Market making oligopoly

This paper analyzes price competition between market makers who set costly capacity constraints before they intermediate between producers and consumers. The key finding is that the unique perfect equilibrium outcome is Cournot if capacity is costly and rationing efficient. This result is interesting for two main reasons: It generalizes Kreps and Scheinkman (1983) to an arbitrary number of market makers, and it contrasts with Stahl (1988) and the broader literature on market making, such as Gehrig (1993), Fingleton (1997) and Rust and Hall (2003), where due to the absence of capacity constraints on the input market the Bertrand paradox typically prevails.Market making; capacity constraints; price competition

Vertical mergers that eliminate double markups are procompetitive

Assuming that oligopolistic downstream firms take intermediate goods prices as given and that upstream and integrated firms choose their quantities first and simultaneously, this note shows that vertical mergers between upstream and downstream firms are procompetitive.Vertical integration

Horizontally Differentiated Market Makers

I present a model of competition between two market makers who are horizontally differentiated. I first show that absent a search market for buyers and sellers, there is a continuum of symmetric equilibria. These equilibria are payoff equivalent for market makers, but affect buyers' and sellers' welfare in opposite ways. Second, I analyze the model when buyers and sellers can also exchange the good in search markets. The model with search markets shares many features with existing models, yet allows competing intermediaries to net a profit in equilibrium. Interestingly, the model exhibits a complementarity between intermediaries' profits in the presence of search markets. Third, I show that every equilibrium in a game with market makers is also an equilibrium in an appropriately defined game with matchmakersMarket making; intermediation and search; horizontal differentiation; market microstructure

Competition between market-making Intermediaries

We introduce capacity constrained competition between market-making intermediaries in a model in which agents can choose between trading with intermediaries, joining a search market or remaining inactive. Recently, market-making by a monopolistic intermediary has been analyzed by Rust and Hall (2003) and Gehrig (1993). Market-makers set publicly observable ask and bid prices. Because market-making involves price setting, without further restrictions competition between market-making intermediaries is Bertrand-like and yields the Walrasian outcome, where the ask-bid spread is zero (Rust and Hall 2003, Gehrig 1993). However, positive ask-bid spreads and competition between market-makers can be observed in reality, e.g. in banking and in retailing. Following Kreps and Scheinkman (1983) and Boccard and Wauthy (2000), we therefore introduce physical capacity constraints. This allows for a gradual transition from monopolistic to perfectly competitive intermediation as the number of intermediaries increases. In particular, we show that given Cournot capacities, intermediaries will set Cournot bid and ask prices in the subsequent subgames, so that the equilibrium of the intermediated market coincides with the Walrasian equilibrium as the number of intermediaries becomes largeMarket-making, capacity constrained competition, market microstructure

A dominant strategy, double clock auction with estimation-based tatonnement

The price mechanism is fundamental to economics but difficult to reconcile with incentive compatibility and individual rationality. We introduce a double clock auction for a homogeneous good market with multidimensional private information and multiunit traders that is deficit‐free, ex post individually rational, constrained efficient, and makes sincere bidding a dominant strategy equilibrium. Under a weak dependence and an identifiability condition, our double clock auction is also asymptotically efficient. Asymptotic efficiency is achieved by estimating demand and supply using information from the bids of traders that have dropped out and following a tâtonnement process that adjusts the clock prices based on the estimates

Fee-Setting Mechanisms: On Optimal Pricing by Intermediaries and Indirect Taxation

Mechanisms according to which private intermediaries or governments charge transaction fees or indirect taxes are prevalent in practice. We consider a setup with multiple buyers and sellers and two-sided independent private information about valuations. We show that any weighted average of revenue and social welfare can be maximized through appropriately chosen transaction fees and that in increasingly thin markets such optimal fees converge to linear fees. Moreover, fees decrease with competition (or the weight on welfare) and the elasticity of supply but decrease with the elasticity of demand. Our theoretical predictions fit empirical observations in several industries with intermediaries

Competitive E?ects of Vertical Integration with Downstream Oligopsony and Oligopoly

We analyze the competitive e?ects of backward vertical integration by a partially vertically integrated ?rm that competes with non-integrated ?rms both upstream and downstream. We show that vertical integration is procompetitive under fairly general conditions. It can be anticompetitive only if the ex ante degree of integration is relatively large. Interestingly, vertical integration is more likely to be anticompetitive if the industry is less concentrated. These results are in line with recent empirical evidence. In addition, we show that even when vertical integration is procompetitive, it is not necessarily welfare enhancing

Assessing the Performance of Simple Contracts Empirically: The Case of Percentage Fees

This paper estimates the cost of using simple percentage fees rather than the broker optimal Bayesian mechanism, using data for real estate transactions in Boston in the mid-1990s. This counterfactual analysis shows that interme- diaries using the best percentage fee mechanisms with fees ranging from 5.4% to 7.4% achieve 85% or more of the maximum profit. With the empirically observed 6% fees intermediaries achieve at least 83% of the maximum profit and with an optimally structured linear fee, they achieve 98% or more of the maximum profit

When is Seller Price Setting with Linear Fees Optimal for Intermediaries?

Mechanisms where sellers set the price and are charged a linear commission fee are widely used by real world intermediaries, e.g. by real estate brokers. Empiri- cally these commission fees exhibit very little variance, both across heterogeneous regional markets and over time. So far, there is no theoretical explanation why such seller price setting mechanisms are used and why the linear fees vary so little. In this paper, we first show that in a Bayesian setup seller price setting with linear fees is revenue equivalent to the intermediary optimal direct mechanism derived by Myerson and Satterthwaite (1983) if and only if the seller’s cost is drawn from a generalized power distribution. Whenever such a mechanism is optimal, the fee structure is independent of the distribution from which the buyer’s valuation is drawn. Second, we derive the intermediary optimal direct mechanism when there are many buyers and possibly many sellers and we show that with one seller any standard auction with linear fees and reserve price setting by the seller (which are used e.g. by eBay) implements this mechanism if the seller’s cost is drawn from a power distribution and if buyers’ valuations are identically distributed. Third, we show that when the number of buyers approaches infinity while there is still one seller, seller price setting and price setting by the intermediary are equivalent, intermediary optimal mechanisms.Brokers; linear commission fees; optimal indirect mechanisms

Dynamic Location Games

We study a location game where consumers are distributed according to some density f and where market entry is costly and occurs sequentially. This permits an endogenous determination of the number of active ¯rms, their locations and the sequence in which these locations are occupied. While in general the analysis of such games is complicated by the fact that equilibrium locations and the sequence of settlement must be determined simul-taneously, we show that they can be independently derived for certain classes of densities including monotone and, under some additional restrictions, hump-shaped and U-shaped ones. For these classes we characterize the subgame perfect equilibrium outcome. More-over, when f is monotone and concave the equilibrium locations in areas where the density is larger tend to be more pro¯table. When f is uniform the number of ¯rms entering in equilibrium is minimal.Spatial competition product differentiation dynamic games entry deterrence