Electoral competition with local externalities

We study a simple model of public opinion formation that posits that interaction between neighbouring agents leads to bandwagons in the dynamics of individual opinion choices, as well as in that of the aggregate process. We then analyze the implication that these findings have in terms of space-time allocation of fundings in an electoral campaign, where two candidates run in a winner-take-all election

Reinforcement learning and the power law of practice: some analytical results

Erev and Roth (1998) among others provide a comprehensive analysis of experimental evidence on learning in games, based on a stochastic model of learning that accounts for two main elements: the Law of Effect (positive reinforcement of actions that perform well) and the Power Law of Practice (learning curves tend to be steeper initially). This note complements this literature by providing an analytical study of the properties of such learning models. Specifically, the paper shows that: (a) up to an error term, the stochastic process is driven by a system of discrete time difference equations of the replicator type. This carries an analogy with Börgers and Sarin (1997), where reinforcement learning accounts only for the Law of Effect. (b) if the trajectories of the system of replicator equations converge sufficiently fast, then the probability that all realizations of the learning process over a possibly infinite spell of time lie within a given small distance of the solution path of the replicator dynamics becomes, from some time on, arbitrarily close to one. Fast convergence, in the form of exponential convergence, is shown to hold for any strict Nash equilibrium of the underlying game.

Learning Strict Nash Equilibria through Reinforcement

This paper studies the analytical properties of the reinforcement learning model proposed in Erev and Roth (1998), also termed cumulative reinforcement learning in Laslier et al (2001). This stochastic model of learning in games accounts for two main elements: the law of effect (positive reinforcement of actions that perform well) and the law of practice (the magnitude of the reinforcement effect decreases with players' experience). The main results of the paper show that, if the solution trajectories of the underlying replicator equation converge exponentially fast, then, with probability arbitrarily close to one, all the realizations of the reinforcement learning process will, from some time on, lie within an " band of that solution. The paper improves upon results currently available in the literature by showing that a reinforcement learning process that has been running for some time and is found suffciently close to a strict Nash equilibrium, will reach it with probability one.Strict Nash Equilibrium, Reinforcement Learning

The dynamics of public opinion under majority rules

This note explains the process of public opinion formation via a locally interactive, space-time analysis. The model we use is a special case of the general framework for modelling social interaction proposed in Blume and Durlauf (2001). In the reduced form of the model we study how each individual, when faced with the choice of one, out of two, opinions, tends to conform to the opinion held by the majority of her neighbours. We consider different, symmetric and asymmetric, majority rules. Depending on the specific behavioral rule, the aggregate process of opinion formation may display contagion on one specific opinion, or consensus among all individuals in the population, or co-existence of both opinions. Whenever consensus obtains, we observe the formation of homogeneous areas (clusters) that seem almost stationary along the dynamics

Consensus, contagion and clustering in a space-time model of public opinion formation

We study a simple model of public opinion formation that posits that interaction between neighbouring agents leads to bandwagons in the dynamics of individual opinions, as well as in that of the aggregate process. We show that in different specifications of the model, there is a tendency for the process to show consensus on one of the two competing opinions. We show how a publicly available poll of current public opinion may lead to a form of contagion, by which public opinion tends to agree with the poll. We point out that, in the absence of a poll, the process displays the feature that, after long time spans, a sequence of states occur which, when viewed locally, remain almost stationary and are characterized by large clusters of individuals of the same opinion. The running metaphor we use is that of a model of pre-electoral public opinion formation, with two candidates running. We provide some heuristic considerations on the implication that these findings could have in terms of space-time allocation of fundings in an electoral campaign.