We study the problem of a seller who wants to maximize her revenue in situations where the outcome of the sale affects the nature of the future interaction between agents. We model those situations by assuming that an agent that does not acquire the object for sale incurs an externality that may depend both on the identity of the sufferer and on the identity of the final purchaser. We describe an optimal auction that has a unique Nash equilibrium in strictly dominant strategies. We show that: 1) Outside options are endogenously determined in equilibrium. Participation constraints and the ''threats'' in case of non-participation play an important role. 2) An optimizing seller can extract surplus also from buyers that do not obtain the auctioned object. 3) The seller is better off by not selling at all (while obtaining some payments) if externalities are large when compared to the pure profits that buyers achieve if they acquire the object. 4) The revenue-maximizing equilibrium is coalition-proof if buyers cannot organize side payments among themselves. (orig.)

We study the optimal design of organizations under the assumption that agents in a contest care about their relative position. A principal determines the number and size of status categories in order to maximize output. We first consider the pure status case without tangible prizes. Our results connect the optimal partition in status categories to properties of the distribution of ability among contestants. The top status category always contains a unique element. For distributions that have an increasing failure rate (IFR), a proliferation of status classes is optimal, whereas the optimal partition involves only two categories if the distribution of abilities is sufficiently concave. Moreover, for IFR distributions, a coarse partition with two status categories achieves at least half of the output obtained in the optimal partition with many categories. Finally, if status is derived solely from monetary rewards, we show that the optimal partition in status classes contains only two categories.

We characterize the set of extreme points of monotonic functions that are either majorized by a given function f or themselves majorize f and show that these extreme points play a crucial role in many economic design problems. Our main results show that each extreme point is uniquely characterized by a countable collection of intervals. Outside these intervals the extreme point equals the original function f and inside the function is constant. Further consistency conditions need to be satisfied pinning down the value of an extreme point in each interval where it is constant. We apply these insights to a varied set of economic problems: equivalence and optimality of mechanisms for auctions and (matching) contests, Bayesian persuasion, optimal delegation, and decision making under uncertainty.

The sensitivity of Bayesian implementation to agents' beliefs about others suggests the use of more robust notions of implementation such as ex post implementation, which requires that each agent's strategy be optimal for every possible realization of the types of other agents. We show that the only deterministic social choice functions that are ex post implementable in generic mechanism design frameworks with multidimensional signals, interdependent valuations, and transferable utilities are constant functions. In other words, deterministic ex post implementation requires that the same alternative must be chosen irrespective of agents' signals. The proof shows that ex post implementability of a nontrivial deterministic social choice function implies that certain rates of information substitution coincide for all agents. This condition amounts to a system of differential equations that are not satisfied by generic valuation functions.

We study auction design for bidders equipped with non-expected utility preferences that exhibit constant risk aversion (CRA). The CRA class is large and includes loss-averse, disappointment-averse, mean-dispersion, and Yaari’s dual preferences as well as coherent and convex risk measures. Any preference in this class displays first-order risk aversion, contrasting the standard expected utility case which displays second-order risk aversion. The optimal mechanism offers “ full-insurance” in the sense that each agent’s utility is independent of other agents’ reports. The seller excludes less types than under risk neutrality and awards the object randomly to intermediate types. Subjecting intermediate types to a risky allocation while compensating them when losing allows the seller to collect larger payments from higher types. Relatively high types are willing to pay more, and their allocation is efficient.

We use the tools of mechanism design combined with the theory of risk measures to analyze how a cash-constrained owner of an asset with known, stochastic returns raises capital from a population of investors who differ in their risk aversion and budget constraints. The issuer partitions the asset’s cash flow into several asset-backed securities, one for each type of investor. The optimal partition conforms to the commonly observed practice of tranching into senior debt, junior debt, and equity. Tranching arises endogenously due to the differences in risk appetites among agents and in the budget constraints they face. (JEL D81, D82, G12, G41, G51)

We study a generalization of the classical monopoly insurance problem under adverse selection (see Stiglitz 1977) where we allow for a random distribution of losses, possibly correlated with the agent’s risk parameter that is private information. Our model explains patterns of observed customer behavior and predicts insurance contracts most often observed in practice: these consist of menus of several deductible-premium pairs or menus of insurance with coverage limits–premium pairs. A main departure from the classical insurance literature is obtained here by endowing the agents with risk-averse preferences that can be represented by a dual utility functional (Yaari 1987). (JEL D81, D82, D86, D91, G22)

We derive the symmetric, revenue-maximizing allocation of several units among agents who take costly actions that influence their values. The problem is equivalent to a reduced-form model where agents have nonexpected utility. The uniform-price auction and the discriminatory pay-your-bid auction with reserve prices that react to both demand and supply constitute symmetric, optimal mechanisms. We also identify a condition under which the overall optimal mechanism is indeed symmetric and illustrate the structure of the optimal asymmetric mechanism when the condition fails. The main tool in our analysis is an integral inequality based on Fan and Lorentz (1954).

We consider a standard social choice environment with linear utilities and independent, one-dimensional, private types. We prove that for any Bayesian incentive compatible mechanism there exists an equivalent dominant strategy incentive compatible mechanism that delivers the same interim expected utilities for all agents and the same ex ante expected social surplus. The short proof is based on an extension of an elegant result due to Gutmann, Kemperman, Reeds, and Shepp (1991). We also show that the equivalence between Bayesian and dominant strategy implementation generally breaks down when the main assumptions underlying the social choice model are relaxed or when the equivalence concept is strengthened to apply to interim expected allocations.