Low-Regret Algorithms for Strategic Buyers with Unknown Valuations in Repeated Posted-Price Auctions

We study repeated posted-price auctions where a single seller repeatedly interacts with a single buyer for a number of rounds. In previous works, it is common to consider that the buyer knows his own valuation with certainty. However, in many practical situations, the buyer may have a stochastic valuation. In this paper, we study repeated posted-price auctions from the perspective of a utility maximizing buyer who does not know the probability distribution of his valuation and only observes a sample from the valuation distribution after he purchases the item. We first consider non-strategic buyers and derive algorithms with sub-linear regret bounds that hold irrespective of the observed prices offered by the seller. These algorithms are then adapted into algorithms with similar guarantees for strategic buyers. We provide a theoretical analysis of our proposed algorithms and support our findings with numerical experiments. Our experiments show that, if the seller uses a low-regret algorithm for selecting the price, then strategic buyers can obtain much higher utilities compared to non-strategic buyers. Only when the prices of the seller are not related to the choices of the buyer, it is not beneficial to be strategic, but strategic buyers can still attain utilities of about 75% of the utility of non-strategic buyers.</p

New Models qnd Algorithms for Bandits and Markets

Inspired by advertising markets, we consider large-scale sequential decision making problems in which a learner must deploy an algorithm to behave optimally under uncertainty. Although many of these problems can be modeled as contextual bandit problems, we argue that the tools and techniques for analyzing bandit problems with large numbers of actions and contexts can be greatly expanded. While convexity and metric-similarity assumptions on the process generating rewards have yielded some algorithms in existing literature, certain types of assumptions that have been fruitful in offline supervised learning settings have yet to even be considered. Notably missing, for example, is any kind of graphical model approach to assuming structured rewards, despite the success such assumptions have achieved in inducing scalable learning and inference with high-dimensional distributions. Similarly, we observe that there are countless tools for understanding the relationship between a choice of model class in supervised learning, and the generalization error of the best fit from that class, such as the celebrated VC-theory. However, an analogous notion of dimensionality, which relates a generic structural assumption on rewards to regret rates in an online optimization problem, is not fully developed. The primary goal of this dissertation, therefore, will be to fill out the space of models, algorithms, and assumptions used in sequential decision making problems. Toward this end, we will develop a theory for bandit problems with structured rewards that permit a graphical model representation. We will give an efficient algorithm for regret-minimization in such a setting, and along the way will develop a deeper connection between online supervised learning and regret-minimization. This dissertation will also introduce a complexity measure for generic structural assumptions on reward functions, which we call the Haystack Dimension. We will prove that the Haystack Dimension characterizes the optimal rates achievable up to log factors. Finally, we will describe more application-oriented techniques for solving problems in advertising markets, which again demonstrate how methods from traditional disciplines, such as statistical survival analysis, can be leveraged to design novel algorithms for optimization in markets

Essays in auction and market design

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Economics, 2004.Includes bibliographical references.(cont.) the auctioneer are analyzed.This thesis consists of three essays in auction and market design. Chapter 1 studies sequential auctions with potential entry between rounds. In a simple model with two rounds, two initial bidders and one potential entrant, it is shown that every symmetric equilibrium first round bidding function must feature some degree of pooling. In one such equilibrium, the symmetric bidding function is a step function, reflecting the desire of present bidders to hide information from the potential entrant in order to deter entry. Extensions of the simple model to multiple incumbents and uncertain presence of the entrant are discussed. Chapter 2 studies the choice between two modes of trade: selling at a posted price or bargaining. It is shown that the choice of one of the regimes may serve as a signal of quality of the good, otherwise unobservable to buyers. The main result of this chapter is that both modes can coexist on the same market. This result holds both when sellers can choose the quality is given exogenously and when they can not. Chapter 3 examines origins of rules restricting the set of auction formats available to the seller in an auction. While wider set of possible auction formats available to the seller may increase his expected revenue, choice of one of the formats discloses seller's private information; the seller may want to commit to an auction format ex ante to avoid this disclosure. The value of commitment is analyzed in the context of announced versus hidden reservation value choice. A policy of conditional disclosure is introduced, which generates revenue higher than that generated by either of the unconditional policies. In the context of public procurement auctions, implications of expected and unexpected favoritism on the part ofby Andrei Bremzen.Ph.D

Behavioral Aspects of Bargaining and Pricing.

Some remarkable results of the studies in this thesis are that individual behavior seems to be rather well described by theories taking the (im)patience of agents into account. Fairness considerations are found to play an important role not only in bargaining situations but also in competitive markets. At the same time, the impact of fairness varies with the institutional setting. Finally, investigation into the variation of trust accross the Dutch population suggests that age and education affect a basic trust propensity.

Essays In Algorithmic Market Design Under Social Constraints

Rapid technological advances over the past few decades---in particular, the rise of the internet---has significantly reshaped and expanded the meaning of our everyday social activities, including our interactions with our social circle, the media, and our political and economic activities This dissertation aims to tackle some of the unique societal challenges underlying the design of automated online platforms that interact with people and organizations---namely, those imposed by legal, ethical, and strategic considerations. I narrow down attention to fairness considerations, learning with repeated trials, and competition for market share. In each case, I investigate the broad issue in a particular context (i.e. online market), and present the solution my research offers to the problem in that application. Addressing interdisciplinary problems, such as the ones in this dissertation, requires drawing ideas and techniques from various disciplines, including theoretical computer science, microeconomics, and applied statistics. The research presented here utilizes a combination of theoretical and data analysis tools to shed light on some of the key challenges in designing algorithms for today\u27s online markets, including crowdsourcing and labor markets, online advertising, and social networks among others