Mechanism Design with Limited Commitment

We develop a tool akin to the revelation principle for mechanism design with limited commitment. We identify a canonical class of mechanisms rich enough to replicate the payoffs of any equilibrium in a mechanism-selection game between an uninformed designer and a privately informed agent. A cornerstone of our methodology is the idea that a mechanism should encode not only the rules that determine the allocation, but also the information the designer obtains from the interaction with the agent. Therefore, how much the designer learns, which is the key tension in design with limited commitment, becomes an explicit part of the design. We show how this insight can be used to transform the designer's problem into a constrained optimization one: To the usual truthtelling and participation constraints, one must add the designer's sequential rationality constraint.Comment: Added an omitted assumption in Section 4 (see footnote 21 and the proof of Proposition 4.1

Fair Divisions as Attracting Nash Equilibria of Simple Games

We consider the problem of allocating a finite number of divisible homogeneous goods to N = 2 individuals, in a way which is both envy-free and Pareto optimal. Building on Thomson (2005 Games and Economic Behavior), a new simple mechanism is presented here with the following properties: a) the mechanism fully implements the desired divisions, i.e. for each preference profile the set of equilibrium outcomes coincides with the set of fair divisions; b) the set of equilibria is a global attractor for the best-reply dynamics. Thus, players myopically adapting their strategies settle down in an fair division. The result holds even if mixed strategies are used.Fair divisions, envy-free, implementation, best reply dynamics

Optimal complementary auctions

This paper considers the situation where two products are sold by the same seller, but to disjoint sets of potential buyers. Externalities may arise from each market outcome to the other. The paper examines the nature of the seller's optimal mechanism, and, for example in the case of positive externalities, it is shown that the allocation decision in either market depends on the highest types in both markets. The optimal mechanism can be implemented by an indirect mechanism that essentially charges winning bidders for the value of their externalities. The analysis is applied to the sale of public sector franchises including exploration and development rights for oil and gas tracts