2013 Abstracts

Center for Theoretical Economics

2013 Kansas Workshop on Economic Theory -- Abstracts of Papers 

May 10, 2013

Rational Inattention and State Dependent Stochastic Choice

By Andrew Caplin and Mark Dean

Economists are increasingly interested in how attention impacts behavior. Rational inattention theory models the allocation of attention in an optimizing framework. We characterize patterns of stochastic choice consistent with a general model of rational inattention, making no assumptions about attentional costs or constraints. We experimentally elicit "state dependent" stochastic choice data of the form required to test the model. Rational inattention theory does a qualitative better job of matching this data than do random utility models that ignore the link between incentives and attention.

Preference for Flexibility and Randomization under Ambiguity

By Kota Saito

Under ambiguity, an agent might prefer to randomize his choice for hedging. In order to do that, his choice set must be flexible, or must contain more than one element. This paper studies how the flexibility of the agent's choice set affects his randomization over the set and his ambiguity-averse behaviors. As far as we know, this question has yet to be studied theoretically. However, Ellsberg (1961) himself has mentioned the connection between a preference for flexibility and a preference for randomization, as we review in the following paragraphs. This paper provides a step toward filling the gap by providing an axiomatic model that identifies the connection.

Procurement with Adverse Selection and Dynamic Moral Hazard

By Terrence R. Johnson

Consider a principal seeking to contract with one of many firms to undertake a risky project in an environment that suffers from both adverse selection and dynamic moral hazard. The likelihood of project success at each moment depends on the amount of work already completed, which is observed only by the contracted firm. Firms can siphon a portion of the funds intended for the project and use the rest to create an illusion of productivity. Consequently, inefficient firms can bid for contracts simply to siphon, efficient firms who win may shirk, and firms who succeed can siphon funds rather than report success to the principal. I show that under standard assumptions, dynamic contracts can be constructed that mitigate all inefficiency arising from dynamic moral hazard. These contracts can be implemented through a generalization of a procurement auction that features endogenous penalties for failure and time-varying awards for success.

Strategic Experimentation with Congestion: Private and Public Monitoring

By Caroline Thomas

This paper analyses the question of strategic experimentation with direct payoff externalities under public and private monitoring. We consider a multi-armed bandit model in which two players choose between learning about the quality of a Poisson process with unknown arrival rate, and competing for the use of a single shared safe option that can only be used by one player at a time.

We first consider a pure stopping-game where players cannot reverse their decision to switch to the safe option, and show that in equilibrium the players' incentive to preempt one another leads to inefficient unraveling of the switching decision. We then contrast it with a game where the decision to switch to the safe option is revocable, and show that there is a strategic option-value generated by a player's ability to return to her Poisson process in the event of her opponent's successful experimentation. In equilibrium, the player ex-ante most likely to have a good Poisson process occupies the safe option first and forces her opponent to experiment for a finite duration of time. We describe the striking equilibrium dynamics and resulting inefficiencies. We then ask whether the existence of such a strategic option-value arising purely from the player's competition for access to the safe option persists under private monitoring. We show that when a player observes her opponent's behaviour but not his realized payoffs, an equilibrium in which a player forces her opponent to experiment only temporarily exist only if players are ex-ante optimistic enough about the quality of their Poisson process. We characterize the equilibria of the games with private monitoring when the decision to switch to the safe option is revocable and when it is not.

Extending the Scope of Monotone Comparative Statics Results

By Anne-Christine Barthel

Generally we can distinguish between two types of comparative statics problems that have been approached with lattice programming methods. The first type of problem considers the change of the optimal solution to a maximization problem as the objective function changes, the other type the change due to a change in the constraint set. Comparative statics theorems have been developed for both cases under cardinal and ordinal assumptions in the literature; Quah (2007) expanded existing work by making it applicable to optimization problems with a new, weaker order on the constraint sets. 

The idea of this paper is to extend the existing comparative statics results to an even broader class of constrained optimization problems. We combine the two previously mentioned types of maximization problems and apply the existing comparative statics theorems to cases with changes in both the objective function and non-lattice constraint sets. Examples and applications from a variety of areas in economics, such as consumer theory, producer theory and environmental economics, are provided as well.

Trading Dynamics in the Market for Lemons

By Ayca Kaya and Kyungmin Kim

We present a dynamic model of trading under adverse selection. A seller faces a sequence of randomly arriving buyers, each of whom receives a noisy signal about the quality of the asset and makes a price offer. We show that there is generically a unique equilibrium and fully characterize the resulting trading dynamics. Buyers' beliefs about the quality of the asset gradually increase or decrease over time, depending on the initial level. The rich trading dynamics provides a way to overcome a common criticism on dynamic adverse selection, thereby broadening its applicability. We also show that improving asset transparency may lead to gains or losses in efficiency.

Predictive Repeated Game Theory: Measures and Experiments

By Laurent Mathevet and Julian Romero

One of the fundamental results in repeated games is the Folk theorem, which predicts a plethora of equilibrium outcomes. Many have argued that this extreme number of equilibria is a virtue, as it can explain a variety of different behaviors. However, this result leaves us with almost no predictive power. This paper provides measures for evaluating the predictive power of a theory given experimental data. After running experiments with human subjects in the experimental laboratory, we use these measures to compare (subgame perfect Nash) equilibrium theory, Mathevet (2012)'s axiomatic approach, and Ioannou and Romero (2012)'s learning model.

Games with Strategic Heterogeneity

By Andrew J. Monaco and Tarun Sabarwal

This paper studies games with both strategic substitutes and strategic complements, and more generally, games with strategic heterogeneity (GSH). Such games may behave differently from either games with strategic complements or games with strategic substitutes. Under mild assumptions (on one or two players only), the equilibrium set in a GSH is totally unordered (no two equilibria are comparable in the standard product order). Moreover, under mild assumptions (on one player only), parameterized GSH do not allow decreasing equilibrium selections. In general, this cannot be strengthened to conclude increasing selections. Monotone comparative statics results are presented for games in which some players exhibit strategic substitutes and others exhibit strategic complements. For two-player games with linearly ordered strategy spaces, there is a characterization. More generally, there are sufficient conditions. The conditions apply only to players exhibiting strategic substitutes; no conditions are needed for players with strategic complements. Several examples highlight the results.

Price competition, free entry, and welfare in congested markets

By Emerson Melo

In this paper we study the problem of price competition and free entry in congested markets. In many environments, such as communication networks in which network flows are allocated, or transportation networks in which traffic is directed through the underlying road architecture, congestion plays an important role. In particular, we consider a network with multiple origins and a common destination node, where each link is owned by a firm that sets prices in order to maximize profits, whereas users want to minimize the total cost they face, which is given by the congestion cost plus the prices set by firms. In this environment, we introduce the notion of Markovian Traffic Equilibrium to establish the existence and uniqueness of a pure strategy price equilibrium, without assuming that the demand functions are concave nor imposing particular functional forms for the latency functions. We derive explicit conditions to guarantee existence and uniqueness of equilibria. Given this existence and uniqueness result, we apply our framework to study entry decisions and welfare, and establish that in congested markets with free entry, the number of firms exceeds the social optimum.

Global Games Selection in Games with Strategic Substitutes or Complements

By Eric Hoffman

Global games methods are aimed at resolving issues of multiplicity of equilibria and coordination failure that arise in game theoretic models by relaxing common knowledge assumptions about an underlying parameter. These methods have recently received a lot of attention when the underlying complete-information game is one of strategic complements (GSC), which can be embedded into parameterized GSC that produce upper and lower dominance regions, a condition that is crucial to the uniqueness of global games selection. Little has been done in this direction concerning games of strategic substitutes (GSS). Harrison (2003) has shown that when GSS can be parameterized as in the GSC setting to produce upper and lower dominance regions, similar results can be established. This papers argues that such parameterizations are unnatural for many GSS, and instead extends the global games method developed by Carlsson and Van Damme (1993) to N-player, binary choice GSS, using a p-dominance condition as the selection criterion. This method allows for a much wider class of GSS to be considered. As the number of players increases, however, the p-dominance condition becomes more restrictive, an issue that can be resolved when some degree of homogeneity among groups of players can be assumed.