2012 Abstract

Center for Theoretical Economics 

2012 Kansas Workshop on Economic Theory

May 4, 2012

Auction Design with Fairness Concerns:

Subsidies vs. Set Asides 

By Mallesh Pai and Rakesh Vohra

Government procurement and allocation programs often use subsidies and set-asides favoring small businesses and other target groups to address fairness concerns. These concerns are in addition to standard objectives such as efficiency and revenue. We study the design of the optimal mechanism for a seller concerned with effciency, subject to a constraint to favor a target group. In our model, buyers' private values are determined by costly pre-auction investment. If the constraint is distributional, i.e. to guarantee that the target group wins 'sufficiently often', then the constrained efficient mechanism is a at subsidy. This is consistent with findings in the empirical literature. In contrast, if the constraint is to ensure a certain investment level by the target group, the optimal mechanism is a type dependent subsidy. In this case a set aside may be better than a at or percentage subsidy.

Endogenous Budget Constraints in Auctions

By Justin Burkett

In prior literature, bidders' budget constraints have been shown to change revenue and efficiency rankings among auction formats. These results, however, are based on the implicit assumption that the nature of the budget constraint is unaffected by auction rules. I extend the standard symmetric model of auctions for a single good to include principals responsible for deciding on the bidder's budget. Each principal optimally constrains the bidder to mitigate an agency problem between the two. I show that the outcomes of the first and second price auctions generally agree with those from auction models without budget constraints.

Financial Economics without Probablistic Prior 

By Bernard Cornet and Frank Riedel

The treatment of uncertainty in general equilibrium theory in the style of Arrow and Debreu does not require a prior probability on the state space. Finance models nevertheless treat payoffs as random variables, implicitly or explicitly using a known probability distribution. In the light of Knightian uncertainty, we might challenge such an assumption on the probabilistic sophistication of our market model. The present paper shows that one can still develop a sound model of arbitrage pricing under complete Knightian uncertainty as long as certain continuity conditions are met. The pricing functional given by an arbitrage-free market can be identified with a full support martingale measure (instead of equivalent martingale measure). We relate the no arbitrage theory to economic equilibrium by establishing a variant of the Harrison-Kreps-Theorem on viability and no arbitrage. Finally, we consider (super)hedging of contingent claims and embed it in a classical indefinite-dimensional linear programming problem.

Limited Enforcement, Bubbles and Trading in Incomplete Markets 

By Camelia Bejan and Florin Bidian

Rational bubbles are believed to be fragile and unable to explain the trading frenzy associated to price run-ups. With limited enforcement of credit contracts and endogenous debt limits designed to prevent default and allow for maximal credit expansion, a large class of bubbles can be introduced in asset prices by appropriately tightening agents' debt limits. By not affecting consumption, these bubbles are ideally suited to explain a variety of asset pricing puzzles. They can generate large increases in trade volume until they crash. Nonpositivity of debt limits restricts the potential for bubble injections to assets in zero supply or to equilibria with an infinite present value of aggregate endowment. Such equilibria are common in economies with limited enforcement, where interest rates are low to induce debt repayment (Bidian and Bejan 2012).

Preferences for Information and Ambiguity

By Jian Li

This paper studies intrinsic preferences for information and the link between intrinsic information attitudes and ambiguity attitudes in settings with subjective uncertainty. We enrich the standard dynamic choice model in two dimensions. First, we introduce a novel choice domain that allows preferences to be indexed by the intermediate information, modeled as partitions of the underlying state space. Second, conditional on a given information partition, we allow preferences over state-contingent outcomes to depart from expected utility axioms. In particular we accommodate ambiguity sensitive preferences. We show that aversion to partial information is equivalent to a property of static preferences called Event Complementarity. We show that Event Complementarity and aversion to partial information are closely related to ambiguity attitudes. In familiar classes of ambiguity preferences, we identify conditions that characterize aversion to partial information.

Coalitional Stochastic Stability in Games, Networks and Markets 

By Ryoji Sawa

This paper examines a dynamic process of unilateral and joint deviations of agents and the resulting stochastic evolution of social conventions in a class of interactions that includes normal form games, network formation games, and simple exchange economies. Over time agents unilaterally and jointly revise their strategies based on the improvements that the new strategy profile offers them. In addition to the optimization process, there are persistent random shocks on agents utility that potentially lead to switching to suboptimal strategies. Under a logit specification of choice probabilities, we characterize the set of states that will be observed in the long-run as noise vanishes. We apply these results to examples including certain potential games and network formation games, as well as to the formation of free trade agreements across countries.

Treatment Response with Social Interactions:

Partial Identification via Monotone Comparative Statics 

By Natalia Lazzati

However, there is also evidence that introducing a similar but inferior z may hurt y more than x and can even increase the probability of choosing x (attraction effect). We provide a definition of similarity based only on the random choice process and show that z is more like x than y if and only if the correlation between z and x's signals is larger than the correlation between z and y's signals. Our main result establishes that when z and x are correlated and sufficiently close in utility, introducing z hurts y more than x and may even increase the probability of choosing x early in the learning process, but eventually hurts x more than y. Hence, the attraction effect arises when the decision maker is relatively uninformed, while Tversky's hypothesis holds when she becomes sufficiently familiar with the options. We then show that if z is similar to x and sufficiently inferior, the attraction effect never disappears.

Comparative Statics and the Gross Substitutes Property of Consumer Demand

By Anne-Christine Barthel

The gross substitutes property of demand is very useful in trying to understand stability of the standard Arrow-Debreu competitive equilibrium. Unlike most attempts in the literature to derive this property that rely on aspects of the demand curve, we use new results on the comparative statics of demand in Quah (2007) toprovide simple and easy conditions on utility functions that yield the gross substitutes property. Our approach is grounded in the standard comparative statics decomposition of a change in demand due to a change in price into a substitution effect and an income effect. Quah's assumptions on the utility function are helpful to sign the income effect. Combined with an assumption on elasticity of marginal rate of substitution, we can sign the overall effect and obtain gross substitutes. We apply this assumption to the family of constant elasticity of substitution preferences. As a by-product, we also present conditions which yield the gross complements property.