Entry Equilibrium Research Articles

More on Middlemen: Equilibrium Entry and Efficiency in Intermediated Markets

This paper generalizes Rubinstein and Wolinsky's (1987) model of middlemen (intermediation) by incorporating production and search costs, plus more general matching and bargaining. This allows us to study many new issues, including entry, efficiency, and dynamics. In the benchmark model, equilibrium exists uniquely and involves production and intermediation for some parameters but not others. Sometimes intermediation is essential: the market operates if and only if middlemen are active. If bargaining powers are set correctly equilibrium is efficient; if not there can be too much or too little economic activity. This is novel, compared to the original Rubinstein–Wolinsky model, where equilibrium is always efficient.

More on Middlemen: Equilibrium Entry and Efficiency in Intermediated Markets

This paper generalizes Rubinstein and Wolinsky’s model of middlemen (intermediation) by incorporating production and search costs, plus more general matching and bargaining. This allows us to study many new issues, including entry, efficiency and dynamics. In the benchmark model, equilibrium exists uniquely, and involves production and intermediation for some parameters but not others. Sometimes intermediation is essential: the market operates if middlemen are active. If bargaining powers are set correctly equilibrium is efficient; if not there can be too much or too little economic activity. This is novel, compared to the original Rubinstein-Wolinsky model, where equilibrium is always efficient.

Affiliation and Entry in First-Price Auctions with Heterogeneous Bidders: An Analysis of Merger Effects

We study the effects of mergers in timber sale auctions in Oregon. We propose an entry and bidding model within the affiliated private value (APV) framework and with heterogeneous bidders, and establish existence of the entry equilibrium and existence and uniqueness of the bidding equilibrium when the joint distribution of private values belongs to the class of Archimedean copulas. We estimate the resulting structural model, and study merger effects through counterfactual analyses using the structural estimates. We evaluate how merger effects depend on affiliation, entry, and the auction mechanism and find that the seller may benefit from some mergers. (JEL C57, D44, G34, L11, L73)

Reference Pricing with Endogenous Generic Entry

In this paper we study the effect of reference pricing on pharmaceutical prices and expenditures when generic entry is endogenously determined. We develop a Salop-type model where a brand-name producer competes with generic producers in terms of prices. In the market there are two types of consumers: (i) brand biased consumers who choose between brand-name and generic drugs, and (ii) brand neutral consumers who choose between the different generic drugs. We find that, for a given number of firms, reference pricing leads to lower prices of all products and higher brand-name market shares compared with a reimbursement scheme based on simple coinsurance. Thus, in a free entry equilibrium, the number of generics is lower under reference pricing than under coinsurance, implying that the net effects of reference pricing on prices and expenditures are ambiguous. Allowing for price cap regulation, we show that the negative effect on generic entry can be reversed, and that reference pricing is more likely to result in cost savings than under free pricing. Our results shed light on the mixed empirical evidence on the effects of reference pricing on generic entry.

Existence of free entry equilibrium in aggregative games with asymmetric agents

In this paper, we examine a free entry aggregative game where agents can be asymmetric. We show the existence of a pure strategy subgame perfect equilibrium of this game. The proof is a constructive one and therefore we provide a method to derive a subgame perfect equilibrium within a reasonable time.

Free entry versus socially optimal entry

This paper reconsiders the well-known comparison of equilibrium entry levels into a Cournot industry under free entry, second best (control of entry but not production) and first best (control of entry and production). Allowing for the possibility of limited increasing returns to scale in production, this paper generalizes the conclusion of Mankiw and Whinston (1986) [10], that under business-stealing competition, free entry yields more firms than the second-best solution. We also show that under-entry always holds under business-enhancing competition. This confirms the general intuition given by Mankiw and Whinston, which does not rely on the convexity of the cost function. The same result is shown to extend (at a similar level of generality) to the comparison between free entry and the first best socially optimal solution, irrespective of business-stealing. Three illustrative examples are provided, one showing that the second-best and free entry solutions may actually coincide.

Too Much of a Good Thing? Welfare Consequences of Market Transparency

This paper studies welfare consequences of consumer-side market transparency with endogenous entry of firms. Different from most studies, we consider the unique symmetric entry equilibrium, which is in mixed strategies. We identify two effects of market transparency on welfare: a competition effect and a novel market-structure effect. We show, surprisingly, that for almost all demand functions the negative market-structure effect eventually dominates the positive competition effect as the market becomes increasingly transparent. Consumer-side market transparency can therefore be socially excessive even without collusion. The only exception among commonly used demand functions is the set of constant demand functions.

Free Entry and Social Efficiency Under Unknown Demand Parameters

In the paper, I examine free entry in homogeneous product markets and its social efficiency. Previous research on free entry in homogeneous product markets has shown that under Cournot oligopoly with fixed setup costs the free entry equilibrium always delivers excessive entry. In contrast, I demonstrate in this paper that free entry along with excessive entry might also lead to a socially insufficient number of firms when a demand parameter uncertainty is considered. My findings support the validity of the traditional wisdom in industrial organization that free entry is desirable for social efficiency and call for revision of restrictive entry regulation practices which been based on previous research findings.

Inference of Bidderss Risk Attitudes in Ascending Auctions with Endogenous Entry

Bidders’ risk attitudes have key implications for choices of revenue-maximizing auction formats. In ascending auctions, bid distributions do not provide information about risk preference. We infer risk attitudes using distributions of transaction prices and participation decisions in ascending auctions with entry costs. Nonparametric tests are proposed for two distinct scenarios: first, the expected entry cost can be consistently estimated from data; second, the data does not report entry costs but contains exogenous variations of potential competition and auction characteristics. In the first scenario, we exploit the fact that the risk premium required for entry - the difference between ex ante expected profits from entry and the certainty equivalent .is strictly positive if and only if bidders are risk averse. Our test is based on identification of bidders’ ex ante profits. In the second scenario, our test builds on the fact that risk attitudes affect how equilibrium entry probabilities vary with observed auction characteristics and potential competition. We also show identification of risk attitudes in a more general model of ascending auctions with selective entry, where bidders receive entry-stage signals that are correlated with private values.

A spatial economic model under network externalities: symmetric equilibrium and efficiency

This paper studies a spatial economic model under network externalities, assuming a quadratic transport cost function. A classical circular model is applied where the consumers, each with a fixed demand, are uniformly distributed along the circumference of a circle. Assuming symmetric locations of profit-maximizing suppliers, a unique symmetric price equilibrium is derived under both positive and negative network externalities. The price equilibrium is obtained using the tridiagonality property of the demand system. The equilibrium price is higher with negative network externalities than the price without externalities whereas the converse is true with positive network externalities. The efficiency loss of the free entry equilibrium is studied in terms of the price of anarchy. Numerical experiments suggest that the price of anarchy is robust to weak externalities but can be significant under strong network externalities.

Identification in a Duopoly: A Real Options Approach

Two asymmetric potential entrants contemplate entering a new market. Firms differ in their potential profit flows and investment sunk costs. The market demand follows a geometric Brownian motion. This paper shows that under certain parameter conditions, there will be an equilibrium triggered by preemption, and both the lower-revenue firm and the higher-revenue firm could preempt. Moreover, the equilibrium entry sequence may no longer be only triggered by preemption. The paper identifies the joint distribution of the investment sunk costs, and finds the probability of the first entry being triggered by preemption. Given the observation of the first entrant, the identification of the joint distribution of the investment sunk costs allows for prediction of the probability of observing the second entrant.

Endogenous domestic market structure and the effects of a trade cost reduction in a unionised industry

In contrast to the existing partial equilibrium literature considering the effects of a trade cost reduction on unionised wage under a given market structure, we show the effects by determining the domestic market structure endogenously. A lower trade cost reduces the number of active domestic firms, but it increases unionised wage in the active domestic firms under decentralised unions. Although a lower trade cost increases wage in the active domestic firms, it reduces domestic employment and total union utility at the free entry equilibrium. So, a trade cost reduction benefits domestic employed workers by increasing the unionised wage, but its effect on the total domestic workers is not favourable. If there is a centralised union, a lower trade cost reduces the number of active domestic firms, unionised wage, domestic employment and union utility.

Auctions with entry and resale

We study how resale affects auctions with costly entry in a model where bidders possess two-dimensional private information signals: entry costs and valuations. We establish the existence of symmetric entry equilibrium and identify sufficient conditions under which the equilibrium is unique. Our analysis suggests that the opportunity of resale affects both entry and bidding, and, in particular, it induces motivation for speculative entry and resale hunting abstentions. Our numerical results suggest that while expected entry is higher when resale is allowed, the effects of resale on expected revenue and efficiency are both ambiguous.

Inefficient Entry Order in Preemption Games

In a preemption game, players decide when to take an irreversible action. Delaying the action exogenously increases payoffs, but there is an early mover advantage. Riordan (1992) shows that in a preemption game with two asymmetric players, players act in decreasing order of efficiency. This provides a microfoundation to the assumption that entry in a market occurs in the order of profitability, commonly used in the empirical analysis of market entry. We provide a counterexample showing that with more than two players this intuitive result can be reversed. We present a preemption game of entry into a new market. The potential entrants are three asymmetric firms: one efficient firm with high post-entry profits, and two inefficient firms. We show that the set of parameters such that the equilibrium entry order does not reflect the efficiency ranking is nonempty, and analyze which changes in post-entry profits preserve this entry order.

Inefficient entry order in preemption games

In a preemption game, players decide when to take an irreversible action. Delaying the action exogenously increases payoffs, but there is an early mover advantage. Riordan (1992) shows that in a preemption game with two asymmetric players, players act in decreasing order of efficiency. This provides a microfoundation to the assumption that entry in a market occurs in the order of profitability, commonly used in the empirical analysis of market entry. We provide a counterexample showing that with more than two players this intuitive result can be reversed. We present a preemption game of entry into a new market. The potential entrants are three asymmetric firms: one “efficient” firm with high post-entry profits, and two “inefficient firms”. We show that the set of parameters such that the equilibrium entry order does not reflect the efficiency ranking is nonempty, and analyse which changes in post-entry profits preserve this entry order.

Central Place Theory and City Size Distribution

This paper proposes a theory of city size distribution via a hierarchy approach rather than the popular random growth process. It does so by formalizing central place theory using an equilibrium entry model and specifying the conditions under which city size distribution follows a power law. Central place theory describes the way in which a hierarchical city system with difierent layers of cities serving difierently sized market areas is formed from a uniformly populated space. The force driving the city size difierences in this model is the heterogeneity in economies of scale across goods. The city size distribution under a central place hierarchy exhibits a power law if the distribution of scale economies is regularly varying, which is a general class that encompasses many well-known, commonly used distributions. This model is also consistent with a power law for flrms and a number-average-size rule, which is the log-linear relationship between the number and average size of the cities in which an industry is located.

Exclusive Dealing and Market Foreclosure: Further Experimental Results

Naked exclusion is one of the most influential post-Chicago theories of exclusive dealing. It relies on scale effects requiring an entrant to cover at least a certain percentage of the market in order to break even. Under this assumption, Segal and Whinston (2000) show that an incumbent can gain by offering exclusive-dealing contracts even if discriminatory offers are banned: If the incumbent offers the buyers some share of his profit from monopolizing the market, but threatens to charge monopoly prices from a rejecting buyer, the buyers’ simultaneous decision of whether to accept the exclusive-dealing contract is equivalent to a coordination game. Hence, there is a Nash equilibrium in which all buyers accept the exclusivedealing contract, although all buyers would be better off if all of them rejected the contract. The literature on naked exclusion has so far almost exclusively dealt with the strategic interaction between buyers. More specifically, the chief concern in the case with only nondiscriminatory offers available was whether buyers will be able to coordinate on the entry equilibrium. Landeo and Spier (2009, henceforth LS09) make an important contribution to this literature by experimentally testing buyers’ equilibrium selection behaviour. They analyze a reduced version of the game that focuses on the buyers’ coordination game, in some treatments allowing for endogenous offers made by a third player, the incumbent seller. Intuitively, buyers seek to avoid being the only one who rejects the offer, and recognize that their decisions will also influence the incumbent seller’s payoff. Hence, the buyers’ decisions may be influenced by focal points and social preferences.

Optimal Pricing and Entry Rules When a Regulated Dominant Firm Faces a Competitive Fringe

In this paper, we study optimal regulation of a dominant firm facing an unregulated competitive fringe. First, assuming the size of the fringe is fixed, we demonstrate that the usual Ramsey Rule for second-best efficient pricing remains applicable in this context. We also examine the suitability of the Laspeyres price cap and show that it retains its desirable properties. This implies that regulators should continue to apply Laspeyres price cap regulation to the dominant firm after competition has materialized. Then, assuming that price and entry control are regulatory instruments, we characterize the efficient pricing and entry rules. We demonstrate that the free entry equilibrium number of firms will be excessive relative to the efficient number of firms, thereby providing a new Excess Entry Theorem. Finally, we suggest a modification of the Laspeyres price cap that can incentivize the regulated dominant firm to support efficient entry into the fringe.

Buyer Power and Price Discrimination: The Case of the UK Care Home Market

UK Local Authorities purchase care home places on behalf of a large group of people following an assessment of their ability to meet the care home fee from their income and wealth. All other buyers of care home services are atomistic and the care home market is characterised by a large number of relatively small providers. This may give local authorities buyer power. We show the consequences of substantial buyer power by one consumer when sellers are competitive but each faces capacity constraints. In the free entry equilibrium we show that any abuse of this buyer power may lead to part of the market, “the squeezed middle” not being served. We use a microsimulation model to quantify the size of the squeezed middle and assess the implications of the form of the assessment of people’s ability to meet care home fees, for local authorities’ ability to exercise buyer power

Cream Skimming in Financial Markets

We propose a model where investors can choose to acquire costly information that allows them to identify good assets and purchase them in opaque over the counter (OTC) markets. Uninformed investors trade on an organized exchange and only have access to an asset pool that has been (partially) cream-skimmed by informed dealers. We show that when the quality composition of assets for sale is fixed there is always too much information acquisition and cream skimming by dealers in equilibrium. In the presence of moral hazard in origination, we show that the social value of information acquisition and trading by dealers varies inversely with private incentives to acquire information: just when it is socially optimal to limit costly investment in information by dealers, investors' private incentives to acquire information are at their highest, and vice-versa. Thus, equilibrium entry by informed dealers in OTC markets is generically inefficient.