Theoretical Economics September 2017 is now online

TABLE OF CONTENTS, September 2017, Volume 12, Number 3

Full Issue

Articles

Attaining efficiency with imperfect public monitoring and one-sided Markov adverse selection

Daniel Barron

Abstract: I prove an efficiency result for repeated games with imperfect public monitoring in which one player's utility is privately known and evolves according to a Markov process. Under certain assumptions, patient players can attain approximately efficient payoffs in equilibrium. The public signal must satisfy a “pairwise full rank” condition that is somewhat stronger than the monitoring condition required in the Folk Theorem proved by Fudenberg, Levine, and Maskin (1994). Under stronger assumptions, the efficiency result partially extends to settings in which one player has private information that determines every player's payoff. The proof is partially constructive and uses an intuitive technique to mitigate the impact of private information on continuation payoffs.

Keywords: Repeated Bayesian games, efficiency

JEL classification: C72, C73

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Equilibria in symmetric games: theory and applications

Andreas Hefti

Abstract: This article presents a new approach to analyze the equilibrium set of symmetric, differentiable games by separating between multiple symmetric equilibria and asymmetric equilibria. This separation allows to investigate, for example, how various parameter constellations affect the scope for multiple symmetric or asymmetric equilibria, or how the equilibrium set depends on the nature of the strategies. The approach is particularly helpful in applications because (1) it allows to reduce the complexity of the uniqueness-problem to a two-player game, (2) boundary conditions are less critical compared to standard procedures, and (3) best-replies need not be everywhere differentiable.
The usefulness of the separation approach is illustrated with several examples, including an application to asymmetric games and to a two-dimensional price-information game.

Keywords: Symmetric games, uniqueness, symmetric equilibrium, oligopoly

JEL classification: C62, C65, C72, L13, D43

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Preventing bank runs

David Andolfatto, Ed Nosal, Bruno Sultanum

Abstract: Diamond and Dybvig (1983) is commonly understood as providing a formal rationale for the existence of bank-run equilibria. It has never been clear, however, whether bank-run equilibria in this framework are a natural byproduct of the economic environment or an artifact of suboptimal contractual arrangements. In the class of direct mechanisms, Peck and Shell
(2003) demonstrate that bank-run equilibria can exist under an optimal contractual arrangement. The difficulty of preventing runs within this class of mechanism is that banks cannot identify whether withdrawals are being driven by psychology or by fundamentals. Our solution to this problem is an indirect mechanism with the following two properties. First, it provides depositors an incentive to communicate whether they believe a run is on or not. Second, the mechanism threatens a suspension of convertibility conditional on what is revealed in these communications. Together, these two properties can eliminate the prospect of bank-run equilibria in the Diamond-Dybvig environment.

Keywords: Bank runs, optimal deposit contract, financial fragility

JEL classification: D82, E58, G21

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Choice overload and asymmetric regret

Gökhan Buturak, Özgür Evren

Abstract: We propose a model of "choice overload" which refers to a stronger tendency to select the default option in larger choice problems. Our main finding is a behavioral characterization of an asymmetric regret representation that depicts a decision maker who does not consider the possibility of experiencing regret for choosing the default option. By contrast, the value of ordinary alternatives is subject to regret. The calculus of regret for ordinary alternatives is identical to that in Sarver's (2008) anticipated regret model, despite the fact that the primitives of the two theories are different. Our model can also be applied to choice problems with the option to defer the decision.

Keywords: Choice overload, anticipated regret, subjective states, choice deferral

JEL classification: D11, D81

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Friends and enemies: a model of signed network formation

Timo Hiller

Abstract: I propose a simple model of signed network formation, where agents make friends to extract payoffs from weaker enemies. The model thereby accounts for the interplay between friendship and alliance on one hand and enmity and antagonism on the other. Nash equilibrium configurations are such that, either everyone is friends with everyone, or agents can be partitioned into different sets, where agents within the same set are friends and agents in different sets are enemies. Any strong Nash equilibrium must be such that a single agent is in an antagonistic relationship with everyone else.  Furthermore, we show that Nash equilibria cannot be Pareto ranked. This paper offers a game-theoretic foundation for a large body of work on signed networks, called structural balance theory, which has been studied in sociology, social psychology, bullying, international relations and applied physics. The paper also contributes to the literature on contests and economics of conflict.

Keywords: Signed network formation, structural balance, contest success function, bullying, economics of conflict, international relations

JEL classification: D74, D85, F51

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Bayesian games with a continuum of states

Ziv Hellman, Yehuda Levy

Abstract: We show that every Bayesian game with purely atomic types has a measurable Bayesian equilibrium when the common knowledge relation is smooth.  Conversely, for any common knowledge relation that is not smooth, there exists a type space that yields this common knowledge relation and payoffs such that the resulting Bayesian game will not have any Bayesian equilibrium.  We show that our smoothness condition also rules out two paradoxes involving Bayesian games with a continuum of types: the impossibility of having a common prior on components when a common prior over the entire state space exists, and the possibility of interim betting/trade even when no such trade can be supported ex ante.

Keywords: Bayesian games, Bayesian equilibrium, common priors, continuum of states

JEL classification: C72

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Sovereign debt and incentives to default with uninsurable risks

Gaetano Bloise, Herakles Polemarchakis, Yiannis Vailakis

Abstract: We show that sovereign debt is unsustainable if debt contracts are not supported by direct sanctions and default carries only a ban from ever borrowing in financial markets even in the presence of uninsurable risks and time-varying interest rate. This extension of Bulow and Rogoff (1989) requires that the present value of the endowment be finite under the most optimistic valuation. We provide examples where this condition fails and sovereign debt is sustained by the threat of loss of insurance opportunities upon default, despite the fact that the most pessimistic valuation of the endowment, the natural debt limit, is finite.

Keywords: Sovereign risk, Ponzi games, reputational debt, incomplete markets

JEL classification: F34, H63

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Active learning with a misspecified prior

Drew Fudenberg, Gleb Romanyuk, Philipp Strack

Abstract: We study learning and information acquisition by a Bayesian agent whose prior belief is misspecified in the sense that it assigns probability zero to the true state of the world. At each instant, the agent takes an action and observes the corresponding payoff, which is the sum of a fixed but unknown function of the action and an additive error term. We provide a complete characterization of asymptotic actions and beliefs when the agent's subjective state space is a doubleton.
A simple example with three actions shows that in a misspecified environment a myopic agent's beliefs converge while a sufficiently patient agent's beliefs do not. This illustrates a novel interaction between misspecification and the agent's subjective discount rate.

Keywords: Active learning, learning in games, mis-specified models

JEL classification: D83,D90

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Rational expectations and farsighted stability

Bhaskar Dutta, Rajiv Vohra

Abstract: In the study of farsighted coalitional behavior, a central role is played by the von Neumann-Morgenstern (1944) stable set and its modification that incorporates farsightedness. Such a modification was first proposed by Harsanyi (1974) and has recently been re-formulated by Ray and Vohra (2015).
The farsighted stable set is based on a notion of indirect dominance in which an outcome can be dominated by a chain of coalitional `moves' in which each coalition that is involved in the sequence eventually stands to gain.  However, it does not require that each coalition make a maximal move, i.e., one that is not Pareto dominated (for the members of the coalition in question) by another. Consequently, when there are multiple continuation paths the farsighted stable set can yield unreasonable predictions. We restrict coalitions to hold common, history independent expectations that incorporate maximality regarding the continuation path.  This leads to two related solution concepts: the rational expectations farsighted stable set (REFS) and the strong rational expectations farsighted stable set (SREFS). We apply these concepts to  simple games and to pillage games to illustrate the consequences of imposing rational expectations for farsighted stability.

Keywords: Stable sets, farsightedness, consistency, maximality, rational expectations, simple games, pillage games

JEL classification: C71, D72, D74

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Capital-labor substitution, structural change and growth

Francisco Alvarez-Cuadrado, Ngo Long, Markus Poschke

Abstract: There is growing interest in multi-sector models that combine aggregate balanced growth, consistent with the well-known Kaldor facts, with systematic changes in the sectoral allocation of resources, consistent with the Kuznets facts. Although variations in the income elasticity of demand across goods played an important role in initial approaches, recent models stress the role of supply-side factors in this process of structural change, in particular sector-specific technical change and sectoral differences in factor proportions. We explore a general framework that features an additional supply-side mechanism and also encompasses these two known mechanisms. Our model shows that sectoral differences in the degree of capital-labor substitutability -- a new mechanism -- are a driving force for structural change. When the flexibility to combine capital and labor differs across sectors, a factor rebalancing effect is operative. It tends to make production in the more flexible sector more intensive in the input that becomes more abundant. As a result, growth rates of sectoral capital-labor ratios can differ and, if this effect dominates, shares of each factor used in a given sector can move in different directions. We identify conditions under which this occurs and analyze the dynamics of such a case. We also provide some suggestive evidence consistent with this new mechanism. A quantitative analysis suggests that this channel was an important contributor to structural change out of agriculture in the United States.

Keywords: Capital-labor substitution, balanced growth, structural change

JEL classification: O40, O41, O30

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Efficient and strategy-proof allocation mechanisms in economies with many goods

Takeshi Momi

Abstract: In this paper, we show that in pure exchange economies where the number of goods equals or exceeds the number of agents, any Pareto-efficient and strategy-proof allocation mechanism always allocates the total endowment to some single agent even if the receivers vary.

Keywords: Social choice, strategy-proofness, Pareto efficiency, exchange economy

JEL classification: D71

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Preference discovery and experimentation

Kevin Cooke

Abstract: I provide axiomatic foundations for a model of taste uncertainty with endogenous learning through consumption. In this setting, uncertainty is over an unobservable, subjective state space. Preference over lottery-menu pairs is sufficient to identify the state space and the learning process.  In this model, the agent is viewed as if he learns the utility of an object upon its consumption. This information is used to improve choice from the follow-on menu. This implies a trade-off between consumption value and information leading to experimentation.  I provide a behavioral definition of experimentation.  While the literature focuses on identifying subjective states through a demand for flexibility, I show that experimentation also (partially) identifies taste uncertainty.

Keywords: Taste uncertainty, experimentation, endogenous learning, subjective state space, learning through consumption, decision theory

JEL classification: D11, D83

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Characterization and uniqueness of equilibrium in competitive insurance

Vitor Farinha Luz

Abstract: This paper provides a complete characterization of equilibria in a game-theoretic version of Rothschild and Stiglitz (1976)’s model of competitive insurance. I allow for stochastic contract offers by insurance firms and show that a unique symmetric equilibrium always exists. Exact conditions under which the equilibrium involves mixed strategies are provided. The mixed equilibrium features: (i) cross-subsidization across risk levels, (ii) dependence of offers on the risk distribution and (iii) price dispersion generated by firm randomization over offers.

Keywords: Asymmetric and private information, mechanism design, oligopoly, economics of contracts, insurance

JEL classification: C72, D43, D82, D86, G22

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Double auction with interdependent values: incentives and efficiency

Fuhito Kojima, Takuro Yamashita

Abstract: We study a double auction environment where buyers and sellers have inter-dependent valuations and multiunit demand and supply. We propose a new mechanism, the groupwise-price mechanism. We show that the mechanism satisfies ex post incentive compatibility, individual rationality, feasibility, non-wastefulness, and no budget deficit. Moreover, the mechanism is asymptotically efficient in that the trade outcome in the mechanism converges to the efficient level as in a competitive equilibrium as the numbers of the buyers and sellers become large. Our groupwise-price mechanism is the first double auction mechanism with these properties in the interdependent values setting.

Keywords: Double auction, interdependent values, multi-unit demand and supply, ex post incentive compatibility, asymptotic efficiency

JEL classification: D44, D47, D82

 
 

 

Publication Date: 
Monday, October 2, 2017

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