Showing papers in "Theoretical Economics in 2009"

Strategy-proofness and single-crossing

Abstract: This paper analyzes strategy-proof collective choice rules when individuals have single-crossing preferences on a finite and ordered set of social alternatives. It shows that a social choice rule is anonymous, unanimous, and strategy-proof on a maximal single-crossing domain if and only if it is an extended median rule with n 1 fixed ballots distributed over the individuals’ most preferred alternatives. As a by-product, the paper also proves that strategy-proofness implies the tops-only property. It also offers a strategic foundation for the so-called “single-crossing version” of the Median Voter Theorem, by showing that the median ideal point can be implemented in dominant strategies by a direct mechanism in which every individual reveals his true preferences.

Asymptotic ordinal inefficiency of random serial dictatorship

Abstract: We establish that the fraction of preference profiles for which the random serial dictatorship allocation is ordinally efficient vanishes for allocation problems with many object types. We consider also a probabilistic setting where in expectation agents have moderately similar preferences reflecting varying popularity across objects. In this setting we show that the probability that the random serial dictatorship mechanism is ordinally efficient converges to zero as the number of object types becomes large. We provide results with similarly negative content for allocation problems with many objects of each type. One corollary is that ordinal efficiency is a strict refinement of ex-post efficiency at most preference profiles.

A resurrection of the Condorcet Jury Theorem

Abstract: This paper analyzes the optimal size of a deliberating committee where (i) there is no conflict of interest among individuals and (ii) information acquisition is costly. The committee members simultaneously decide whether to acquire information, and then make the ex-post efficient decision. The optimal committee size, k*, is shown to be bounded. The main result of this paper is that any arbitrarily large committee aggregates the decentralized information more efficiently than the committee of size k*-2. This result implies that oversized committees generate only small inefficiencies.

Choice deferral and ambiguity aversion

Abstract: When confronted with uncertain prospects, people often exhibit both choice deferral and Ellsberg-type ambiguity aversion. This paper obtains a joint representation for these behavioral phenomena. The decision maker as portrayed by my model is willing to choose an uncertain prospect f over g rather than to defer this choice if and only if the expected utility of f is greater that or equal to the expected utility of g for every probability measure in a convex and closed set . This set is interpreted as a collection of the decision maker’s possible future beliefs. When choices cannot be deferred, the decision maker evaluates every uncertain prospect via an"-mixture of the least favorable element in the set and her current probabilistic belief p 2 . All components of my model are derived from observable preferences in an essentially unique way.

Robust Virtual Implementation

Abstract: In a general interdependent preference environment, we characterize when two payotypes can be distinguished by their rationalizable strategic choices without any prior knowledge of their beliefs and higher order beliefs. We show that two payotypes are strategically distinguishable if and only if they satisfy a separability condition. The separability condition for each agent essentially requires that there is not too much interdependence in preferences across agents. A social choice function - mapping payotype pro…les to outcomes - can be robustly virtu- ally implemented if there exists a mechanism such that every equilibrium on every type space achieves an outcome arbitrarily close to the social choice function. This de…nition is equivalent to requiring virtual implementation in iterated deletion of strategies that are strictly dominated for all beliefs. The social choice function is robustly measurable if strategically indistinguishable payotypes receive the same allocation. We show that ex post incentive compatibility and robust measurability are necessary and su¢ cient for robust virtual implementation.

Coalition formation under power relations

Abstract: We analyze the structure of a society driven by power relations. Our model has an exogenous power relation over the set of coalitions of agents. Agents determine the social order by forming coalitions. The power relations determine the ranking of agents in society for any social order. We study a cooperative game in partition function form and introduce a solution concept, the stable social order, which exists and includes the core. We investigate a refinement, the strongly stable social order, which incorporates a notion of robustness to variable power relations. We provide a complete characterization of strongly stable social orders.

Monopolistic group design with peer effects

Abstract: In a range of settings, private firms manage peer effects by sorting agents into different groups, be they schools, communities, or product categories. This paper considers such a firm, which controls group entry by setting a series of anonymous prices. We show that private provision systematically leads to two distortions relative to the efficient solution: first, agents are segregated too finely; second, too many agents are excluded from all groups. We demonstrate that these distortions are a consequence of anonymous pricing and do not depend upon the nature of the peer effects. This general approach also allows us to assess the way the ‘returns to scale’ of peer technology and the cost of group formation affect the optimal group structure.

Informed principal problems in generalized private values environments

Abstract: We show that a solution to the problem of mechanism selection by an informed principal exists in a large class of environments with “generalized private values”: the agents’ payo! functions are independent of the principal’s type. The solution is an extension of Maskin and Tirole’s (1990) strong unconstrained Pareto optimum. Our main condition for existence is that given any type profile the best possible outcome for the principal is the worst possible outcome for all agents. This condition is satisfied in most market environments. We also compute some examples of strong unconstrained Pareto optima and give an example for non-existence.

The Coase conjecture with incomplete information on the monopolist's commitment

Abstract: A key to the Coase conjecture is the monopolist’s inability to commit to a price, which leads consumers to believe that a high current price will be followed by low future prices. This paper studies the robustness of the Coase conjecture with respect to these beliefs of consumers. In particular, there is uncertainty over whether the monopolist is committed to a price (i.e. she may be a commitment type). Consequently, consumers are no longer certain that the price will change over time. I consider two kinds of commitment types. A behavioral commitment type charges an exogenously given price, while the rational commitment type optimally chooses a price. I show that the Coase conjecture is robust with regard to uncertainty over the monopolist’s commitment. When the probability of behavioral types is sufficiently small, as in the original Coase conjecture, the monopolist earns the competitive profit. When the probability of behavioral types is positive, unlike in the original Coase conjecture, there is positive delay. But the delay disappears as the probability approaches zero. When the commitment type is rational, unless the probability of the commitment type is sufficiently high, both normal and committed monopolists charge the competitive price, and thus there is no delay.