We consider the classic principal-agent model of contract theory, in which a principal designs an outcome-dependent compensation scheme to incentivize an agent to take a costly and unobservable action. When all of the model parameters-including the full distribution over principal rewards resulting from each agent action-are known to the designer, an optimal contract can in principle be computed by linear programming. In addition to their demanding informational requirements, such optimal contracts are often complex and unintuitive, and do not resemble contracts used in practice.This paper examines contract theory through the theoretical computer science lens, with the goal of developing novel theory to explain and justify the prevalence of relatively simple contracts, such as linear (pure commission) contracts. First, we consider the case where the principal knows only the first moment of each action's reward distribution, and we prove that linear contracts are guaranteed to be worst-case optimal, ranging over all reward distributions consistent with the given moments. Second, we study linear contracts from a worst-case approximation perspective, and prove several tight parameterized approximation bounds.

Designing double auctions is a complex problem, especially when there are restrictions on the sets of buyers and sellers that may trade with one another. The goal of this paper is to develop "black-box reductions" from doubleauction design to the exhaustively-studied problem of designing single-sided mechanisms.We consider several desirable properties of a double auction: feasibility, dominant-strategy incentive-compatibility, the still stronger incentive constraints offered by a deferred-acceptance implementation, exact and approximate welfare maximization, and budget-balance. For each of these properties, we identify sufficient conditions on the two one-sided mechanisms-one for the buyers, one for the sellers-and on the method of composition, that guarantee the desired property of the double auction.Our framework also offers new insights into classic double-auction designs, such as the VCG and McAfee auctions with unit-demand buyers and unit-supply sellers.

We study interdependent value settings [Milgrom and Weber 1982] and extend several fundamental results from the well-studied independent private values model to these settings. For revenue-optimal mechanism design, we give conditions under which Myerson's virtual value-based mechanism remains optimal with interdependent values. One of these conditions is robustness of the truthfulness and individual rationality guarantees, in the sense that they are required to hold ex post. We then consider an even more robust class of mechanisms called "prior independent" (a.k.a. "detail free"), and show that by simply using one of the bidders to set a reserve price, it is possible to extract near-optimal revenue in an interdependent values setting. This shows that a considerable level of robustness is achievable for interdependent values in singleparameter environments.

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Competitive equilibrium from equal incomes (CEEI) is a classic solution to the problem of fair and efficient allocation of goods (Foley 1967, Varian 1974). Every agent receives an equal budget of artificial currency with which to purchase goods, and prices match demand and supply. However, a CEEI is not guaranteed to exist when the goods are indivisible even in the simple two-agent, single-item market. Yet it is easy to see that, once the two budgets are slightly perturbed (made generic), a competitive equilibrium does exist. In this paper, we aim to extend this approach beyond the single-item case and study the existence of equilibria in markets with two agents and additive preferences over multiple items. We show that, for agents with equal budgets, making the budgets generic—by adding vanishingly small random perturbations—ensures the existence of equilibrium. We further consider agents with arbitrary nonequal budgets, representing nonequal entitlements for goods. We show that competitive equilibrium guarantees a new notion of fairness among nonequal agents and that it exists in cases of interest (such as when the agents have identical preferences) if budgets are perturbed. Our results open opportunities for future research on generic equilibrium existence and fair treatment of nonequals.

Most results in revenue-maximizing mechanism design hinge on "getting the price right" -offering to sell a good to bidders at a price low enough to encourage a sale, but high enough to garner non-trivial revenue.Getting the price right can be hard work, especially when the seller has little or no a priori information about bidders' valuations. Moreover, this approach becomes prohibitively challenging when there are multiple indivisible goods on the market, in which case getting the prices right is a long-standing open problem, even for matching markets with symmetric bidders (each of whom seeks a single good).In this paper we apply a robust approach to designing auctions for revenue. Instead of relying on prior knowledge regarding bidder valuations, we "let the market do the work" and let prices emerge from competition for scarce goods. We analyze the revenue guarantees of one of the simplest imaginable implementations of this idea: first, enhance competition in the market, whether by increasing demand or by limiting supply; second, run a standard second-price (Vickrey) auction. Enhancing competition is a natural way to bypass lack of knowledge -a seller who does not know how to set prices can instead set quantities (of bidders and/or goods on the market). We prove that simultaneously for many valuation distributions, this achieves expected revenue at least as good as the optimal revenue in the original market or guarantees a constant approximation to it.Our robust and simple approach thus provides a handle on the elusive optimal revenue in multi-item matching markets, and shows when the use of welfare-maximizing Vickrey auctions is justified even if revenue is a priority. By establishing quantitative trade-offs, our work provides guidelines for a seller in choosing among alternative revenue-extracting strategies: sophisticated pricing based on market research, advertising to draw additional bidders, and limiting supply to create scarcity on the market.

Understanding when equilibria are guaranteed to exist is a central theme in economic theory, seemingly unrelated to computation. This paper shows that the existence of pricing equilibria is inextricably connected to the computational complexity of related optimization problems: demand oracles, revenue-maximization, and welfare-maximization. This relationship implies, under suitable complexity assumptions, a host of impossibility results. We also suggest a complexity-theoretic explanation for the lack of useful extensions of the Walrasian equilibrium concept: such extensions seem to require the invention of novel polynomial-time algorithms for welfare-maximization.

We study a Bayesian persuasion setting with binary actions (adopt and reject) for Receiver. We examine the following question -how well can Sender perform, in terms of persuading Receiver to adopt, when ignorant of Receiver's utility? We take a robust (adversarial) approach to study this problem; that is, our goal is to design signaling schemes for Sender that perform well for all possible Receiver's utilities. We measure performance of signaling schemes via the notion of (additive) regret: the difference between Sender's hypothetically optimal utility had she known Receiver's utility function and her actual utility induced by the given scheme.