Multiarm bandit problems have been used to model the selection of competing scientific theories by boundedly rational agents. In this paper, 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.
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. (shrink)
The Pasadena game is an example of a decision problem which lacks an expected value, as traditionally conceived. Easwaran (2008) has shown that, if we distinguish between two different kinds of expectations, which he calls ‘strong’ and ‘weak’, the Pasadena game lacks a strong expectation but has a weak expectation. Furthermore, he argues that we should use the weak expectation as providing a measure of the value of an individual play of the Pasadena game. By considering a modified version of (...) the Pasadena game, I argue that weak expectations may provide a very poor measure of the value of an individual play of the game, and hence should not be used to value individual plays unless further information is taken into consideration. (shrink)
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. (shrink)
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. (shrink)
It is certainly the case that morality governs the interactions that take place between individuals. But what if morality exists because of these interactions? This book argues for the claim that much of the behaviour we view as 'moral' exists because acting in that way benefits each of us to the greatest extent possible, given the socially structured nature of society. Drawing upon aspects of evolutionary game theory, the theory of bounded rationality, and computational models of social networks, it shows (...) both how moral behaviour can emerge in socially structured environments, and how it can persist even when it is not typically viewed as 'rational' from a traditional economic perspective. Since morality consists of much more than mere behaviour, this book also provides a theory of how moral principles and the moral sentiments play an indispensable role in effective choice, acting as 'fast and frugal heuristics' in social decision contexts. (shrink)
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. These explanatory approaches often rely on the fact that, in certain evolutionary models, the basin of attraction of "fair" or "just" strategies occupies a certain percentage of the state space. I sketch a proof of a general representation theorem for a large class of evolutionary game theoretic models played on a social network, in (...) the hope that this will contribute to a greater understanding of the basins of attraction of such models -- and hence the evolution of social norms. More precisely, I show how many kinds of social networks can be translated into random boolean networks. The interesting and useful part of this result is that, for many social networks, one can find a bijection $f$ between the state space of the social network and the state space of the random boolean network, such that the state $S`$ follows the state $S$ under the dynamical laws of the social network if and only if $f(S`)$ follows the state $f(S)$ under the dynamics of the random boolean network. In some cases, it is not possible to find such a bijection; in these cases, one can find an injection $f$ with the property that if $S`$ follows $S$ under the dynamics of the social network, then $f(S`)$ follows $f(S)$ under the dynamics of the random boolean network. I then use this method to catalog all the basins of attraction for some simple two-strategy games (the prisoner`s dilemma and the stag hunt) played on a ring, drawing on the work of Wuensche and Lesser (1992). (shrink)
Rachlin's idea that altruism, like self-control, is a valuable, temporally extended pattern of behavior, suggests one way of addressing common problems in developing a rational choice explanation of individual altruistic behavior. However, the form of Rachlin's explicitly behaviorist account of altruistic acts suffers from two faults, one of which questions the feasibility of his particular behaviorist analysis.
One common interpretation of the Hobbesian state of nature views itas a social dilemma, a natural extension of the well-knownprisoner''s 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 Hobbes''s 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 Hobbes''ssolution of commonwealth by institution – the favored solution forHobbesian social contract theories – will not work in the state ofnature viewed this way. (shrink)
Evolutionary game theoretic accounts of justice attempt to explain our willingness to follow certain principles of justice by appealing to robustness properties possessed by those principles. Skyrms (1996) offers one sketch of how such an account might go for divide-the-dollar, the simplest version of the Nash bargaining game, using the replicator dynamics of Taylor and Jonker (1978). In a recent article, D'Arms et al. (1998) criticize his account and describe a model which, they allege, undermines his theory. I sketch a (...) theory of evolutionary explanations of justice which avoids their methodological criticisms, and develop a spatial model of divide-the-dollar with more robust convergence properties than the models of Skyrms (1996) and D'Arms et al. (1998). (shrink)