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Article Excerpt
I. INTRODUCTION
The research reported here explores both conditions under which tacit collusion develops and the remedies that might be taken to transform tacit collusion into a competitive solution. The issue is approached from the point of view of four broad questions. Can we create economic environments within which tacit collusion emerges (in the absence of conspiracy)? Such an environment can be viewed as a "tacit collusion incubator." A successful incubator would provide an opportunity to study the details of phenomena that have difficulty surviving in other environments. Can the evolving behavior be understood in terms of game-theoretic models and if so, can the behavior be understood in terms of equilibrium selection? Is the underlying model robust in the sense of predicting behavior when possibly collusion breaking, institutional perturbations are imposed? The overall goal is to direct focus on the principles that operate in the hope that an understanding of the principles will help us understand the phenomenon in the numerous, different, complex environments found naturally occurring.
The institutional setting is an auction in which game-theoretic models have a natural interpretation within which multiple equilibria exist. In the context of the game-theoretic models, the question is focused on the several equilibria of non-repeated game models and the conditions under which some equilibria are favored by the data and others are not. Specifically, one equilibrium is favorable to the buyers (labeled "tacit collusion") and another is favorable to the seller (labeled "competitive"). If the system has a tendency to go to one, under what conditions can the system be made to naturally gravitate to the other and what role can theory play in identifying the conditions?
Collusion among several (five or more) agents has never been observed in an experimental market environment in the absence of conspiracy and/or special facilitating devices. Consequently, few experimental studies have addressed the issue of how to stop tacit collusion once it has started. This paper addresses the issue in two steps. First, we identify an experimental environment in which tacit collusive-type behavior evolves naturally and quickly and does so without the aid of verbal communication and without the aid of side payments. We call it the "collusion incubator" environment. Second, we explore the use and effectiveness of vehicles that hold a potential for disrupting or terminating collusion. Because of the complexity of the issues, the large set of potential collusion "'remedies" and necessarily sparse data, we use an exploratory methodology. Institutional changes are implemented in sequences that depend upon what has been observed. The exploratory approach is frequently used under such circumstances.
Two different experimental environments were developed and explored. One environment is labeled "collusion conducive" or "collusion incubator." It was designed with the purpose of creating an environment in which tacit collusion would evolve. This environment necessarily abstracts from parameters that might exist naturally and differs dramatically from the parameters studied in other experiments. The purpose is to create and study phenomenon that is difficult to find in any form. Indeed, tacit collusion in a multiple item auction has never been (convincingly) observed. The reliable creation of phenomenon that is thought to exist is a first step to understand the conditions under which it might be found, observe the basic principles at work in its evolution, and identify how it might be detected if it exists in more complex environments. Thus, as is the case with experimental methods in all science, the extreme divorce of the experimental environment from the naturally occurring environment is very useful, if not necessary.
The second environment, labeled "competitive conducive," involves changes in the first environment, implemented for the purpose of studying the stability of (tacit) collusive behavior. For convenience, from time to time we may refer to these two environments as the "collusive" environment and the "competitive" environment even though the latter will take various forms as we study how collusion can be extinguished.
Both the collusive and competitive environments have common structural elements and some common institutional elements. The common environment has "repeated game" features in that agents participated in a series of auctions. Except as otherwise noted, the number of items equaled the number of participants. Preferences of agents were additive, in the sense that no synergies existed. Except under the case of special treatments that will be discussed later, the preferences over the items had two important symmetries that we thought would be supportive of (tacit) collusive behavior.
The first property of preferences we will call "strong ordinal symmetry"--if on Item X agent i had the m-th highest value and agent j had the n-th highest value, then agent i had the n-th highest value on the item where individual j had the m-th highest value. As will be discussed, this pattern of symmetry has a type of "folded" property in that it has the potential for simultaneously placing any two individuals in two, exactly opposite conflicts. This pattern of relationships holds the possibility that competition can "unfold" into tacit collusion, as pairs are able to find a mutually beneficial equilibrium. If i and j do not compete, then both face a "next in line" with a similar conflict. The sequential resolution of these conflicts can theoretically result in an "unfolding" from one equilibrium to a completely different one.
The second feature of preferences we will call "item-aligned" preferences. For any item that an individual preferred the most, that individual also had the highest value among all agents. That is, each had his or her "own item" in the sense that it was clear that in any bidding contest an individual would always "win" the item that the individual preferred the most. In that sense, we can label an item as "individual i's item" as if it is clear who would get it. Thus, except in the special cases discussed later, each agent had the highest value among all agents for one item and that was also the item that was most valuable to the individual agent.
The issue is how the institutions might interact with these basic structural features to determine equilibrium. Institutional issues aside, how the two structural features might work together suggests why they might be supportive of collusion. Suppose agent i's item is A. If j has the second highest value then i has the second highest value on B where j has the highest value. If they compete then i will pay j's value for A and j will pay i's value for B. If they do not compete, then they face competition from agents whose values are third from the top, and if competition can be removed at that level through the same mechanism then competition is encountered at still a lower level. This "unfolding" of competition is what the environment was designed to facilitate. The issue is how the unfolding might be facilitated by institutions and more importantly, what institutions might "reverse" the process if a (tacit) collusive equilibrium evolved. Thus, partial success would be the creation of an environment in which collusion would naturally evolve.
The basic institutional framework studied is the simultaneous, continuous, ascending price auction. The collusive conducive environment operated under conditions of full information. All preferences, payoffs, and bids and the identification numbers of bidders were public information. By contrast, the competitive conducive environment operated with less public information and with slightly different rules that operated within the auction.
The primary objective was to learn if the collusive conducive environment could facilitate the (tacit) collusive equilibrium. (1) As mentioned in the introductory paragraph, the creation of the tacit collusive outcome was definitely not a foregone conclusion because collusion with a large number of agents had never before been observed. Early experiments had demonstrated that symmetry is an important feature in moving solutions away from simple competitive outcomes toward more cooperative ones (Plott, 1982) and more recent research by Sherstyuk and her co-authors successfully produced tacit collusion in auctions with no more than three bidders, but in more complex environments prices almost always converge to near the competitive equilibrium. (2)
The first basic result is that within the collusive conducive environment the system equilibrated quickly to the (tacit) collusive equilibrium. Several measures and characteristics of this process are chronicled in the results section of the paper. The process does not seem to have the sequential property as suggested by the unfolding property but instead is discontinuous, with an almost "jump" toward the equilibrium. Thus, the first part of the study was very successful. Collusive equilibria emerged and did so reliably under collusive conducive conditions.
The second result is that collusive equilibria, once established, are stable in the sense that removal of central properties of the collusive conducive environment did not force the auction away from the collusive equilibrium. Public information about preferences and about bidder identification did not change the equilibrium. Several changes in auction rules had no effect. Disruptions of the strong, ordinal symmetry by removing some of the items did not disrupt the equilibrium. Only when a "maverick" preference was introduced under conditions of lack of public information about preferences, the collusive equilibrium was quickly disrupted and the system evolved to the competitive solution. The "maverick" was an agent who had the same most preferred item as one of the other agents.
The context of these results needs emphasis. While the study answers some questions, it certainly does not answer all questions. Exactly what theory might be applied remains open, including more detailed analysis of "one shot" game models, the application of repeated game concepts, or whether or not game theory itself is an appropriate tool for understanding the phenomenon. How the results might be translated to complex fieldwork remains unaddressed. The questions posed here are primarily empirical with only crude steps toward adequate theory and the results are reported in the hope that theorists will be challenged to provide convincing theory of what is observed.
The paper is outlined as follows. In Section II, the background experimental work is discussed. Our experiments build on that literature. Section III contains the details of the experimental environments. The details of the preferences and institutions are found there. Section IV is the experimental design that explains the number of experiments and the conditions that were in place for each experiment. Section V discusses models and theory. The correspondence between the game-theoretic solutions and the experimental procedures in the auctions are discussed in detail. Section VI contains the results, which are divided into two sections. The first section of the results explains the nature of the collusive equilibrium and how it is reached. The second section of the results explains the changes in the environment that we implemented as attempts to make the collusive equilibrium switch itself to the competitive equilibrium. Section VII is a summary of conclusions.
II. BACKGROUND EXPERIMENTAL WORK
There are very few empirical examples of collusion in auctions in the absence of conspiracy or without the aid of facilitating devices. Hendricks and Porter (1988) study the bidding of drainage leases on the Outer Continental Shelf. Their findings suggest that there are coordination in bids among firms that own tracts adjacent to the lease for sale. Cramton and Schwarz (2000) report what appear to be attempts to collude in FCC spectrum auction but have no evidence of actual, price influencing collusion. In particular, they point out how bidders used the last several digits of the bids to signal their intents.
Of course, since bidder values are typically unknown in the field, collusion is hard to document. This difficulty can be easily overcome by laboratory experiments, since values of the bidders can be chosen by the experimenters. Isaac and Plott (1981) are the first to study conspiracy experimentally. Isaac and Walker (1985) allow explicit communications among bidders in auctions, and they observe conspiracies in 7 out of 12 auction series. Tacit collusion in auctions with standard procedure, however, is rarely observed in earlier experimental studies. Even when it is observed, tacit collusion is unstable and the prices easily converge back to competitive levels; see, for example, Burns (1985) and Clauser and Plott (1993). In a related industrial organization context, Isaac and Smith (1985) search for predatory behavior in constraint of competition and do not find any. Kagel (1995) surveys earlier experiments on collusions in auctions.
Recently, a sequence of experiments successfully observed robust tacit collusion in special auction institutions. Sherstyuk (1999) studies ascending auctions under common values. In her experiments, each auction consists of two units of items and three bidders, who demand one unit only. She introduces in the auction a particular bid improvement rule: bidders are allowed to submit a bid that equals the highest outstanding bid. If there are multiple highest bidders on the items, a lottery will be run to decide the winner. With this bid improvement rule, Sherstyuk reports persistent and stable tacit collusions: bidders match each other's low bids in most of the auctions. Sherstyuk (2002) obtains similar results under private values.
Robust tacit collusion in auctions with "standard institutions and procedures" is first observed by Kwasnica and Sherstyuk (2007). In their environment, there are two items for sale in an ascending auction with either two or five bidders, who value both items. The experimental environment conforms to the theoretical conditions of Brusco and Lopomo's (2002), and the auction results are broadly consistent with the theoretical predictions: when there are two bidders only, they often tacitly collude through splitting the two items. No collusion is found in auctions with five bidders. Kwasnica and Sherstyuk (2007) also examine the role of complementarity in collusions. They find that complementarities between items reduce collusion. However, when the level of complementarity is moderate, bidders still tacitly collude by taking turns to win the auction. A survey of recent results on collusion in auction can be found in Sherstyuk (forthcoming).
III. COLLUSION INCUBATOR/COLLUSION-CONDUCIVE ENVIRONMENTS
Each experiment starts with a collusion-conducive environment. In this environment, each auction consists of eight subjects and eight items....
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