Price competition, price dispersion, unique equilibrium
We study a canonical model of simultaneous price competition between firms that sell a homogeneous good to consumers who are characterized by the number of prices they are exogenously aware of. Our setting subsumes many employed in the literature over the last several decades. We show there is a unique equilibrium if and only if there exist some consumers who are aware of exactly two prices. The equilibrium we derive is in symmetric mixed strategies. Furthermore, when there are no consumers aware of exactly two prices, we show there is an uncountable-infinity of asymmetric equilibria in addition to the symmetric equilibrium. Our results show the paradigm generically produces a unique equilibrium. We also show that the commonly-sought symmetric equilibrium (which also nests the textbookBertrand pure strategy equilibrium as a special case) is robust to perturbations in consumer behaviour, while the asymmetric equilibria are not.
© 2020 The Editorial Board of The Journal of Industrial Economics and John Wiley & Sons Ltd
Hotellin-Downs, political competition, equilibrium existence, idealism
In the classic Hotelling–Downs model of political competition, no pure strategy equilibrium with three or more strategic candidates exists when the distribution of voters’ preferred policies is unimodal. I study the effect of introducing two idealist candidates to the model who are non-strategic (i.e., fixed to their policy platforms), while allowing for an unlimited number of strategic candidates. Doing so, I show that equilibrium is restored for a non-degenerate set of unimodal distributions. In addition, the equilibria have the following features: (1) the left-most and right-most candidates (i.e., extremists) are idealists; (2) strategic candidates never share their policy platforms, which instead are spread out across the policy space; and (3) if more than one strategic candidate enters, the distribution of voter preferences must be asymmetric. I also show that equilibria can accommodate idealist fringes of candidates toward the extremes of the political spectrum.
Consumer choice, context effects, sampling
Consumers’ choices are typically influenced by the choice context in ways that standard models cannot explain. We provide a concise explanation of the attraction, compromise and similarity effects. The model, Multi-Attribute Decision by Sampling (MADS), posits that the evaluation of a choice option is based on its relative position in the market distribution as first inferred and then sampled by the decision-maker. The inferred market distribution is assumed to be systematically influenced by the choice options. The value of a choice option is assumed to be determined by the number of sampled comparators that the option dominates. We specify conditions on the sampling distribution that are sufficient for MADS to predict the three context effects. We tested the model using a novel experimental design with 1200 online participants. In the first experiment, prior to making a choice participants were shown a selection of market options designed to change their beliefs about the market distribution. Participants’ subsequent choices were affected as predicted. The effect was strong enough to impact the size of two of the three classic context effects significantly. In the second experiment, we elicited individuals’ estimates of distributions of market options and found the estimates to be systematically influenced by the choice set as predicted by the model. It is concluded that MADS, a model based on simple binary ordinal comparisons, is sufficient to account for the three classic context effects.
With permission of Elsevier