Online Learning in Multi-unit Auctions

We consider repeated multi-unit auctions with uniform pricing, which are widely used in practice for allocating goods such as carbon licenses. In each round, $K$ identical units of a good are sold to a group of buyers that have valuations with diminishing marginal returns. The buyers submit bids for the units, and then a price $p$ is set per unit so that all the units are sold. We consider two variants of the auction, where the price is set to the $K$-th highest bid and $(K+1)$-st highest bid, respectively. We analyze the properties of this auction in both the offline and online settings. In the offline setting, we consider the problem that one player $i$ is facing: given access to a data set that contains the bids submitted by competitors in past auctions, find a bid vector that maximizes player $i$'s cumulative utility on the data set. We design a polynomial time algorithm for this problem, by showing it is equivalent to finding a maximum-weight path on a carefully constructed directed acyclic graph. In the online setting, the players run learning algorithms to update their bids as they participate in the auction over time. Based on our offline algorithm, we design efficient online learning algorithms for bidding. The algorithms have sublinear regret, under both full information and bandit feedback structures. We complement our online learning algorithms with regret lower bounds. Finally, we analyze the quality of the equilibria in the worst case through the lens of the core solution concept in the game among the bidders. We show that the $(K+1)$-st price format is susceptible to collusion among the bidders; meanwhile, the $K$-th price format does not have this issue

Computational aspects of combinatorial pricing problems

Combinatorial pricing encompasses a wide range of natural optimization problems that arise in the computation of revenue maximizing pricing schemes for a given set of goods, as well as the design of profit maximizing auctions in strategic settings. We consider the computational side of several different multi-product and network pricing problems and, as most of the problems in this area are NP-hard, we focus on the design of approximation algorithms and corresponding inapproximability results. In the unit-demand multi-product pricing problem it is assumed that each consumer has different budgets for the products she is interested in and purchases a single product out of her set of alternatives. Depending on how consumers choose their products once prices are fixed we distinguish the min-buying, max-buying and rank-buying models, in which consumers select the affordable product with smallest price, highest price or highest rank according to some predefined preference list, respectively. We prove that the max-buying model allows for constant approximation guarantees and this is true even in the case of limited product supply. For the min-buying model we prove inapproximability beyond the known logarithmic guarantees under standard complexity theoretic assumptions. Surprisingly, this result even extends to the case of pricing with a price ladder constraint, i.e., a predefined relative order on the product prices. Furthermore, similar results can be shown for the uniform-budget version of the problem, which corresponds to a special case of the unit-demand envy-free pricing problem, under an assumption about the average case hardness of refuting random 3SAT-instances. Introducing the notion of stochastic selection rules we show that among a large class of selection rules based on the order of product prices the maxbuying model is in fact the only one allowing for sub-logarithmic approximation guarantees. In the single-minded pricing problem each consumer is interested in a single set of products, which she purchases if the sum of prices does not exceed her budget. It turns out that our results on envyfree unit-demand pricing can be extended to this scenario and yield inapproximability results for ratios expressed in terms of the number of distinct products, thereby complementing existing hardness results. On the algorithmic side, we present an algorithm with approximation guarantee that depends only on the maximum size of the sets and the number of requests per product. Our algorithm’s ratio matches previously known results in the worst case but has significantly better provable performance guarantees on sparse problem instances. Viewing single-minded as a network pricing problem in which we assign prices to edges and consumers want to purchase paths in the network, it is proven that the problem remains APX-hard even on extremely sparse instances. For the special case of pricing on a line with paths that are nested, we design an FPTAS and prove NP-hardness. In a Stackelberg network pricing game a so-called leader sets the prices on a subset of the edges of a network, the remaining edges have associated fixed costs. Once prices are fixed, one or more followers purchase min-cost subnetworks according to their requirements and pay the leader for all pricable edges contained in their networks. We extend the analysis of the known single-price algorithm, which assigns the same price to all pricable edges, from cases in which the feasible subnetworks of a follower form the basis of a matroid to the general case, thus, obtaining logarithmic approximation guarantees for general Stackelberg games. We then consider a special 2-player game in which the follower buys a min-cost vertex cover in a bipartite graph and the leader sets prices on a subset of the vertices. We prove that this problem is polynomial time solvable in some cases and allows for constant approximation guarantees in general. Finally, we point out that results on unit-demand and single-minded pricing yield several strong inapproximability results for Stackelberg pricing games with multiple followers

Mechanism Design Theory in Control Engineering: A Tutorial and Overview of Applications in Communication, Power Grid, Transportation, and Security Systems

This article provides an introduction to the theory of mechanism design and its application to engineering problems. Our aim is to provide the fundamental principles of the theory of mechanism design for control engineers and theorists along with the state-of-the-art methods in engineering applications. We start our exposition with a brief overview of game theory highlighting the key notions that are necessary to introduce mechanism design, and then we offer a comprehensive discussion of the principles in mechanism design. Finally, we explore four key applications of mechanism design in engineering, i.e., communication networks, power grids, transportation, and security systems

Antitrust in Times of Information Technology: An Analysis of Big Tech Monopoly Cases

The information technology industry is one of the most rapidly growing yet concentrated markets existing today. Big Tech monopolies and their increasingly anticompetitive behavior posits risks for competition, technological innovation and consumer welfare. This ranges from price discrimination, limiting consumer choices to the unethical use of data. The particular nature of information technology, with its network effects and negligible marginal costs, incentivizes and facilitates predatory market practices making antitrust analysis in this industry extremely complex. Certain schools of antitrust thought are more sensitive (namely the post-Chicago school) to these implications than others, though antitrust application is still lacking in both the European Union and the United States. This thesis thoroughly analyzed the landmark Microsoft and Google antitrust cases to find that it is imperative to increase antitrust oversight globally and identified the specific technological elements that antitrust bodies need to pay attention to in order to improve their antitrust applications in the information technology industry

A Corporative Theory of Corporate Law and Governance

ABSTRACT This book investigates how a corporation, as a legal entity with certain specific attributes, but lacking human form, can take action in the real world of human activity. It contends that a corporation must take such action through, and by means of, an organization, both inside and outside its corporate legal limits, consisting of real individual persons and groups of persons. The corporation thus presents itself both as a legal entity assuming the legal form of a corporation and as a social entity taking the form of an organization. One form overlays the other. Those with whom it has legal relations, its legal counterparties, are also, in respect of its organization, participants in that organization. This theory of, or perspective on, the corporation and its governance is explicated here as corporative. The corporation comes into being, is situated, participates, and is embedded, in a complex sociopolitical-economic environment, which includes its legal counterparties and organizational participants. In addition to shareholders, they include employees, customers, suppliers, creditors, local, regional, and national communities, polities and governments, and non-governmental and other organizations, including those whose objectives include the environment, sustainability, governance, and social responsibility. Despite arguments from advocates of shareholder primacy and maximizing shareholder value, neither the corporation nor any of its participants, including shareholders, have any single objective. Instead, such participants have a variety of objectives which may be consistent to varying degrees with those of each other and with those of the corporation. However, the prosperity and well-being of corporations and their organizational participants, and the groups and other organizations of which organizational participants are members, at a macro-level, are, in many ways, interdependent. Today, prompted by various concerns (including the environment, sustainability, technology, changes in employment and other economic engagement patterns, and increasing income disparities), corporations, industry groups and NGOs, like governments, educational institutions, and other organizations, are facing challenges to the continued viability of contemporary capitalism and of its paradigmatic vehicle, the corporation. Addressing these challenges requires that corporations be considered in the context of the complex socio-political-economic environment in which they are situated and of which they partake. Drawing on analysis of corporate statutes and other relevant law, and historical, social, political, economic, organizational, business, and other theory, information and analysis, this work elucidates the corporative theory of, or perspective on, the corporation. It outlines how this might be applied in analyzing the corporation and its governance from a legal perspective. It illustrates how organizational participants may, and do, influence the behaviour of the relevant corporations; and how corporations may, and do, influence the behaviour of organizational participants. This contributes to understanding how such relationships may be employed, not only to save capitalism and the corporation, but to advance common interests in human prosperity, happiness, meaning, and even simple sustenance