Optimal auction with resale—a characterization of the conditions

Zheng has proposed a seller-optimal auction for (asymmetric) independent-private-value environments where inter-bidder resale is possible. Zheng’s construction requires novel assumptions—Resale Monotonicity, Transitivity, and Invariance—on the bidders’ value distribution profile. The only known examples of distribution profiles satisfying these assumptions in environments with three or more bidders are uniform distributions. Using inverse virtual valuation functions as a novel tool, we characterize the set of distribution profiles satisfying Zheng’s assumptions. Our characterization result shows that the assumptions, while being strong, are satisfied by many non-uniform distribution profiles. Hence, Zheng’s result applies more generally than one may have thought before. A crucial step in our analysis is to show that Invariance implies Resale Monotonicity and Transitivity.     

Veto-based delegation

In a principal-agent model with hidden information and no monetary transfers, I establish the veto-power principle: the principal can implement an optimal outcome through veto-based delegation with a properly chosen default decision. This result demonstrates the exact nature of commitment powers required by the principal: to design the default outcome and to ensure that she has almost no formal control over the agent's decisions.     

Stochastic mechanisms in settings without monetary transfers: The regular case

We analyze relative performance of stochastic and deterministic mechanisms in an environment that has been extensively studied in the literature on communication (e.g., [Vincent P. Crawford, Joel Sobel, Strategic information transmission, Econometrica 50 (6) (1982) 1431-1451]) and optimal delegation (e.g., [Bengt Holmström, On the theory of delegation, in: M. Boyer, R.E. Kihlstrom (Eds.), Bayesian Models in Economic Theory, North-Holland, 1984, pp. 115-141]): a principal-agent model with hidden information, no monetary transfers, and single-peaked preferences. We demonstrate that under the common assumption of quadratic payoffs and a certain regularity condition on the distribution of private information and the agent's bias, the optimal mechanism is deterministic. We also provide an explicit characterization of this mechanism.     

Task scheduling and moral hazard

We study a two-period moral hazard problem with risk-neutral and wealth-constrained agents and three identical tasks. We show that the allocation of tasks over time is important if there is a capacity constraint on the number of tasks that can be performed in one period. We characterize the optimal schedule of tasks over time and the optimal assignment of tasks to agents conditional on the outcomes of previous tasks. In particular, we show that delaying tasks is optimal if and only if the effect of an agent’s effort on the probability of success is relatively low. We have benefitted from helpful discussions with A. Roider, L. Samuelson, and U. Schweizer. The paper has been substantially improved due to the detailed and very valuable comments of an Associate Editor. Financial support by Deutsche Forschungsgemeinschaft, SFB/TR15, is gratefully acknowledged.