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In auctions, bidders compete with one another in their attempt to 1 purchase the goods that are up for sale • But buyer competition may be reduced or disappear when a ring of colluding bidders is present. The purpose of the participants to a ring is to eliminate buyer competition and to realize a gain over vendors. When all participants are members of the ring, this is done by purchasing the item at the reserve price and splitting the spoils (the difference between the item market value and the reserve price) among the participants. "The term ring apparently derives from the fact that in a settlement sale following the auction, members of the collusive arrangement form a circle or ring to facilitate observation of their trading behavior by the ring leader" (Cassady jr. (1967)). If the coalition members knew other players' values, the problem faced by the ring might be easily solved: the player with the highest value should submit a serious bid and the other members, on the contrary, only phony bids. However, ring participants do not usually know the values of other members. Therefore, ring members have to find out some mechanism which selects the player who has to bid seriously and, eventually, esta­ blish side payments paid to each of the losers2.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract
In auctions, bidders compete with one another in their attempt to purchase the goods that are up for sale1. But buyer competition may be reduced or disappear when a ring of colluding bidders is present. The purpose of the participants to a ring is to eliminate buyer competition and to realize a gain over vendors. When all participants are members of the ring, this is done by purchasing the item at the reserve price and splitting the spoils (the difference between the item market value and the reserve price) among the participants. “The term ring apparently derives from the fact that in a settlement sale following the auction, members of the collusive arrangement form a circle or ring to facilitate observation of their trading behavior by the ring leader” (Cassady jr. (1967)). If the coalition members knew other players’ values, the problem faced by the ring might be easily solved: the player with the highest value should submit a serious bid and the other members, on the contrary, only phony bids. However, ring participants do not usually know the values of other members. Therefore, ring members have to find out some mechanism which selects the player who has to bid seriously and, eventually, establish side payments paid to each of the losers2.
Angelo Artale

Chapter 2. The Experiment

Abstract
This chapter is organized as follows. Section 2.1 sums up the most recent contributions on collusion in auctions. The experimental set-up and technology are described in Section 2.2. Section 2.3 reports the theory of collusion in first-price auctions with emphasis on the contribution of McAfee and McMillan (1992). Section 2.4 describes the mechanisms used by experimental subjects. That is, we describe the rules chosen by experimental subjects to implement collusion. Section 2.5 strategically analyzes the mechanisms used by experimental subjects. We assume that, given that players have chosen some mechanism, they will play according to it. We ask which is the best strategy for the proposed mechanism. We compare the experimental data with the theoretical predictions. For each observed mechanism, we calculate the ex-ante expected payoff when players play according to the theoretical prediction, and compare this with the observed payoff on average. As we will see, the most commonly used mechanism is not an optimal one, that is, it is not a mechanism which selects as winner the player with the highest value when players play rationally. Nevertheless, because of the bounded rationality of experimental subjects, it reaches the efficient result in most of the cases.
Angelo Artale

Chapter 3. A Descriptive Model

Abstract
In this chapter, we present a descriptive model which characterizes experimental subjects’ behavior when they play the announcement mechanism. The observation of experimental data and, particularly, some regularities in the deviation of data on average from theoretical predictions suggest that there is a possible explanation of aggregated data. We have observed that players are divided into two groups: players who cheat and players who do not cheat (see Subsection 2.5.2). Moreover, the average values from which players start to cheat are very close for the three different positions (81.7, 81.2 and 80.5). We will say that a value is low when it is strictly lower than 81, and high when it is equal to or higher than 81. As we have seen in Subsection 2.5.2, players who cheat do not do so according to the theoretical prediction. There, we have proposed a simple model that describes how players who cheat announce their values. Our aim, in this section, is to present a more general model, which assigns the conditional probability that a player cheats when he announces in the different positions, given his value and the others’ announcements. To estimate these probabilities, we use a logit model. After having estimated the probability that a player cheats when he announces in one of the three positions (Section 3.1), we show how the descriptive model works (Section 3.2). We simulate players’ behavior in our descriptive model, and we compare the simulated players’ behavior with experimental subjects behavior.
Angelo Artale

Chapter 4. Mechanisms of Collusion

Abstract
In this chapter, we analyze the mechanisms presented in Chapter 2. We will start showing how the probability distribution of the values in our experimental set-up looks like (Section 4.1). Section 4.2 analyzes a particular equilibrium of the announcement mechanism, Section 4.3 the equilibria of the bid-bargain mechanism. In Subsection 4.3.1, we investigate the optimality of the bid-bargain mechanism and compare it with the announcement mechanism. In Section 4.4, we show an algorithm to calculate the equilibria of the lattice mechanism. The optimality of this mechanism is investigated in Subsection 4.4.1. As we will see, the lattice mechanism can give very bad expected payoffs depending on the assigned partition of the values. In Subsection 4.4.2, we show the partition with four intervals which guarantees the highest expected payoff for the set of values of our experiment. The first-price auction mechanism is analyzed in Section 4.5. Section 4.6 sums up the most important results.
Angelo Artale

Chapter 5. Two Extensions

Abstract
In this chapter we consider two interesting extensions. The case of the lattice mechanism with continuous bids is investigated in Section 5.1. In Section 5.2, we consider the case of a coalition of two players which bids non-cooperatively versus an individual bidder.
Angelo Artale

Chapter 6. Conclusion

Abstract
We have opened this work asking the question: “Which mechanisms, if any, are likely to be observed when human subjects have to solve a given implementation problem?”. The implementation problem we have investigated is that which is faced by a ring of bidders who participate in a first-price auction. In 92% of all rounds, players agreed on some collusive mechanism and implemented it. The mechanisms used by human players are very simple. Playing according to the most frequently used mechanism, they announced their values. In eleven auctions, players did not care about the announcing order; in one auction, they used a random mechanism to choose in which order to announce; in one auction, they specified the sequence of announcements so that Player i (i=1,2,3) once announced as first one, once as second one and so on. The player who made the highest announcement bid the reserve price and splitted equally the difference between his announcement minus the reserve price among the other two players. This mechanism is not incentive-compatible but subjects, in most of the rounds, announced their true values. Because of this, experimental subjects reached the optimal allocation in most of the cases.
Angelo Artale

Backmatter

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