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.

No abstract

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.