Elsevier

Economics Letters

Volume 114, Issue 2, February 2012, Pages 208-211
Economics Letters

A simple model of herd behavior, a comment

https://doi.org/10.1016/j.econlet.2011.09.024Get rights and content

Abstract

In this paper we analyze the role played by the tie-breaking assumptions in Banerjee’s model of herd behavior. Changing one assumption we obtain three important results: players’ strategies are parameter dependent; an incorrect herd could be reversed; a correct herd is irreversible.

Highlights

► We analyze the role played by the tie-breaking assumptions in reaching the equilibrium in Banerjee’s model of herd behavior. ► We replaced one of the tie-breaking rules. ► Result1: players’ strategies are parameter dependent. ► Result 2: an incorrect herd can be reversed. ► Result3: a correct herd is irreversible.

Introduction

Banerjee in his analysis tries to demonstrate the hypothesis of ‘herd behavior’: everyone is doing what everyone else is doing, even when his or her private information suggests acting differently. The model is a sequential decision-making game with one wining action and three possible information states of the subjects: correct, wrong or no information. Banerjee shows that as soon as the first two players choose the same action, all subsequent players will follow them, independently from their private information. Such an irreversible queue (“lock-in”)–caused by the individual rational behavior to gain a better information position by looking at what other subjects are doing–may result in a non-optimal equilibrium since the imitated action may be a non-wining one. In other words, considering the society as a whole, it might be more efficient if the individuals could not observe the actions of other individuals, i.e. have less information when taking their decisions.

Banerjee’s model has two important features: it has both a very simple and intuitive structure and it gives very strong results. Besides the rationality assumption, we suppose that the decision-making process of each player is based on a set of three tie-breaking rules, indicating what he/she has to do on each occasion (e.g. when he/she is indifferent between two or more actions). In other words, “each of these assumptions is made to minimize the possibility of herding” (Banerjee, 1992, 803). It can easily be seen that the rules chosen by Banerjee are not the only plausible ones. In what follows, we will therefore examine if there is any critical relation between the tie-breaking rules and the overall dynamics of the model. In particular, we will show that by choosing an alternative decision rule in case the first player has no signal, the possibility of an irreversible queue starting from the first player is generally smaller, and consequently also the probability of an inefficient lock-in. This will result in a welfare gain.

The main goal of this paper is to present some possible extensions to Banerjee’s model, which will show the robustness of the original results, as well as the presence of analytical complexities in the extended models.

Section snippets

“A simple model of herd behavior” under different assumption sets

Let A=[0,1]R be the set of all possible investments, where only aA pays a positive pay-off. Let S=[0,1]R be the set of all possible signals, where only sS signals to invest in a. The aim of the game is to invest in a. The pay-off is one when action a is chosen and zero otherwise. There is a population of N players who take their decision sequentially and in a fixed order. Each player knows the choices made by those before him/her but is not aware of the information which these choices

Welfare analysis

In order to compare the two assumption sets it would be interesting to compute the ex ante average welfare of the population of decision-makers (assuming that the order of moves is randomly chosen). Since the game, under the new assumptions, is parameter dependent for each subject, it is possible to disentangle between two cases: (i) the two models lead to the same strategy; (ii) the two models lead to a different strategy.

First of all using Eq. (10) if n=3 we can plot the couple of α and β

Conclusion

In this work we extended Banerjee’s model of herd behavior replacing one of its fundamental and ‘innocuous’ assumptions. More precisely, we replaced Assumption A (whenever a decision-maker has no signal and everyone else has chosen zero, he/she will always choose zero), with Assumption A1 (whenever a decision-maker has no signal and everyone else has chosen zero, he/she will always choose randomly among all possible actions).

The consequence of this slight change in the assumptions’ set leads to

References (1)

  • A. Banerjee

    A simple model of herd behaviour

    Quarterly Journal of Economics

    (1992)

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