It takes two to tango: Equilibria in a model of sales

Abstract

We show that the Varian model of sales with more than two firms has two types of equilibria: a unique symmetric equilibrium, and a continuum of asymmetric equilibria. ln contrast, the 2-firm game has a unique equilibrium that is symmetric. For the n-firm case the asymmetric equilibria imply mixed strategies that can be ranked by first-order stochastic dominance. This enables one to rule out asymmetric equilibria on economic grounds by constructing a metagame in which both firms and consumers are players. The unique subgame perfect equilibrium of this metagame is symmetric. Journal ojEconomic Literature Classification Number:22. O

Mobile tax base as a global common

“…There are notable exceptions, but the general validity of the claim becomes evident if one recalls the Wildasin (1988) or the Zodrow-Mieskowski (1986) frameworks of tax competition that have become the workhorses for analysing tax competition. 2 In this respect, much of this analysis is structurally similar to what would be considered as Bertrand or price competition in the context of the competition between …rms. Other types of 'price'competition for capital have also been explored: standard auctions ( Countries can use other means of competition by which they can try and acquire a larger share of the tax base, and some of these competition modes make the tax base a common pool resource.…”

“…Bhagwati and Dellalfar (1973), Bhagwati (1976) and Raymond (1973) were among the …rst to discuss the downsides of this competition. 2 Any list of seminal contributions to this capital tax competition literature will notoriously be unfair to some authors, but should include Zodrow and Mieszkowski (1986), Wilson (1986), Wildasin (1988), Gordon (1986Gordon ( , 1992 and Sinn (1990). I gladly leave a possible blame of omissions to the excellent surveys by Wilson (1999), Wildasin and Wilson (2004), Fuest, Huber and Mintz (2005) and Sørensen (2007).…”

Consumer Stockpiling and Competitive Promotional Strategies

“…If none of the rival firms charges a price lower than t-an event that occurs with probability 1 − F 0 t n−1 -strategic consumers do not have the opportunity to stockpile and transition to s = 0, where the firms' continuation payoff is V 0 . With complementary probability, 1 − 1 − F 0 t n−1 , at least one of the firms charges a price lower than t allowing consumers to stockpile 7 Symmetric equilibrium is also the unique subgame perfect equilibrium among all possible symmetric and asymmetric equilibria (Baye et al 1992). and transition to s = 1 with firms' continuation payoff of V 1 .…”

“…We solve for symmetric equilibrium, which is also unique subgame perfect (Baye et al 1992). We use the same logic as Narasimhan (1988) to rule out mass points in the interior of the support.…”

Contests with rank-order spillovers

“…For instance, in a variant of the classic Bertrand model due to Varian (1980), two sellers simultaneously set a price and sell to three inelastic segments of demand with common choke price, r. One of these inelastic segments consists of price-sensitive consumers who are aware of both prices in the market and who purchase from the lower-price seller, while the other two segments are attached to different firms and are each aware of only the price of that firm to which they are attached (as long as that price is at or below the choke price). Baye et al (1992) have shown that this game has a structure similar to that of a first-price all-pay auction in which the bid is the difference between the choke price and a firm's price. In this context, the bid corresponds to the opportunity cost of the lost revenue from the seller's own uninformed segment that results from reducing price in order to attempt to capture the "prize" consisting of the demand of the informed price-sensitive consumer segment.…”