J. McKenzie Alexander

Random Boolean Networks and Evolutionary Game Theory

Recent years have seen increased interest in the question of whether it is possible to provide an evolutionary game‐theoretic explanation for certain kinds of social norms. I sketch a proof of a general representation theorem for a large class of evolutionary game‐theoretic models played on a social network, in hope that this will contribute to a greater understanding of the long‐term evolutionary dynamics of such models, and hence the evolution of social norms.

Follow the leader : local interactions with influence neighborhoods

We introduce a dynamic model for evolutionary games played on a network where strategy changes are correlated according to degree of influence between players. Unlike the notion of stochastic stability (Foster and Young, 1990), which assumes mutations are stochastically independent and identically distributed, our framework allows for the possibility that agents correlate their strategies with the strategies of those they trust, or those who have influence over them. We show that the dynamical properties of evolutionary games, where such influence neighborhoods appear, differ dramatically from those where all mutations are stochastically independent, and establish some elementary convergence results relevant for the evolution of social institutions.

Learning to Signal in a Dynamic World

Sender–receiver games, first introduced by David Lewis ([1969]), have received increased attention in recent years as a formal model for the emergence of communication. Skyrms ([2010]) showed that simple models of reinforcement learning often succeed in forming efficient, albeit not necessarily minimal, signalling systems for a large family of games. Later, Alexander et al. ([2012]) showed that reinforcement learning, combined with forgetting, frequently produced both efficient and minimal signalling systems. In this article, I define a ‘dynamic’ sender–receiver game in which the state–action pairs are not held constant over time and show that neither of these two models of learning learn to signal in this environment. However, a model of reinforcement learning with discounting of the past does learn to signal; it also gives rise to the phenomenon of linguistic drift. 1 Introduction 2 Dynamic Signalling Games with Reinforcement Learning   2.1 Introducing new states   2.2 Swapping state–action pairs 3 Discounting the Past   3.1 Learning to signal in a dynamic world   3.2 An unexpected outcome: linguistic drift 4 Conclusion Appendix: A Markov Chain Analysis  1 Introduction 2 Dynamic Signalling Games with Reinforcement Learning   2.1 Introducing new states   2.2 Swapping state–action pairs   2.1 Introducing new states   2.2 Swapping state–action pairs 3 Discounting the Past   3.1 Learning to signal in a dynamic world   3.2 An unexpected outcome: linguistic drift   3.1 Learning to signal in a dynamic world   3.2 An unexpected outcome: linguistic drift 4 Conclusion Appendix: A Markov Chain Analysis 

Preferential Attachment and the Search for Successful Theories

Multiarm bandit problems have been used to model the selection of competing scientific theories by boundedly rational agents. In this article, I define a variable-arm bandit problem, which allows the set of scientific theories to vary over time. I show that Roth-Erev reinforcement learning, which solves multiarm bandit problems in the limit, cannot solve this problem in a reasonable time. However, social learning via preferential attachment combined with individual reinforcement learning, which discounts the past, does.

Group Dynamics In The State Of Nature

One common interpretation of the Hobbesian state of nature views itas a social dilemma, a natural extension of the well-knownprisoners dilemma to a group context. Kavka (1986)challenges this interpretation, suggesting that the appropriate wayto view the state of nature is as a quasi social dilemma. Iargue that Hobbess remarks on the rationality of keeping covenantsin the state of nature indicate that the quasi social dilemma doesnot accurately represent the state of nature. One possiblesolution, I suggest, views the state of nature as a social dilemmabetween groups rather than individuals. Although thiscleanly represents the strategic problem faced in the state ofnature, it also means we should take intergroup dynamics intoaccount when putting forth a solution. I argue that Hobbesssolution of commonwealth by institution – the favored solution forHobbesian social contract theories – will not work in the state ofnature viewed this way.One common interpretation of the Hobbesian state of nature views itas a social dilemma, a natural extension of the well-knownprisoners dilemma to a group context. Kavka (1986)challenges this interpretation, suggesting that the appropriate wayto view the state of nature is as a quasi social dilemma. Iargue that Hobbess remarks on the rationality of keeping covenantsin the state of nature indicate that the quasi social dilemma doesnot accurately represent the state of nature. One possiblesolution, I suggest, views the state of nature as a social dilemmabetween groups rather than individuals. Although thiscleanly represents the strategic problem faced in the state ofnature, it also means we should take intergroup dynamics intoaccount when putting forth a solution. I argue that Hobbesssolution of commonwealth by institution – the favored solution forHobbesian social contract theories – will not work in the state ofnature viewed this way.

Local interactions and the dynamics of rational deliberation

Whereas The Stag Hunt and the Evolution of Social Structure supplements Evolution of the Social Contract by examining some of the earlier work’s strategic problems in a local interaction setting, no equivalent supplement exists for The Dynamics of Rational Deliberation. In this article, I develop a general framework for modeling the dynamics of rational deliberation in a local interaction setting. In doing so, I show that when local interactions are permitted, three interesting phenomena occur: (a) the attracting deliberative equilibria may fail to agree with any of the Nash equilibria of the underlying game, (b) deliberative dynamics which converged to the same deliberative outcome in The Dynamics of Rational Deliberation may lead to different deliberative outcomes here, and (c) Bayesian deliberation seems to be more likely to avoid nonstandard deliberative outcomes, contrary to the result reported in The Dynamics of Rational Deliberation, which argued in favour of the Brown–von Neumann–Nash dynamics.

Why the Angels Cannot Choose

Decision theory faces a number of problematic gambles which challenge it to say what value an ideal rational agent should assign to the gamble, and why. Yet little attention has been devoted to the question of what an ideal rational agent is, and in what sense decision theory may be said to apply to one. I show that, given one arguably natural set of constraints on the preferences of an idealized rational agent, such an agent is forced to be indifferent among entire families of goods, and hence cannot choose among them. This result illustrates the dangers of speaking of the choices of an ‘ideal rational agent’ when one does not make precise the exact nature of the idealizing assumptions. The result may also be viewed as providing an upper bound on the kinds of idealizing assumptions which can be made for rational agents, beyond which the very concept of choice becomes attenuated.

Cheap Talk, Reinforcement Learning, and the Emergence of Cooperation

Cheap talk has often been thought incapable of supporting the emergence of cooperation because costless signals, easily faked, are unlikely to be reliable. I show how, in a social network model of cheap talk with reinforcement learning, cheap talk does enable the emergence of cooperation, provided that individuals also temporally discount the past. This establishes one mechanism that suffices for moving a population of initially uncooperative individuals to a state of mutually beneficial cooperation even in the absence of formal institutions.

Social Deliberation: Nash, Bayes, and the Partial Vindication of Gabriele Tarde

At the very end of the 19th century, Gabriele Tarde wrote that all society was a product of imitation and innovation. This view regarding the development of society has, to a large extent, fallen out of favour, and especially so in those areas where the rational actor model looms large. I argue that this is unfortunate, as models of imitative learning, in some cases, agree better with what people actually do than more sophisticated models of learning. In this paper, I contrast the behaviour of imitative learning with two more sophisticated learning rules (one based on Bayesian updating, the other based on the Nash-Brown-von Neumann dynamics) in the context of social deliberation problems. I show for two social deliberation problems, the Centipede game and a simple Lewis sender-receiver game, that imitative learning provides better agreement with what people actually do, thus partially vindicating Tarde.

PSA 2000 Symposium Paper VolumeIntroduction

This volume contains a selection of the symposium papers presented at the biennial meeting of the Philosophy of Science Association held in Vancouver, Canada, November 2–4, 2000. The complete program for the PSA 2000 conference, abstracts, presented papers, and longer versions of some of the papers presented in this volume can be found at the official PSA web page. Selecting symposium papers for publication was difficult because of the high quality of the symposium papers submitted. Much of the work involved in reviewing these papers was done by the members of the PSA 2000 program committee: