With the increasing reliance on game theory as a foundation for auctions and electronic commerce, ecient algorithms for computing equilibria in multiplayer general-sum games are of great theoretical and practical interest. The computational complexity of nding a Nash equilibrium for a one-shot bimatrix game is a well known open problem. This paper treats a related but distinct problem, that of nding a Nash equilibrium for an average-payo repeated bimatrix game, and presents a polynomial-time algorithm. Our approach draws on the well known \folk theorem" from game theory and shows how nite-state equilibrium strategies can be found eciently and expressed succinctly.

The First Trading Agent Competition (TAC) was held from June 22nd to July 8th, 2000. TAC was designed to create a benchmark problem in the complex domain of emarketplaces and to motivate researchers to apply unique approaches to a common task. This article

This article describes the task-specific details of, and the general motivations behind, the four top-scoring agents. First, we discuss general strategies used by most of the participating agents. We then report on the strategies of the four top-placing agents. We conclude with suggestions for improving the design of future trading agent competitions

In business-related interactions such as the on-going highstakes FCC spectrum auctions, explicit communication among participants is regarded as collusion, and is therefore illegal. In this paper, we consider the possibility of autonomous agents engaging in implicit negotiation via their tacit interactions. In repeated general-sum games, our testbed for studying this type of interaction, an agent using a "best-response" strategy maximizes its own payoff assuming its behavior has no effect on its opponent. This notion of best response requires some degree of learning to determine the fixed opponent behavior. Against an unchanging opponent, the best-response agent performs optimally, and can be thought of as a "follower," since it adapts to its opponent. However, pairing two best-response agents in a repeated game can result in suboptimal behavior. We demonstrate this suboptimality in several different games using variants of Q-learning as an example of a best-response strategy. We then examine two "leader" strategies that induce better performance from opponent followers via stubbornness and threats. These tactics are forms of implicit negotiation in that they aim to achieve a mutually beneficial outcome without using explicit communication outside of the game.

In complicated, interacting auctions, a fundamental problem is the prediction of prices of goods in the auctions, and more broadly, the modeling of uncertainty regarding these prices. In this paper, we present a machine-learning approach to this problem. The technique is based on a new and general boosting-based algorithm for conditional density estimation problems of this kind. This algorithm, which we present in detail, is at the heart of ATTac-2001, a top-scoring agent in the recent Trading Agent Competition (TAC-01). We describe how ATTac-2001 works, the results of the competition, and controlled experiments evaluating the effectiveness of price prediction in auctions.

In repeated general-sum games, an agent using a "best response" strategy maximizes its own payoff assuming its behavior has no effect on its opponent. This notion of best response requires some degree of learning to determine the fixed opponent behavior.

Abstract. Auctions are becoming an increasingly popular method for transacting business, especially over the Internet. This paper presents a general approach to building autonomous bidding agents to bid in multiple simultaneous auctions for interacting goods. The core of our approach is learning a model of the empirical price dynamics based on past data and using the model to analytically calculate, to the greatest extent possible, optimal bids. This approach is fully implemented as ATTac-2001, a top-scoring agent in the second Trading Agent Competition (TAC-01). ATTac-2001 uses boosting techniques to learn conditional distributions of auction clearing prices. We present experiments demonstrating the effectiveness of this predictor relative to several reasonable alternatives. 1

Simultaneous ascending auctions present agents with the exposure problem: bidding to acquire a bundle risks the possibility of obtaining an undesired subset of the goods. Auction theory provides little guidance for dealing with this problem. We present a new family of decisiontheoretic bidding strategies that use probabilistic predictions of final prices. We focus on selfconfirming price distribution predictions, which by definition turn out to be correct when all agents bid decision-theoretically based on them. Bidding based on these is provably not optimal in general, but our experimental evidence indicates the strategy can be quite effective compared to

Abstract. Auctions are an area of great academic and commercial interest, from tiny auctions for toys on eBay to multi-billion-dollar auctions held by governments for resources or contracts. Although there has been significant research on auction theory, especially from the perspective of auction mechanisms, studies of autonomous bidding agents and their interactions are relatively few and recent. This paper examines several autonomous agent bidding strategies in the context of FAucS, a faithful simulation of a complex FCC spectrum auction. We introduce punishing randomized strategic demand reduction (PRSDR), a novel bidding strategy by which bidders can partition available goods in a mutually beneficial way without explicit inter-agent communication. When all use PRSDR, bidders obtain significantly better results than when using a reasonable baseline approach. The strategy automatically detects and punishes non-cooperating bidders to achieve robustness in the face of agent defection, and performs well under alternative conditions. The PRSDR strategy is fully implemented and we present detailed empirical results. 1

Sponsored search is a rapidly growing business and there is tremendous industry and research interest in improving the designs and functioning of the sponsored search marketplace. Launching new designs and enhanced features for the sponsored search marketplace requires careful evaluation of their potential consequences to user experience and financial impact on the multiple parties (advertisers, publishers and marketplace operator) involved. The complexity of market dynamics makes it difficult to draw definite conclusions about the market without comprehensive testing. While limited field testing is often performed, it has several disadvantages: limited control over design parameters, limited sample sizes and scenarios that can be tested. Simulation testing is a viable option. Though some previous works have reported on the use of simulations, most of these are ad hoc and intended to test specific scenarios. In this paper, we describe the design of a general purpose simulation framework that supports the evaluation of alternative designs and features. We initially discuss the functional and architectural requirements for implementation of this framework. From a methodological perspective, there is a need to simulate a "micro-market " – a small scale representation of a complete market – for effective evaluation. Hence, we next describe how micro-market data samples are generated and an approach to scaling the metrics produced from simulations, using such samples, to represent an entire market. Finally, we relate our experiences in applying this simulation framework to evaluating designs and features for sponsored search at Yahoo!