Transfer of information between senders and receivers, of one kind or another, is essential to all life. David Lewis introduced a game theoretic model of the simplest case, where one sender and one receiver have pure common interest. How hard or easy is it for evolution to achieve information transfer in Lewis signaling?. The answers involve surprising subtleties. We discuss some if these in terms of evolutionary dynamics in both finite and infinite populations, with and without mutation.
BrianSkyrms presents a fascinating exploration of how fundamental signals are to our world. He uses a variety of tools -- theories of signaling games, information, evolution, and learning -- to investigate how meaning and communication develop. He shows how signaling games themselves evolve, and introduces a new model of learning with invention. The juxtaposition of atomic signals leads to complex signals, as the natural product of gradual process. Signals operate in networks of senders and receivers at all (...) levels of life. Information is transmitted, but it is also processed in various ways. That is how we think -- signals run around a very complicated signaling network. Signaling is a key ingredient in the evolution of teamwork, in the human but also in the animal world, even in micro-organisms. Communication and co-ordination of action are different aspects of the flow of information, and are both effected by signals. (shrink)
In this book, BrianSkyrms, a recognised authority on game and decision theory, investigates traditional problems of the social contract in terms of evolutionary dynamics. Game theory is employed to offer new interpretations of a wide variety of social phenomena, including justice, mutual aid, commitment, convention and meaning. Skyrms 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 read by students and professionals in a wide range of disciplines: political science, philosophy, decision theory, economics and biology. (shrink)
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. (shrink)
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. (shrink)
This is a 'state of the art' collection of essays on the relation between probabilities, especially conditional probabilities, and conditionals. It provides new negative results which sharply limit the ways conditionals can be related to conditional probabilities. There are also positive ideas and results which will open up new areas of research. The collection is intended to honour Ernest W. Adams, whose seminal work is largely responsible for creating this area of inquiry. As well as describing, evaluating, and applying Adams' (...) work the contributions extend his ideas in directions he may or may not have anticipated, but that he certainly inspired. In addition to a wide range of philosophers of science, the volume should interest computer scientists and linguists. (shrink)
The problem of trust is discussed in terms of David Hume’s meadow-draining example. This is analyzed in terms of rational choice, evolutionary game theory and a dynamic model of social network formation. The kind of explanation that postulates an innate predisposition to trust is seen to be unnecessary when social network dynamics is taken into account.
Both the quantity of information and the informational content of a signal are defined in the context of signaling games. Informational content is a generalization of standard philosophical notions of propositional content. It is shown how signals that initially carry no information may spontaneously acquire informational content by evolutionary or learning dynamics. It is shown how information can flow through signaling chains or signaling networks.
Some of the concerns which motivate attempts to provide a philosophical reduction of nomological necessity are briefly introduced in I. In II, Hempel's treatment of the paradoxes is contrasted with a position which holds that nomological necessity is a pragmatic dimension of laws of nature, and that this pragmatic dimension is of such a type that it prevents laws of nature from contraposing. Such a position is, however, untenable unless (i) the sense of 'pragmatics' at issue is specified, and the (...) possibility of pragmatic differences resulting in differences in confirmation is defended, and (ii) a relevant pragmatic difference between contrapositives is indicated. III attempts to satisfy condition (i) by developing a new sense of pure pragmatics and argues that some remarks by Goodman and Scheffler together with work on the logic of explanation by Dr. Rescher and myself suggest that nomological contrapositives are not pragmatically equivalent (i.e. substitutable salva veritate in the pure pragmatics of an ideal scientific language). If such is the case, condition (ii) is also satisfied. (shrink)
Edited by three leading figures in the field, this exciting volume presents cutting-edge work in decision theory by a distinguished international roster of contributors. These mostly unpublished papers address a host of crucial areas in the contemporary philosophical study of rationality and knowledge. Topics include causal versus evidential decision theory, game theory, backwards induction, bounded rationality, counterfactual reasoning in games and in general, analyses of the famous common knowledge assumptions in game theory, and evaluations of the normal versus extensive form (...) formulations of complex decision problems. (shrink)
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. (shrink)
If it was a matter of hunting a deer, everyone well realized that he must remain faithful to his post; but if a hare happened to pass within reach of one of them, we cannot doubt that he would have gone off in pursuit of it without scruple..." Rousseau's story of the hunt leaves many questions open. What are the values of a hare and of an individual's share of the deer given a successful hunt? What is the probability that (...) the hunt will be successful if all participants remain faithful to the hunt? Might two deer hunters decide to chase the hare? (shrink)
We consider the Stag Hunt in terms of Maynard Smith’s famous Haystack model. In the Stag Hunt, contrary to the Prisoner’s Dilemma, there is a cooperative equilibrium besides the equilibrium where every player defects. This implies that in the Haystack model, where a population is partitioned into groups, groups playing the cooperative equilibrium tend to grow faster than those at the non-cooperative equilibrium. We determine under what conditions this leads to the takeover of the population by cooperators. Moreover, we compare (...) our results to the case of an unstructured population and to the case of the Prisoner’s Dilemma. Finally, we point to some implications our findings have for three distinct ideas: Ken Binmore’s group selection argument in favor of the evolution of efficient social contracts, Sewall Wright’s Shifting Balance theory, and the equilibrium selection problem of game theory. (shrink)
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. (shrink)
To coordinate action, information must be transmitted, processed, and utilized to make decisions. Transmission of information requires the existence of a signaling system in which the signals that are exchanged are coordinated with the appropriate content. Signaling systems in nature range from quorum signaling in bacteria [Schauder and Bassler (2001), Kaiser (2004)], through the dance of the bees [Dyer and Seeley (1991)], birdcalls [Hailman, Ficken, and Ficken (1985), Gyger, Marler and Pickert (1987), Evans, Evans, and Marler (1994), Charrier and (...) Sturdy (2005)], and alarm calls in many species [Seyfarth and Cheney (1990), Green and Maegner (1998) ,Manser, Seyfarth and Cheney (2002)], up to human language. Information processing includes filtering – that is discarding irrelevant information and passing along what is important – and integration of multiple pieces of information. Integration includes logical inference and voting. Finally, the information must be used to make decisions with consequences for payoffs that drive evolution or learning. (shrink)
Does the philosophy of Radical Probabilism have enough structure to enable it to address fundamental epistemological questions? The requirement of dynamic coherence provides the structure for radical probabilist epistemology. This structure is sufficient to establish (i) the value of knowledge and (ii) long run convergence of degrees of belief.
Signals regarding the behavior of others are an essential element of human moral systems and there are important evolutionary connections between language and large-scale cooperation. In particular, social communication may be required for the reputation tracking needed to stabilize indirect reciprocity. Additionally, scholars have suggested that the benefits of indirect reciprocity may have been important for the evolution of language and that social signals may have coevolved with large-scale cooperation. This paper investigates the possibility of such a coevolution. Using the (...) tools of evolutionary game theory, we present a model that incorporates primitive “moral signaling” into a simple setting of indirect reciprocity. This model reveals some potential difficulties for the evolution of “moral signals.” We find that it is possible for “moral signals” to evolve alongside indirect reciprocity, but without some external pressure aiding the evolution of a signaling system, such a coevolution is unlikely. (shrink)
Paul Valéry1 Valéry’s “Variation sur Descartes” excellently evokes the vanishing act that has haunted philosophy ever since Darwin overturned the Cartesian tradition. If my body is composed of nothing but a team of a few trillion robotic cells, mindlessly interacting to produce all the large-scale patterns that tradition would attribute to the nonmechanical workings of my mind, there seems to be nothing left over to be me. Lurking in Darwin’s shadow there is a bugbear: the incredible Disappearing Self.2 One of (...) Darwin’s earliest critics saw what was coming and could scarcely contain his outrage. (shrink)
The structure of Reichenbach's pragmatic vindication of induction is analysed in detail. The argument is seen to proceed in two stages, the first being a pragmatic justification of the frequency interpretation of probability which is taken as a license for considering the aim of induction to be the discovery of limiting relative frequencies, and the second being the pragmatic justification of induction itself. Both justifications are found to contain flaws, and the arguments used to support Reichenbach's definition of the aim (...) of induction presuppose the availability of a type of predicate which generates paradoxes closely related to Goodman's "grue-bleen" paradox. Next, Salmon's "Criterion of Linguistic Invariance" is evaluated as a canon of inductive logic, which singles out the "straight rule" from an infinite class of convergent inductive rules. Upon close examination, its credentials are seen to be unimpressive. In connection with Salmon's work on linguistic invariance, we take a closer look at the impact of the Goodman paradox on probability estimator rules like Reichenbach's "straight rule." We find that its undesirable consequences for such systems of inductive logic cannot be escaped by Salmon's solution, or indeed by any solution whose motivating idea is to rule "queer" predicates out of court. Finally, the discussion of the Goodman paradox leads us to a modest methodological proposal for systems of inductive logic which incorperate probability estimator rules of the type at issue. (shrink)
Subjunctive conditionals are fundamental to rational decision both in single agent and multiple agent decision problems. They need explicit analysis only when they cause problems, as they do in recent discussions of rationality in extensive form games. This paper examines subjunctive conditionals in the theory of games using a strict revealed preference interpretation of utility. Two very different models of games are investigated, the classical model and the limits of reality model. In the classical model the logic of backward induction (...) is valid, but it does not use subjunctive conditionals; the relevant subjunctive conditionals do not even make sense. In the limits of reality model the subjunctive conditionals do make sense but backward induction is valid only under special assumptions. (shrink)
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. (shrink)
Two examples demonstrate the possibility of extremely complicated non-convergent behavior in evolutionary game dynamics. For the Taylor-Jonker flow, the stable orbits for three strategies were investigated by Zeeman. Chaos does not occur with three strategies. This papers presents numerical evidence that chaotic dynamics on a strange attractor does occur with four strategies. Thus phenomenon is closely related to known examples of complicated behavior in Lotka-Volterra ecological models.
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. (shrink)
We study a simple game theoretic model of information transfer which we consider to be a baseline model for capturing strategic aspects of epistemological questions. In particular, we focus on the question whether simple learning rules lead to an efficient transfer of information. We find that reinforcement learning, which is based exclusively on payoff experiences, is inadequate to generate efficient networks of information transfer. Fictitious play, the game theoretic counterpart to Carnapian inductive logic and a more sophisticated kind of learning, (...) suffices to produce efficiency in information transfer. (shrink)
In species capable of learning, including our own, individuals can modify their behavior by some adaptive process. Important classes of behavior - mating, predation, coalitions, trade, signaling, and division of labor - involve interactions between individuals. The agents involved learn two things: with whom to interact and how to act. That is to say that adaptive dynamics operates both on structure and strategy.
We consider the following signaling game. Nature plays first from the set {1, 2}. Player 1 (the Sender) sees this and plays from the set {A, B}. Player 2 (the Receiver) sees only Player 1’s play and plays from the set {1, 2}. Both players win if Player 2’s play equals Nature’s play and lose otherwise. Players are told whether they have won or lost, and the game is repeated. An urn scheme for learning coordination in this game is as (...) follows. Each node of the desicion tree for Players 1 and 2 contains an urn with balls of two colors for the two possible decisions. Players make decisions by drawing from the appropriate urns. After a win, each ball that was drawn is reinforced by adding another of the same color to the urn. A number of equilibria are possible for this game other than the optimal ones. However, we show that the urn scheme achieves asymptotically optimal coordination. (shrink)
Pre‐play signals that cost nothing are sometimes thought to be of no significance in interactions which are not games of pure common interest. We investigate 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. (shrink)
The partial cooperation displayed by subjects in the Centipede Game deviates radically from the predictions of traditional game theory. Even standard, infinite population, evolutionary settings have failed to provide an explanation for this behavior. However, recent work in finite population evolutionary models has shown that such settings can produce radically different results from the standard models. This paper examines the evolution of partial cooperation in finite populations. The results reveal a new possible explanation that is not open to the standard (...) models and gives us reason to be cautious when employing these otherwise helpful idealizations. *Received January 2007; revised November 2007. †To contact the author, please write to: Department of Logic and Philosophy of Science, University of California, 3151 Social Science Plaza A, Irvine, CA 92697-5100; e-mail: rsmead@uci.edu. (shrink)
The replicator dynamics have been used to study the evolution of a population of rational agents playing the Nash bargaining game, where an individual's "fitness" is determined by an individual's success in playing the game. In these models, a population whose initial conditions was randomly chosen from the space of population proportions converges to a state of fair division approximately 62% of the time. (Higher rates of convergence to final states of fair division can be obtained by introducing artificial correlations (...) into the models.) Spatial models of the Nash bargaining game exhibit considerably more robust convergence properties. These properties are considered at length, and a sufficient condition for convergence to fair division is proved. (shrink)
Bell's Theorem is proved for locality and conservation formulated in terms of subjunctive conditionals with chance consequents, rather than the usual conditional probability formulation. This brings into sharp focus the minimal counterfactual assumptions needed for Bell's theorem.
The question of coherence of rules for changing degrees of belief in the light of new evidence is studied, with special attention being given to cases in which evidence is uncertain. Belief change by the rule of conditionalization on an appropriate proposition and belief change by "probability kinematics" on an appropriate partition are shown to have like status.
even if an equilibrium is asymptotically stable, that is no guarantee that the system will reach that equilibrium unless we know that the system's initial state is sufficiently close to the equilibrium. Global stability of an equilibrium, when we have it, gives the equilibrium a much more powerful explanatory role. An equilibrium is globally asymptotically stable if the dynamics carries every possible initial state in the interior of the state space to that equilibrium. If an equilibrium is globally stable, it (...) can have.. (shrink)
Since monkeys certainly understand much that is said to them by man, and when wild, utter signal-cries of danger to their fellows; and since fowls give distinct warnings for danger on the ground, or in the sky from hawks (both, as well, a third cry, intelligible to dogs), may not some unusually wise ape-like animal have imitated the growl of a beast of prey, and thus told his fellow-monkeys the nature of the expected danger? This would have been the first (...) step in the formation of a language. (shrink)
This volume is the product of the Proceedings of the 9th International Congress of Logic, Methodology and Philosophy of Science and contains the text of most of ...
In recent years, many scholars have suggested that the Baldwin effect may play an important role in the evolution of language. However, the Baldwin effect is a multifaceted and controversial process and the assessment of its connection with language is difficult without a formal model. This paper provides a first step in this direction. We examine a game-theoretic model of the interaction between plasticity (represented by Herrnstein reinforcement learning) and evolution in the context of a simple language game. (...) Additionally, we describe three distinct aspects of the Baldwin effect: the Simpson–Baldwin effect, the Baldwin expediting effect and the Baldwin optimizing effect. We find that a simple model of the evolution of language lends theoretical plausibility to the existence of the Simpson–Baldwin and the Baldwin optimizing effects in this arena, but not the Baldwin expediting effect. (shrink)
Maher (1992b) advances an objection to dynamic Dutch-book arguments, partly inspired by the discussion in Levi (1987; in particular by Levi's case 2, p. 204). Informally, the objection is that the decision maker will "see the dutch book coming" and consequently refuse to bet, thus escaping the Dutch book. Maher makes this explicit by modeling the decision maker's choices as a sequential decision problem. On this basis he claims that there is a mistake in dynamic coherence arguments. There is really (...) no formal mistake in classical dynamic coherence arguments, but the discussions in Maher and Levi do suggest interesting ways in which the definition of dynamic coherence might be strengthened. Such a strengthened "sequentialized" notion of dynamic coherence is explored here. It so happens that even on the strengthened standards for a Dutch book, the classic dynamic coherence argument for conditioning still goes through. (shrink)
Recent research into the evolution of higher cognition has piqued an interest in the effect of natural selection on the ability of creatures to respond to their environment (behavioral plasticity). It is believed that environmental variation is required for plasticity to evolve in cases where the ability to be plastic is costly. We investigate one form of environmental variation: frequency dependent selection. Using tools in game theory, we investigate a few models of plasticity and outline the cases where selection would (...) be expected to maintain it. Ultimately we conclude that frequency dependent selection is likely insuffcient to maintain plasticity given reasonable assumptions about its costs. This result is very similar to one aspect of the well-discussed Baldwin effect, where plasticity is first selected for and then later selected against. We show how in these models one would expect plasticity to grow in the population and then be later reduced. Ultimately we conclude that if one is to account for the evolution of behavioral plasticity in this way, one must appeal to a very particular sort of external environmental variation. (shrink)
Reinforcement schemes are a class of non-Markovian stochastic processes. Their non-Markovian nature allows them to model some kind of memory of the past. One subclass of such models are those in which the past is exponentially discounted or forgotten. Often, models in this subclass have the property of becoming trapped with probability 1 in some degenerate state. While previous work has concentrated on such limit results, we concentrate here on a contrary effect, namely that the time to become trapped may (...) increase exponentially in 1/x as the discount rate, 1− x, approaches 1. As a result, the time to become trapped may easily exceed the lifetime of the simulation or of the physical data being modeled. In such a case, the quasi-stationary behavior is more germane. We apply our results to a model of social network formation based on ternary (three-person) interactions with uniform positive reinforcement. (shrink)
Learning to take turns in repeated game situations is a robust phenomenon in both laboratory experiments and in everyday life. Nevertheless, it has received little attention in recent studies of learning dynamics in games. We investigate the simplest and most obvious extension of fictitious play to a learning rule that can recognize patterns, and show how players using this rule can spontaneously learn to take turns.
This paper discusses the explanatory significance of the equilibrium concept in the context of an example of extremely complicated dynamical behavior. In particular, numerical evidence is presented for the existence of chaotic dynamics on a "strange attractor" in the evolutionary game dynamics introduced by Taylor and Jonker [also known as the "replicator dynamics"]. This phenomenon is present already in four strategy evolutionary games where the dynamics takes place in a simplex in three dimensional space-the lowest number of dimensions in (...) which such a strange attractor is possible. From a dynamical point of view, it is the attractor-rather than the equilibrium-that is of prime interest. (shrink)
We investigate a simple stochastic model of social network formation by the process of reinforcement learning with discounting of the past. In the limit, for any value of the discounting parameter, small, stable cliques are formed. However, the time it takes to reach the limiting state in which cliques have formed is very sensitive to the discounting parameter. Depending on this value, the limiting result may or may not be a good predictor for realistic observation times.
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. (shrink)
We compare replicator dynamics for some simple games with and without the addition of conformist bias. The addition of conformist bias can create equilibria, it can change the stability properties of existing equilibria, it may leave the equilibrium structure intact but change the relative size of basins of attraction, or it may do nothing at all. Examples of each of the foregoing are given.
