Gabor Virag

Gambling By Auctions

We provide theoretical and empirical analysis of a selling mechanism used by an Internet web-site that combines important features of auctions and gambling. This is the first analysis of such a selling mechanism, which provides insights into how the two kinds of behavior might be related in real life. The winner of the object is the bidder with the highest bid not submitted by any other bidder. In the equilibrium of our game theoretical model, each bid made with positive probability yields the same probability of winning. Bidders are more likely to submit higher bids, and the bid distribution does not depend on the value of the object or the highest bid allowed if one controls for the number of bidders. Most of these key theoretical predictions are confirmed by the data.

Competing auctions: Finite markets and convergence

The literature on competing auctions offers a model where sellers compete for buyers by setting reserve prices. An outstanding conjecture (e.g., Peters and Severinov 1997) is that the sellers post prices close to their marginal costs when the market becomes large. This conjecture is confirmed in this paper: we show that if all sellers have zero costs, then the equilibrium reserve price converges to 0 in distribution. Under further conditions there is a symmetric pure strategy equilibrium. In this equilibrium, if the ratio of buyers to sellers increases, then the equilibrium reserve price increases, and the reserve price is decreasing in the size of the market. Convergence of reserve prices occurs at the fast rate of 1/n if the ratio of buyers to sellers is held constant.

High profit equilibria in directed search models

We consider a model of directed search where the sellers are allowed to post mechanisms with entry fees. Regardless of the number of buyers and sellers, the sellers are able to extract all the surplus of the buyers by introducing entry fees and making price schedules positively sloped in the number of buyers arriving to their shops. This is in contrast to results that are achieved for large markets under the assumption that sellers cannot influence the utility of any particular buyer (market utility assumption), in which case buyers obtain strictly positive rents. If there is a bound on the prices or on the entry fees that can be charged, then the equilibrium with full rent extraction does not exist any more, and the market utility assumption is restored for large markets.

MARKET POWER AND EFFICIENCY IN A SEARCH MODEL

We build a theoretical model to study the welfare effects and resulting policy implications of firms’ market power in a frictional labor market. Our environment has two main characteristics: wages play a role in allocating labor across firms and there is a finite number of agents. We find that the decentralized equilibrium is inefficient and that the firms’ market power results in the misallocation of workers from the highto the low-productivity firms. A minimum wage forces the low-productivity firms to increase their wage, leading them to hire even more often thereby exacerbating the inefficiencies. Moderate unemployment benefits can increase welfare because they limit firms’ market power by improving the workers’ outside option.

Repeated common value auctions with asymmetric bidders

Abstract This paper considers a first price common value auction with one-sided private information among bidders. An object is rented each period to the highest bidder without revealing the bids made in previous periods. The paper extends single crossing arguments used in static games to show the existence of equilibrium in this repeated auction. The model predicts that bidders bid more aggressively in a repeated auction than in a static auction, because a higher bid increases the amount of information learned through bidding. The aggressive bidding behavior also implies that the per period revenue of the repeated auction is higher than that of the one-period counterpart. This bidding behavior leads to a theoretical explanation for the winners curse in repeated auctions. In addition, the model yields predictions like an increasing wage schedule over time and the institution of a signing bonus that are consistent with labor market observations.

Skill Requirements, Search Frictions, And Wage Inequality

We analyze wage inequality, extending the Burdett and Mortensen (International Economic Review 39 (1998), 257-73) model by incorporating worker heterogeneity through skill requirements. We provide sufficient conditions for existence of an equilibrium where more productive firms offer higher wages. The unique such equilibrium is characterized in a closed form solution. Both within- and between-group inequality are explicitly calculated. We then calibrate the model to explain the joint movement of both within- and between-group inequality in the late 1980s and 1990s, an explanation that has been elusive in the literature so far.

Collusive Equilibria in Directed Search Models

We consider a model of directed search where the sellers are allowed to post general mechanisms. Regardless of the number of buyers and sellers, the sellers are able extract all the surplus of the buyers by introducing entry fees and making their price schedule positively sloped in the number of buyers arriving to their shops. Therefore, shopping card membership fees - similar to our entry fee component - may act as a collusion device between sellers. If there is a lower bound on the prices or there is an upper bound on the entry fees that can be charged, then the equilibrium with full rent extraction may not exist any more. However, the seller optimal equilibrium still features positive entry fees and increasing price schedules. When the constraint is on the entry fees in the seller optimal equilibrium all sellers offer auctions. This implies that if the firms can coordinate on an equilibrium they would not choose a fixed price one (studied by Burdett, Shi and Wright (2001)) or one without entry fees (as in Coles and Eeckhout (2003)). When the market becomes infinitely large, and the sellers face constraints on the prices or entry fees they can choose, then any equilibrium yields the same profits and the sellers cannot sustain collusion in equilibrium.

Efficiency and competition in the long run: The survival of the unfit

In a dynamic contest the current incumbent competes against a randomly assigned entrant in a private value all pay auction each period. We focus on equilibria where the beliefs about the incumbents type and the employed strategies are stationary. We show that inefficient types survive, even if the entrants arrive very frequently, because the entrant plays more aggressively than the incumbent, allowing a low type entrant to win against a high type incumbent. In an example we show that if the incumbent is challenged more often, then the equilibrium type of the incumbent is higher on average. When the value of the prize is the same for all players (the case studied in the public choice literature), the equilibrium rent of the bidders is fully dissipated as the incumbent is challenged infinitely often. The technical contribution lies in showing the existence of stationary equilibrium in an incomplete information game.

Market outcomes and dynamic patent buyouts

Patents are a useful but imperfect reward for innovation. In sectors like pharmaceuticals, where monopoly distortions seem particularly severe, there is growing international political pressure to identify new reward mechanisms which complement the patent system and reduce prices. Innovation prizes and other non-patent rewards are becoming more prevalent in government’s innovation policy, and are also widely implemented by private philanthropists. In this paper we describe situations in which a patent buyout is effective, using information from market outcomes as a guide to the payment amount. We allow for the fact that sales may be manipulable by the innovator in search of the buyout payment, and show that in a wide variety of cases the optimal policy still involves some form of patent buyout. The buyout uses two key pieces of information: market outcomes observed during the patent’s life, and the competitive outcome after the patent is bought out. We show that such dynamic market information can be effective at determining both marginal and total willingness to pay of consumers in many important cases, and therefore can generate the right innovation incentives.

Auctions with resale: Reserve prices and revenues

We study auctions with resale and reserve prices. We characterize the equilibrium, and compare the revenues of the first price auction with that of the second price auction. We show that several results change when a reserve price is introduced. First, the second-price auction may yield higher revenues than the first-price auction. Second, the strong bidder is more likely to win than the weak bidder.