game so that a desirable outcome is reached even though the agents in the game behave selfishly. This is a difficult problem because the designer is uncertain about the agents' preferences and the agents may lie about their preferences. Traditionally, the focus in mechanism design has been on designing mechanisms that are appropriate for a range of settings. While this approach has produced a number of famous mechanisms, much of the space of possible settings is still left uncovered. In contrast, in automated mechanism design (AMD), a mechanism is computed on the fly for the setting at hand---a universally applicable approach.

A key trend in the world—especially in electronic commerce—is a demand for higher levels of expressiveness in the mechanisms that mediate interactions, such as the allocation of resources, matching of peers, and elicitation of opinions from large and diverse communities. Intuitively, one would think that this increase in expressiveness would lead to more efficient mechanisms (e.g., due to better matching of supply and demand). However, until now we have lacked a general way of characterizing the expressiveness of these mechanisms, analyzing how it impacts the actions taken by rational agents—and ultimately the outcome of the mechanism. In this technical report we introduce a general model of expressiveness for mechanisms. Our model is based on a new measure which we refer to as the maximum impact dimension. The measure captures the number of different ways that an agent can impact the outcome of a mechanism. We proceed to uncover a fundamental connection between this measure and the concept of shattering from computational learning theory. We also provide a way to determine an upper bound on the expected efficiency of any mechanism under its most efficient Nash equilibrium which, remarkably, depends only on the mechanism’s expressiveness. We show that for any setting and any prior over agent preferences, the

Mechanism design is the art of designing the rules of the game so that desirable systemwide outcomes are obtained even though every agent in the system acts based on self-interest.

Mechanism design is the study of preference aggregation protocols that work well in the face of self-interested agents. We present the first general-purpose techniques for automatically designing multistage mechanisms. These can reduce elicitation burden by only querying agents for information that is relevant given their answers to previous queries. We first show how to turn a given (e.g., automatically designed using constrained optimization techniques) single-stage mechanism into the most efficient corresponding multistage mechanism given a specified elicitation tree. We then present greedy and dynamic programming (DP) algorithms that will determine the elicitation tree (optimal in the DP case). Next, we show how the query savings inherent in the multistage model can be used to design the underlying single-stage mechanism to maximally take advantage of this approach. We illustrate all of these techniques on an optimal auction example. Finally, we present negative results on the design of multistage mechanisms that do not correspond to dominant-strategy single-stage mechanisms: an optimal multistage mechanism in general has to randomize over queries to hide information from the agents.

Mechanism design has traditionally been a largely analytic process, relying on assumptions such as fully rational bidders. In practice, however, these assumptions may not hold, making bidder behavior difficult to model and complicating the design process. To address this issue, we propose a different approach to mechanism design. Instead of relying on analytic methods that require specific assumptions about bidders, our approach is to create a self-adapting mechanism that adjusts auction parameters in response to past auction results. In this paper, we describe our approach and then present an example of its implementation to illustrate its efficacy.

In a combinatorial auction, there are multiple items for sale, and bidders are allowed to place a bid on a bundle of these items rather than just on the individual items. A key problem in this and similar settings is that of strategic bidding, where bidders misreport their true preferences in order to effect a better outcome for themselves. The VCG payment scheme is the canonical method for motivating the bidders to bid truthfully. We study two related problems concerning the VCG payment scheme: the problem of revenue guarantees, and that of collusion. The existence of such problems is known by many; in this paper, we lay out their full extent.

In a combinatorial auction, a set of items is for sale, and agents can bid on subsets of these items. In a voting setting, the agents decide among a set of alternatives by having each agent rank all the alternatives. Many of the key research issues in these two domains are similar. The aim of this paper is to give a convenient side-by-side comparison that will clarify the relation between the domains, and serve as a guide to future research. 1

Previous research on automated mechanism design (proposed in UAI-02) assumed that the outcome space was flatly represented, which makes that work inapplicable if the outcome space is exponential, as it is, for example, in multi-item auctions.

Game theory is a popular tool for designing interaction protocols for agent systems. It is currently not clear how to extend this to open agent systems. By “open ” we mean that foreign agents will be free to enter and leave different systems at will. This means that agents will need to be able to work with previously unseen protocols. There does not yet exist any agreement on a standard way in which such protocols can be specified and published. Furthermore, it is not clear how an agent could be given the ability to use an arbitrary published protocol; the agent would need to be able to work out a strategy for participation. To address this we propose a machine readable language in which a game theory mechanism can be written in the form of an agent interaction protocol. This language allows the workings of the protocol to be made public so that agents can inspect it to determine its properties and hence their best strategy. Enabling agents to automatically determine the game theoretic properties of an arbitrary interaction protocol is difficult. Rather than requiring agents to find the equilibrium of a game, we propose that a recommended equilibrium will be published along with the protocol; agents can then check the recommendation to decide if it is indeed an equilibrium. We present an algorithm for this decision problem. We also develop an equilibrium which simplifies the complexity of the checking problem, while still being robust to unilateral deviations. 1 1

ions (Conitzer, Derryberry, & Sandholm 2004). It also introduces an expressive bidding protocol for matching donations to charities (Conitzer & Sandholm 2004e), as well as an expressive bidding protocol for general settings in which agents' actions impose externalities on the other agents (that is, affect the other agents' utilities). Mechanism design with strategic agents While having a good outcome optimization algorithm is necessary for preference aggregation to be successful, it is not sufficient. The reason is that generally, the agents' preferences are not known beforehand and will have to be elicited Copyright c # 2005, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. from them. Unfortunately, agents will misreport their preferences if it is in their interest to do so. This may lead to the outcome optimization algorithm choosing an outcome that is good under the reported preferences, but bad under the agents' true preferences. The soluti