Ratifiability of Efficient Collusive Mechanisms in Second-Price Auctions with Participation Costs

We investigate whether efficient collusive bidding mechanisms are affected by potential information leakage from bidders' decisions to participate in them within the independent private values setting. We apply the concept of ratifiability introduced by Cramton and Palfrey (1995) and show that when the seller uses a second-price auction with participation costs, the standard efficient cartel mechanisms such as preauction knockouts analyzed in the literature will not be ratified by cartel members. A high-value bidder benefits from vetoing the cartel mechanism since doing so sends a credible signal that she has high value, which in turn discourages other bidders from bidding in the seller's auction.Auctions, collusion, ratifiability

Nonratifiability of the Cartel Mechanism in First-Price Sealed-Bid Auction with Participation Costs

McAfee and McMillan (1992) investigate the coordinated biding strategies in a strong cartel, in which the cartel members can exclude new entrants and can make transfer payments, and show that the strong cartel mechanism is incentive-compatible and efficient. In this paper however, we show the strong cartel mechanism is no longer ratifiable in the presence of participation cost, in which case the bidder with the highest value in the cartel would have incentive to veto for the collusive mechanism. This behavior could make the maximum benefit for the winning bidder

On Ratifiability of Efficient Cartel Mechanisms in First-Price Auctions with Participation Costs and Information Leakage

This paper investigates whether an efficient all-inclusive cartel mechanism studied by McAfee and McMillan (1992) can still preserve its efficiency when bidders can update their information through the cartel’s collusive mechanism and there is a cost to participate in the seller’s auction within the independent private values setting. It is shown that, when the seller uses the first-price auction, the usual efficient cartel mechanisms will no longer be ratifiable in the presence of both participation costs and potential information leakage. The bidder with the highest value in the cartel will have incentive to betray, sending a credible signal of his high value and thus discouraging other bidders from participating in the seller’s auction. However, the cartel mechanisms would still be efficient if either participation cost or information leakage, but not both, is present

On Ratifiability of Efficient Cartel Mechanisms in First-Price Auctions with Participation Costs and Information Leakage

This paper investigates whether an efficient all-inclusive cartel mechanism studied by McAfee and McMillan (1992) can still preserve its efficiency when bidders can update their information through the cartel’s collusive mechanism and there is a cost to participate in the seller’s auction within the independent private values setting. It is shown that, when the seller uses the first-price auction, the usual efficient cartel mechanisms will no longer be ratifiable in the presence of both participation costs and potential information leakage. The bidder with the highest value in the cartel will have incentive to betray, sending a credible signal of his high value and thus discouraging other bidders from participating in the seller’s auction. However, the cartel mechanisms would still be efficient if either participation cost or information leakage, but not both, is present

Cartel Mechanism Design: Nonratifiable Conditions of Collusive Behavior

This dissertation is about an open question of cartel ratifiable conditions. My research goal is to establish a mechanism which is able to detect and explain cartels' activities. My research question in the second chapter is whether or not an efficient cartel mechanism is ratifiable in the first-price sealed-bid auction format with participation costs. R. McAfee and J. McMillan study the coordinated bidding strategies in a strong cartel, which is incentive-compatible and efficient. This chapter investigates this efficient collusive mechanism with two important conditions (1) bidders can update their information through a cartel's prior auction and (2) they have to pay participation costs to participate in seller's auction. The concept of ratifiability, introduced by P. Cramton and T. Palfrey, is applied to explore the first-price sealedbid auction with participation costs. I discovered that the efficient cartel mechanism, such as pre-auction knockout, would be ratified when either of the two conditions exists. However, this mechanism is no longer ratifiable when both conditions exist. The bidder with the highest value in the cartel would have incentive to betray, since doing so sends a credible signal of high value. Hence, the other bidders will be discouraged from participating in the seller's auction and the highest-value bidder maximizes his revenue. In the third chapter, I studied the seller's strategy when she faces a cartel in an auction mechanism. An active seller's optimal strategy is to raise the reserve price to a level that is higher than her own valuation. The collusive mechanism is sustainable even though its revenue is extracted by the higher reserve price. If the seller is authorized to change the auction mechanism, she can receive the expected payoff, prevent the formation of a ring and keep the auction efficient. Further, I presented two methods that could deter a cartel under specific conditions. One is the residual claimants method as proposed by Y. Che and J. Kim and the other is to set a positive participation cost as outlined in the first chapter. The residual claimants method can inhibit a ring in many cases, but it may have some trouble in preventing an efficient cartel mechanism when there is only one participant in the seller's auction. In the fourth chapter, I investigated how to achieve external efficiency in a repeated game. In particular, I looked into the allocation of the budgeted that allows an authority, such as the government, to differentiate collusive behavior and to expose agents to external threats. A threshold level of the budget payment is found in an incentive compatible collusive mechanism for which the government can prevent an agent from participating. In a two-stage model, I showed that if the government can boost exemption or have more budget to subsidize agents, it is less likely that a ring will be formed

Mechanism design with partially-specified participation games

This paper considers the implementation of an economic outcome under complete information when the strategic and informational details of the participation game are partially-specified. This means that full participation is required to be a subgame-perfect equilibrium for a large variety of extensive modifications of the simultaneous-move participation game in the same vein as Kalai [Large Robust Games, Econometrica 72 (2004) 1631-1665].Ce papier considère l'implémentation d'une allocation en information complète lorsque les détails stratégiques et informationnels sont spécifiés de manière partielle. Il est alors exigé que l'issue de décision de participation de tous les agents soit un équilibre en sous-jeux parfait pour une vaste gamme de perturbations du jeu simultané de participation dans la même veine que Kalai [Large Robust Games, Econometrica 72 (2004) 1631-1665]

Essays in Industrial Organization

This dissertation studies a few topics in industrial organization. In the first two chapters, I study the education market from the perspective of industrial organization. Chapter 3 studies second-price auctions with participation costs. Chapters 1 and 2 study the high school market of a large city in China that introduced a policy allowing public schools to offer both free and priced admission options within a centralized admission mechanism. Chapter 1 introduces the institutional background, such as details of the admission mechanism, the schools and their price levels, and the new policy. I then present descriptive analysis. I also estimate a high school value-added regression, where I regress exit exam scores on entrance exam scores and other variables. I interpret the value-added as the high school quality. Results show that quality increases after the implementation of the policy. A difference-in-differences regression further shows that top-tier schools are able to increase their value-added more. I use these results as both inputs and motivating facts for my study in Chapter 2. Chapter 2 formally develops a demand and supply model. On the demand side, students consider both their preferences for a school and their probabilities of being admitted to that school to file a report of preferences. I develop an algorithm to quickly find students\u27 optimal reports, and this algorithm helps to reduce the computational burden in demand estimation. On the supply side, I model schools as maximizing a weighted average of profit and quality, so as to allow for the existence of excess demand for good schools. Demand estimation using students\u27 strategic reports quantifies the extent to which students with higher entrance exam scores care more about quality relative to price. Supply side estimation shows that top-tier schools have lower marginal costs of quality and thus choose higher quality. Counterfactual analysis shows that introducing subsidies to low income students while keeping the current priced admission options would give students more equal access to good schools, while keeping the quality gain brought by market incentives. Another counterfactual analysis shows that the quality gain brought by market incentives is driven by an increase in funds to improve quality and schools\u27 preference for quality. Chapter 3 studies equilibria and efficiency in second-price auctions with public participation costs. This is joint work with Jos\\u27{e}-Antonio Esp\\u27{i}n-S\\u27{a}nchez and \\u27{A}lvaro Parra. We generalize previous results by allowing arbitrary heterogeneity in bidders\u27 distributions of valuations and in their participation costs. We develop a notion of bidder strength, based on the best response of a bidder when all of her opponents play the same strategy she does. We then show that a \emph{herculean equilibrium}, in which stronger bidders have a lower participation threshold than weaker bidders, exists in general environments. In other words, the order of bidders given by their strength, which is a non-equilibrium concept and can be easily calculated for each bidder using only one equation, predicts the order of the participation thresholds in a certain equilibrium which exists in general. Combined with a sufficient condition for equilibrium uniqueness that we further provide, bidders\u27 strength points out the direction for finding and simplifies the formulation of the equilibrium. Furthermore, even though all equilibria are \emph{ex-post} inefficient, an \emph{ex-ante} efficient equilibrium always exists. Therefore, under the uniqueness condition, the \emph{herculean equilibrium} is the unique equilibrium of the game and is \emph{ex-ante} efficient

Theories on Auctions with Participation Costs

In this dissertation I study theories on auctions with participation costs with various information structure. Chapter II studies equilibria of second price auctions with differentiated participation costs. We consider equilibria in independent private values environments where bidders? entry costs are common knowledge while valuations are private information. We identify two types of equilibria: monotonic equilibria in which a higher participation cost results in a higher cutoff point for submitting a bid, and neg-monotonic equilibria in which a higher participation cost results in a lower cutoff point. We show that there always exists a monotonic equilibrium, and further, that the equilibrium is unique for concave distribution functions and strictly convex distribution functions with some additional conditions. There exists a neg-monotonic equilibrium when the distribution function is strictly convex and the difference of the participation costs is sufficiently small. We also provide comparative static analysis and study the limit status of equilibria when the difference in bidders' participation costs approaches zero. Chapter III studies equilibria of second price auctions when values and participation costs are both privation information and are drawn from general distribution functions. We consider the existence and uniqueness of equilibrium. It is shown that there always exists an equilibrium for this general economy, and further there exists a unique symmetric equilibrium when all bidders are ex ante homogenous. Moreover, we identify a sufficient condition under which we have a unique equilibrium in a heterogeneous economy with two bidders. Our general framework covers many relevant models in the literature as special cases. Chapter IV characterizes equilibria of first price auctions with participation costs in the independent private values environment. We focus on the cutoff strategies in which each bidder participates and submits a bid if his value is greater than or equal to a critical value. It is shown that, when bidders are homogenous, there always exists a unique symmetric equilibrium, and further, there is no other equilibrium when valuation distribution functions are concave. However, when distribution functions are elastic at the symmetric equilibrium, there exists an asymmetric equilibrium. We find similar results when bidders are heterogenous

Essays in mechanism design

This thesis consists of essays in the field of mechanism design