culture in determining right and wrong. Typically, the social sciences say “no”, pointing at the diversity of moral beliefs. Most philosophers (along with people of moral conviction) feel that there must be some deeper source of morality than the trends and fads of culture. Unfortunately, the nature and source of such standards has remained something of a mystery. Recent work on the evolution of norms has changed this picture dramatically.

The proper treatment of correlation in evolutionary game theory has unexpected connections with recent philosophical discussions of the theory of rational decision. The Logic of Decision (Jeffrey 1983) provides the correct framework for correlated evolutionary game theory and a variant of "ratifiability" is the appropriate generalization of "evolutionarily stable strategy". The resulting theory unifies the treatment of correlation due to kin, population viscosity, detection, signaling, reciprocal altruism, and behavior-dependent contexts. It is shown that (1) a strictly dominated strategy may be selected, and (2) under conditions of perfect correlation a strictly efficient strategy must be selected.

The question of diachronic coherence, coherence of degrees of belief across time, is investigated within the context of Richard Jeffrey’s radical probabilism. Diachronic coherence is taken as fundamental, and coherence results for degrees of belief at a single time, such as additivity, are recovered only with additional assumptions. Additivity of probabilities of probabilities is seen to be less problematic than additivity of first-order probabilities. Without any assumed model of belief change, diachronic coherence applied to higher-order degrees of belief yields the martingale property.

Carnap's Inductive Logic, like most philosophical discussions of induction, is designed for the case of independent trials. To take account of periodicities, and more generally of order, the account must be extended. From both a physical and a probabilistic point of view, the first and fundamental step is to extend Carnap's inductive logic to the case of finite Markov chains. Kuipers (1988) and Martin (1967) suggest a natural way in which this can be done. The probabilistic character of Carnapian inductive logic(s) for Markov chains and their relationship to Carnap's inductive logic(s) is discussed at various levels of Bayesian analysis.