Continuum Of Buyers Research Articles

How Efficient are Decentralized Auction Platforms?

Abstract We model a decentralized, dynamic auction market platform in which a continuum of buyers and sellers participate in simultaneous, single-unit auctions each period. Our model accounts for the endogenous entry of agents and the impact of intertemporal optimization on bids. We estimate the structural primitives of our model using Kindle sales on eBay. We find that just over one-third of Kindle auctions on eBay result in an inefficient allocation with deadweight loss amounting to 14% of total possible market surplus. We also find that partial centralization—for example, running half as many 2-unit, uniform-price auctions each day—would eliminate a large fraction of the inefficiency, but yield lower seller revenues. Our results also highlight the importance of understanding platform composition effects—selection of agents into the market—in assessing the implications of market redesign. We also prove that the equilibrium of our model with a continuum of buyers and sellers is an approximate equilibrium of the analogous model with a finite number of agents.

Optimal nonlinear pricing by a monopolist with information ambiguity

We consider the optimal nonlinear pricing by an ambiguity-averse monopolist. The monopolist's subjective belief about the distribution of buyers is described by ϵ-contamination of an additive probability. We find that under a maxmin utility decision rule and with a continuum of buyers, ambiguity aversion leads to bunching at the bottom in the optimal contract, and the distortion at the bottom is reduced. Other high valuation buyers are offered the same quantity as in the case without ambiguity, but they get a greater discount.

Equilibrium pricing with positive externalities

We study the problem of selling an item to strategic buyers in the presence of positive historical externalities, where the value of a product increases as more people buy and use it. This increase in the value of the product is the result of resolving bugs or security holes after more usage. We consider a continuum of buyers that are partitioned into types where each type has a valuation function based on the actions of other buyers. Given a fixed sequence of prices, or price trajectory, buyers choose a day on which to purchase the product, i.e. they have to decide whether to purchase the product early in the game or later after more people already own it. We model this strategic setting as a game, study existence and uniqueness of the equilibria, and design an FPTAS to compute an approximately revenue-maximizing pricing trajectory for the seller in two special cases: the symmetric settings in which there is just a single buyer type, and the linear settings that are characterized by an initial type-independent bias and a linear type-dependent influenceability coefficient.

Market Power and Information Revelation in Dynamic Trading

We study a strategic model of dynamic trading where agents are asymmetrically informed over common value sources of uncertainty. There is a continuum of buyers and a finite number n of sellers. All buyers are uninformed, while at least one seller is privately informed about the true state of the world. When n = 1, full information revelation never occurs in equilibrium and the only information transmission happens in the first period. With n > 1 the outcome depends both on the structure of the sellers' information and, even more importantly, on the intensity of competition allowed by the trading rules. When there is intense competition (absence of clienteles), information is fully and immediately revealed to the buyers in every equilibrium for n large enough, regardless of the number of informed sellers. On the other hand, for trading arrangements characterized by less intense forms of competition (presence of clienteles), for any n we always have equilibria where information is never fully revealed. Moreover, in that case, when only one seller is informed, for many parameter configurations there are no equilibria with full information revelation, even for large n.

Foundations of dynamic monopoly and the coase conjecture

Subgame-perfect equilibria are characterized for a market in which the seller quotes a price each period. Assume zero costs, positive interest rate, continuum of buyers, and some technical conditions. If buyers' valuations are positive then equilibrium is unique, buyers' strategies are stationary, and the price sequence is determinant along the equilibrium path but possibly randomized elsewhere. Otherwise a continuum of stationary equilibria can exist, but at most one with analytic strategies. Coase's conjecture is verified for stationary strategies: reducing the period length drives all prices to zero or the least valuation. Connections to bargaining models are described.