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Innovations in algorithmic game theory

Periodic Report Summary 1 - IAGT (Innovations in algorithmic game theory)

Summary of progress toward objectives.

Objective 1:

Truth and justice: the interplay between incentive compatibility and envy-freeness in algorithmic mechanism design.

The objective is to study mechanisms for an allocation of objects among agents, where agents have no incentive to lie about their true values (incentive-compatible) and for which no agent will seek to exchange outcomes with another (envy-free). Mechanisms satisfying each requirement separately have been studied extensively, but there are few results on mechanisms achieving both. Our objective is to study the interplay between these two natural properties, one seeking for truthfulness and the other for fairness.

In the paper " Mechanisms and impossibilities for truthful, envy-free allocations", which was published in the Symposium on Algorithmic Game Theory, 2012, (co-authored with John K. Lai), we study mechanisms for combinatorial auctions that are simultaneously incentive compatible (IC), envy free (EF) and efficient in settings with {\em capacitated} valuations --- a subclass of subadditive valuations introduced by \citet{Cohen11}. Capacitated agents have valuations which are additive up to a publicly known capacity. The main result of \citet{Cohen11} is the assertion that the Vickrey-Clarke-Groves mechanism with Clarke pivot payments is EF (and clearly IC and efficient) in the case of homogeneous capacities. The main open problem raised by \citet{Cohen11} is whether the existence result extends beyond homogeneous capacities. We resolve the open problem, establishing that no mechanism exists that is simultaneously IC, EF and efficient for capacitated agents with heterogeneous capacities. In addition, we establish the existence of IC, EF, and efficient mechanisms in the special cases of capacitated agents with heterogeneous capacities, where (i) there are only two items; or (ii) the individual item values are binary. Finally, we show that the last existence result does not extend to the stronger notion of {\em Walrasian} mechanisms, i.e. mechanisms whose allocation and payments correspond to a Walrasian equilibrium.

In addition, in the paper "On Maxsum Fair Cake Divisions", which was published in AAAI 2012 (co-authored with Steven J. Brams, John K. Lai, Jamie Morgenstern and Ariel D. Procaccia), we consider the problem of selecting fair divisions of a heterogeneous divisible good among a set of agents. Recent work focused on designing algorithms for computing maxsum---social welfare maximizing---allocations under the fairness notion of envy-freeness. Maxsum allocations can also be found under alternative notions such as equitability. In this paper, we examine the properties of these allocations. In particular, we provide conditions for when maxsum envy-free or equitable allocations are Pareto optimal and give examples where fairness with Pareto optimality is not possible. We also prove that maxsum envy-free allocations have weakly greater welfare than maxsum equitable allocations when agents have structured valuations, and we derive an approximate version of this inequality for general valuations.

Objective 2: Complete versus incomplete information: quantifying the loss in social welfare arising due to partial information.

It is very common that the participants of a distributed system are required to make decisions based on their own local views rather than on a global view of the system. This lack of global view may have severe implications on the overall system’s performance. The goal is to quantify these implications.

In the paper "Signaling schemes for revenue maximization", which was published in ACM Conference on Electronic Commerce 2012 (co-authored with Yuval Emek, Iftah Gamzu, Renato Paes Leme and Moshe Tennenholtz), we introduce the study of signaling when conducting a second price auction of a probabilistic good whose actual instantiation is known to the auctioneer but not to the bidders. This framework can be used to model impressions selling in display advertising. We establish several results within this framework. First, we study the problem of computing a signaling scheme that maximizes the auctioneer's revenue in a Bayesian setting. We show that this problem is polynomially solvable for some interesting special cases, but computationally hard in general. Second, we establish a tight bound on the minimum number of signals required to implement an optimal signaling scheme. Finally, we show that at least half of the maximum social welfare can be preserved within such a scheme.

Objective 3: A prescriptive approach for playing games.

A fundamental question is whether game theory can provide recommendations to agents regarding their course of action. The challenge is to identify scenarios in which a prescriptive recommendation can be given to an agent or a set of agents.

In the paper "Signaling schemes for revenue maximization", which was published in ACM Conference on Electronic Commerce 2012 (co-authored with Yuval Emek, Iftah Gamzu, Renato Paes Leme and Moshe Tennenholtz), we consider the problem of instructing an auctioneer how to construct an optimal signaling scheme. A concrete example is a prescription of what attributes to reveal to potential advertisers about the underlying impression.

Summary of the progress of training and integration activities:

During my time in Harvard University I had the pleasure to work closely with the Econ-CS group. I learned a lot about the connection between practical and theoretical themes through numerous talks and seminars I attended regularly. In addition, I regularly sat in several classes, including the class of Prof. David Parkes on Algorithmic Game Theory (in Computer Science), and the class of Prof. Al Roth (a Nobel Laureate) on market design (in Economics), where he described real-life market design problems in which the theory of matching applies. Some prominent examples are kidney exchange and the assignments of students to schools. In addition to the insights I gained into the practical market design problems, I also learned new theoretical tools, which I then applied in my research. One of the skills I hoped to strengthen is mentoring and working with students. During my time at Harvard, I worked closely with John Lai, a PhD student at the Econ-CS group, and we were successful in co-authoring at least two papers. I also extended my collaborations with scholars from the Boston area (including Harvard University, MIT and MSR New England).