Robust learning equilibrium

2005

Abstract. Auction mechanism design has traditionally been a largely analytic process, relying on assumptions such as fully rational bidders. In practice, however, bidders behave unpredictably, making them difficult to model and complicating the design process. To address this challenge, we present an adaptive auction mechanism: one that learns to adjust its parameters in response to past empirical bidder behavior so as to maximize an objective function such as auctioneer revenue.

Journal of Economic Behavior & Organization, 1994

Inexperienced bidders in first-price common value auctions suffer from a winner's curse _ losing money on average. With experience bidders approximate the Nash equilibrium.

Journal of Economic Theory

We consider a single-item, independent private value auction environment with two bidders: a leader, who knows his valuation, and a follower, who privately chooses how much to learn about his valuation. We show that, under some conditions, an ex-post efficient revenuemaximizing auction-which solicits bids sequentially-partially discloses the leader's bid to the follower, to influence his learning. The disclosure rule that emerges is novel; it may reveal to the follower only a pair of bids to which the leader's actual bid belongs. The identified disclosure rule, relative to the first-best, induces the follower to learn less when the leader's valuation is low and more when the leader's valuation is high.

2020

First-price auctions have very recently swept the online advertising industry, replacing second-price auctions as the predominant auction mechanism on many platforms. This shift has brought forth important challenges for a bidder: how should one bid in a first-price auction, where unlike in second-price auctions, it is no longer optimal to bid one's private value truthfully and hard to know the others' bidding behaviors? In this paper, we take an online learning angle and address the fundamental problem of learning to bid in repeated first-price auctions, where both the bidder's private valuations and other bidders' bids can be arbitrary. We develop the first minimax optimal online bidding algorithm that achieves an $\widetilde{O}(\sqrt{T})$ regret when competing with the set of all Lipschitz bidding policies, a strong oracle that contains a rich set of bidding strategies. This novel algorithm is built on the insight that the presence of a good expert can be leverage...

Neural Computation, 1999

This article presents a new application of stochastic adaptive learning algorithms to the computation of strategic equilibria in auctions. The proposed approach addresses the problems of tracking a moving target and balancing exploration (of action space) versus exploitation (of better modeled regions of action space). Neural networks are used to represent a stochastic decision model for each bidder. Experiments confirm the correctness and usefulness of the approach.

Games and Economic Behavior, 2001

are gratefully acknowledged.

2020

In games of incomplete information individual players make decisions facing a combination of structural uncertainty about the underlying parameters of the environment, and strategic uncertainty about the actions undertaken by their partners. How well are human actors able to cope with these uncertainties, and what models best describe their learning in such environments? We use a double auction task with different competitive and informational environments to characterize learning abilities of the single human participants (buyers) in a range of adaptive learning models covering reinforcement learning, directional learning and belief learning. Results show that real behaviour is best described using simple models of directional learning type with minimal knowledge assumptions about information efficiency of prices. This behavior is consistent with bounded rationality and risk aversion: human subjects try to maximize their chance for transaction, and do so using the simplest learning...

2016

This dissertation considers the robustness of private value and common value kdouble auctions when those markets are populated by regret minimizers. Regret minimizing agents, unlike typical expected utility maximizers, need not commit to a single prior in their decision rule. In fact, it is a feature of the minimax regret decision rule that is not based on any prior. This makes the decision rule an interesting one for agents who face Knightian Uncertainty. A decision problem involves Knightian uncertainty if the agents know the possible outcomes but not those outcomes’ probabilities – as may be the case in a new market. This dissertation shows that in a private value k-double auction, minimax regret traders will not converge to price-taking behavior as the market grows. Similarly, in a common value auction, traders’ behavior may depend on the parameter k, but does not depend on the number of other traders in the market. The invariance of regret minimizing traders’ strategies to the ...

2015

We consider a single-item, independent private value auction environment with two bidders: the leader, who knows his valuation, and the follower, who exerts an effort that affects the probability distribution of his valuation, which he then learns. We provide sufficient conditions under which an ex-post efficient revenue-maximizing auction solicits bids sequentially and partially discloses the leader’s bid to the follower, thereby influencing the follower’s effort. This disclosure rule, which is novel, is non-monotone and prescribes sometimes revealing only a pair to which the leader’s bid belongs and sometimes revealing the bid itself. The induced effort distortion relative to the first-best is discussed.

2021

We show that strategic market games, the non-cooperative implementation of a matching with transfers or an assignment game, are weakly acyclic. This property ensures that many common learning algorithms will converge to Nash equilibria in these games, and that the allocation mechanism can therefore be decentralized. Convergence hinges on the appropriate price clearing rule and has different properties for betterand best-response dynamics. We tightly characterize the robustness of this convergence in terms of so-called schedulers for both types of dynamics.