A Note on Budget Balance under Interim Participation Constraints: The Case of Independent Types

We provide a simple proof of the equivalence between ex ante and ex post budget balance constraints in Bayesian mechanism design with independent types when participation decisions are made at the interim stage. The result is given an interpretation in terms of efficient allocation of risk.

Robust mechanism design and dominant strategy voting rules

We develop an analysis of voting rules that is robust in the sense that we do not make any assumption regarding voters’ knowledge about each other. In dominant strategy voting rules, voters’ behavior can be predicted uniquely without making any such assumption. However, on full domains, the only dominant strategy voting rules are random dictatorships. We show that the designer of a voting rule can achieve Pareto improvements over random dictatorship by choosing rules in which voters’ behavior can depend on their beliefs. The Pareto improvement is achieved for all possible beliefs. The mechanism that we use to demonstrate this result is simple and intuitive, and the Pareto improvement result extends to all equilibria of the mechanism that satisfy a mild refinement. We also show that the result only holds for voters’ interim expected utilities, not for their ex post expected utilities.robust mechanism design; dominant strategies; voting; Gibbard-Satterthwaite theorem

When are signals complements or substitutes?

The paper introduces a notion of complementarity (substitutability) of two signals which requires that in all decision problems each signal becomes more (less) valuable when the other signal becomes available. We provide a general characterization which relates complementarity and substitutability to a Blackwell-comparison of two auxiliary signals. In a special setting with a binary state space and binary, symmetric signals, we find an explicit characterization that permits an intuitive interpretation of complementarity and substitutability. We demonstrate how these conditions extend to the general case. Finally, we study implications of complementarity and substitutability for information acquisition and in a second price auction.

Strategically Simple Mechanisms

We define and investigate a property of mechanisms that we call "strategic simplicity," and that is meant to capture the idea that, in strategically simple mechanisms, strategic choices require limited strategic sophistication. We define a mechanism to be strategically simple if choices can be based on first-order beliefs about the other agents' preferences and first-order certainty about the other agents' rationality alone, and there is no need for agents to form higher-order beliefs, because such beliefs are irrelevant to the optimal strategies. All dominant strategy mechanisms are strategically simple. But many more mechanisms are strategically simple. In particular, strategically simple mechanisms may be more flexible than dominant strategy mechanisms in the bilateral trade problem and the voting problem

Efficient compromising

Two agents must select one of three alternatives. Their ordinal rankings are commonly known and diametrically opposed. Efficiency requires choosing the alternative the agents rank second whenever the weighted sum of their von Neumann Morgenstern utilities is higher than under either agent's favorite alternative. The agents' utilities of the middle-ranked alternative are i.i.d., privately observed random variables. In our setup, which is closely related to a public goods problem where agents face liquidity constraints but no participation constraints, decision rules that truthfully elicit utilities and implement efficient decisions do not exist. We provide analytical and numerical results on second-best rules