2009 Abstracts

Center for Theoretical Economics 

2009 Kansas Workshop on Economic Theory -- Abstracts of Papers 

June 19, 2009

A Simple Model of Bankruptcy in General Equilibrium

By Matthew Hoelle

In this paper, I introduce a simple model of household bankruptcy into a dynamic general equilibrium model. The basic idea is that households can trade in assets in the initial state and then choose not to fulfill their portfolio commitments in future states. When this occurs, the returns to creditors must be diluted in order for markets to clear. Under this formulation, I prove that a bankruptcy equilibrium exists and even show how the result generalizes to a model with real costs of bankruptcy. I also study how a production model can be analyzed using the exact same framework where the production model is such that (i) firms finance production using the bond market and (ii) both firms and households can declare bankruptcy. 

Existence of Equilibria in Financial Markets

With Restricted Participation

By Bernard Cornet and Ramu Gopalan 

It is well known that equilibrium asset prices will not offer arbitrage opportunities to individuals. Using an approach that dates back to Cass (1984), we seek to isolate arbitrage free asset prices that are also equilibrium asset prices. However we do this when each agent's portfolio choice is restricted to a closed, convex set containing zero (as in Siconolfi, 1986). In the presence of such portfolio restrictions we need to confine our attention to market arbitrage free asset prices. We also describe a considerably weak condition on the space of income transfers (the union of the agents' payoff sets in linear), that ensure these asset prices to be part of a financial equilibrium. We also show that weakning this condition further to require the union of the payoff sets to be convex results only in a quasi-equilibrium. Staying in the Cass framework, we consider an exchange economy with nominal assets, but allow for multiple (finite) periods and very general preference relations. Moreover we show the existence theorem using the approach of Martins Da-Rocha and Triki (2005), and hence do not resort to the Cass trick. 

Context-Dependent Forward Induction Reasoning

By Pierpaolo Battigalli and Amanda Friedenberg 

This paper studies the case where a game is played in a particular context. The context influences what beliefs players hold. As such, it may affect forward induction reasoning: If players rule out specific beliefs, they may not be able to rationalize observed behavior. The effects are not obvious. Context-laden forward induction may allow outcomes precluded by context-free forward induction. At the formal level, contextual reasoning is defined within an epistemic structure. In particular, we represent contextual forward induction reasoning as "rationality and common strong belief of rationality" (RCSBR) within an arbitrary type structure. (The concept is due to Battigalli-Siniscalchi [6, 2002].) We ask: What strategies are consistent with RCSBR (across all type structures)? We show that the RCSBR is characterized by a solution concept we call Extensive Form Best Response Sets (EFBRS's). We go on to study the EFBRS concept in games of interest.

You Won't Harm Me IF You Fool Me

By Federico Echenique and Eran Shmaya 

A decision maker faces a new theory of how certain events unfold over time. The theory matters for choices she needs to make, but possibly the theory is a fabrication. We show that there is a test which is guaranteed to pass a true theory, and which is also conservative: A false theory will only pass when adopting it over the decision maker's initial theory would not cause substantial harm; if the agent is fooled she will not be harmed. We also study a society of conservative decision makers with different initial theories. We uncover pathological instances of our test: a society collectively rejects most theories, be they true or false. But we also find well-behaved instances of our test, collectively accepting true theories and rejecting false. Our tests builds on tests studied in the literature in the context of non-strategic inspectors. 

A Theory of Temptation without Uncertainty

By Madhav Chandrasckher

The paper studies menu choice problems in which the decision maker faces no ex ante un-certainty about her ex post preferences, yet nevertheless exhibits non-trivial menu preferences due to the presence of self-control problems. We introduce a new class of utilities which generalize the Gul-Pesendorfer (2001, 2005) 'No Self-Control' model. The main results in the paper provide utility representation theorems for this class of utilities. 

Monotone Comparative Statics for Games With 

Strategic Substitutes

By Sunanda Roy and Tarun Sabarwal

Under some conditions, parameterized games with strategic substitutes exhibit monotone comparative statics of equilibria. These conditions relate to a tradeoff between a direct parameter effect and an opposing, indirect strategic substitute effect. If the indirect effect does not dominate the direct effect, monotone comparative statics of equilibria are guaranteed. These conditions are available for best-response functions, differentiable payoff functions, and general payoff functions. Results are extended to payoff functions that my yield best-response correspondences. The analysis applies to asymmetric equilibria. Several examples are provided.