Knightian Analysis of the Vickrey Mechanism

We analyze the Vickrey mechanism for auctions of multiple identical goods when the players have both Knightian uncertainty over their own valuations and incomplete preferences. In this model, the Vickrey mechanism is no longer dominant-strategy, and we prove that all dominant-strategy mechanisms are inadequate. However, we also prove that, in undominated strategies, the social welfare produced by the Vickrey mechanism in the worst case is not only very good, but also essentially optimal.Comment: To appear in Econometric

Robustness of the k-double auction under Knightian uncertainty

This dissertation considers the robustness of private value and common value k-double auctions when those markets are populated by regret minimizers. Regret minimizing agents, unlike typical expected utility maximizers, need not commit to a single prior in their decision rule. In fact, it is a feature of the minimax regret decision rule that is not based on any prior. This makes the decision rule an interesting one for agents who face Knightian Uncertainty. A decision problem involves Knightian uncertainty if the agents know the possible outcomes but not those outcomes' probabilities -- as may be the case in a new market. This dissertation shows that in a private value k-double auction, minimax regret traders will not converge to price-taking behavior as the market grows. Similarly, in a common value auction, traders' behavior may depend on the parameter k, but does not depend on the number of other traders in the market. The invariance of regret minimizing traders' strategies to the size of the markets they inhabit is not an accident of the sealed bid double auction institution. In fact, it is a consequence of the symmetry axiom. The final chapter in this dissertation shows that any agents in a k-double auction who use decision rules that accord with the symmetry axiom, then their bids and asks will not depend on the number of rival traders

Mechanism design with maxmin agents: Theory and an application to bilateral trade

This paper studies mechanism design when agents are maxmin expected utility maximizers. A first result gives a general necessary condition for a social choice rule to be implementable. The condition combines an inequality version of the standard envelope characterization of payoffs in quasilinear environments with an approach for relating agents' maxmin expected utilities to their objective expected utilities under any common prior. The condition is then applied to give an exact characterization of when efficient trade is possible in the bilateral trading problem of Myerson and Satterthwaite, 1983, under the assumption that agents know little beyond each other's expected valuation of the good (which is the information structure that emerges when agents are uncertain about each other's ability to acquire information). Whenever efficient trade is possible, it may be implemented by a relatively simple double auction format. Sometimes, an extremely simple reference price rule can also implement efficient trade

Efficient Implementation with Interdependent Valuations and Maxmin Agents

We consider a single object allocation problem with multidimensional signals and interdependent valuations. When agents signals are statistically independent, Jehiel and Moldovanu show that efficient and Bayesian incentive compatible mechanisms generally do not exist. In this paper, we extend the standard model to accommodate maxmin agents and obtain necessary as well as sufficient conditions under which efficient allocations can be implemented. In particular, we derive a condition that quantifies the amount of ambiguity necessary for efficient implementation. We further show that under some natural assumptions on the preferences, this necessary amount of ambiguity becomes sufficient. Finally, we provide a definition of informational size such that given any nontrivial amount of ambiguity, efficient allocations can be implemented if agents are sufficiently informationally small

Compromise, don't optimize:Generalizing perfect Bayesian equilibrium to allow for ambiguity

We introduce a solution concept for extensive-form games of incomplete information in which players can have multiple priors. Players’ choices are based on the notions of complaints and compromises. Complaints come from hypothetical assessors who have different priors and evaluate the choices of the players. Compromises are choices that aim to make these complaints small. The resulting solution concept is called perfect compromise equilibrium and generalizes perfect Bayesian equilibrium. We use this concept to provide insights into how ambiguity influences Cournot and Bertrand markets, public good provision, markets for lemons, job market signaling, bilateral trade with common value, and forecasting

Optimal Auctions and Pricing with Limited Information

Information availability plays a fundamental role in decision-making for business operations. The present dissertation aims to develop frameworks and algorithms in order to guide a decision-maker in environments with limited information. In particular, in the first part, we study the fundamental problem of designing optimal auctions while relaxing the widely used assumption of common prior. We are able to characterize (near-)optimal mechanisms and associated performance. In the second part of the dissertation, we focus on data-driven pricing in the low sample regime. More precisely, we study the fundamental problem of a seller pricing a product based on historical information consisting of one sample of the willingness-to-pay distribution. By drawing connection with the statistical theory of reliability, we propose a novel approach, using dynamic programming, to characterize near-optimal data-driven pricing algorithms and their performance. In the last part of the dissertation, we delve into the detailed practical operations of the online display advertising marketplace from an information structure perspective. In particular, we analyze the tactical role of intermediaries within this marketplace and their impact on the value chain. In turn, we make the case that under some market conditions, there is a potential for Pareto improvement by adjusting the role of these intermediaries