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New Constructions in Cellular Automata$
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David Griffeath and Cristopher Moore

Print publication date: 2003

Print ISBN-13: 9780195137170

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780195137170.001.0001

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Emerging Markets And Persistent Inequality In A Nonlinear Voter Model

Emerging Markets And Persistent Inequality In A Nonlinear Voter Model

(p.261) Emerging Markets And Persistent Inequality In A Nonlinear Voter Model
New Constructions in Cellular Automata

Nienke A. Oomes

Oxford University Press

Since it is one of the few spin systems that can be studied analytically, the Voter Model has been extensively discussed in the interacting particle systems literature. In the original interpretation of this model, voters choose their political positions with probabilities equal to the voting frequency of their friends. One of the main results is that, in one and two dimensions, the system clusters—i.e., converges to a homogeneous steady state—while heterogeneity can persist only in dimensions higher than two. This chapter develops an economic model that is similar to the Voter Model, in that agents decide between economic positions, conditional on the economic choices of their trade partners. The choices considered here are market production and nonmarket production, where the payoffs associated with market production for a given agent are a function of the amount of market goods produced by others. Intuitively, the more people are producing for the market, the more potential trade partners exist, hence the higher the expected payoff associated with market production. Similarly, the smaller the extent of the market, the lower the expected gains from trade, hence the smaller the incentive to produce for the market. When each agent is assumed to have an equal probability of trading with any other agent in his or.her trade network, the payoffs associated with market production are linearly increasing in the network’s total market output. However, this linearity in payoffs does not necessarily imply that the conditional probability of working for the market is linearly increasing in total market production, as the Voter Model would have it. As it turns out, this follows only if agents believe, mistakenly, that their trade partners will decide to work for the market with a probability that is exactly proportional to their current market output. Clearly, a more general approach is obtained by allowing for different types of expectations agents may have about the production decisions of their trade partners. A model that allows for such an approach is the so-called Nonlinear Voter Model (NLVM), studied by Molofsky et al.

Keywords:   Linear Voter Model, Majority Voter Model, Nash equilibria, Voter Model, best response dynamics, coordination games, endowment variables, myopic agents

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