We present and analyze results from the 2004 Trading Agent Competition supply chain management scenario. We identify behavioral differences between the agents that contributed to their succcess in the competition. In market for components, early procurement remained an important factor despite rule changes from the previous year. We provide additional experimental evidence to confirm that this phenomenon is still rational. Strategic interations also played an important role in procurement; one agent, FreeAgent, employed a strategy designed to block other agents ’ access to suppliers at the start of the game. The different ways agents responded to this challenge were an important factor in the outcome of the tournament. In the customer sales market, average selling prices were a decisive difference between the top agents. Our analysis shows that the economic forces of supply and demand were key factors in determining overall market prices, and that some agents were more adept at finding and exploiting advantageous market conditions. 1

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IIS-0427858, IIS-0234695, and IIS-0121678, as well as a Sloan Fellowship awarded to Tuomas Sandholm, and an IBM Ph.D. Fellowship. The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution, the U.S. government or any other entity. 2

In general, identifying a solution concept only incompletely specifies a mechanism design problem. The designer must consider which among a multiplicity of solutions is likely to be played, as well as the possibility that actual play will not correspond to any solution. Given that actual play is the ultimate determiner of a mechanism’s success, we advocate that designers embrace the corresponding forecasting problem and evaluate candidate mechanisms with respect to belief distributions over players ’ response. Solution concepts can play a useful role in delimiting and structuring belief distributions. We propose that membership of prospective strategy profiles in various solution classes be treated as evidence bearing on their likelihood of play. Flexible solution classes, for example based on approximate equilibrium, degree of dominance, or safety level, provide natural measures (e.g., distance from equilibrium) that can be employed in defining belief distributions. 1.

Strategyproof mechanisms provide robust equilibrium with minimal assumptions about knowledge and rationality but can be unachievable in combination with other desirable properties such as budget-balance, stability against deviations by coalitions, and computational tractability. In the search for maximally-strategyproof mechanisms that simultaneously satisfy other desirable properties, we introduce a new metric to quantify the strategyproofness of a mechanism, based on comparing the payoff distribution, given truthful reports, against that of a strategyproof “reference” mechanism that solves a problem relaxation. Focusing on combinatorial exchanges, we demonstrate that the metric is informative about the eventual equilibrium, where simple regretbased metrics are not, and can be used for online selection of an effective mechanism. 1

We present a functional framework for automated Bayesian and robust mechanism design based on a two-stage game model of strategic interaction between the designer and the mechanism participants, and apply it to several classes of two-player infinite games of incomplete information. Our approach yields optimal or nearly optimal mechanisms in three application domains using various objective functions. By comparing our results with known optimal mechanisms, and in some cases improving on the best known mechanisms, we show that ours is a promising approach to parametric design of indirect mechanisms. 1

Abstract. For a number of years we have been working towards the goal of automatically creating auction mechanisms, using a range of techniques from evolutionary and multi-agent learning. This paper gives an overview of this work. The paper presents results from several experiments that we have carried out, and tries to place these in the context of the overall task that we are engaged in. 1

In many multiagent settings, each agent’s goal is to come out ahead of the other agents on some metric, such as the currency obtained by the agent. In such settings, it is not appropriate for an agent to try to maximize its expected score on the metric; rather, the agent should maximize its expected probability of winning. In principle, given this objective, the game can be solved using game-theoretic techniques. However, most games of interest are far too large and complex to solve exactly. To get some intuition as to what an optimal strategy in such games should look like, we introduce a simplified game that captures some of their key aspects, and solve it (and several variants) exactly. Specifically, the basic game that we study is the following: each agent i chooses a lottery over nonnegative numbers whose expectation is equal to its budget bi. The agent with the highest realized outcome wins (and agents only care about winning). We show that there is a unique symmetric equilibrium when budgets are equal. We proceed to study and solve extensions, including settings where agents must obtain a minimum outcome to win; where agents choose their budgets (at a cost); and where budgets are private information.

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