Expectational coordination in a class of economic models: Strategic substitutabilities versus strategic complementarities

We consider an economic model that features: 1. a continuum of agents 2. an aggregate state of the world over which agents have an infinitesimal influence. We first propose a review, based on work by Jara (2007), of the connections between the eductive viewpoint that puts emphasis on Strongly Rational Expectations equilibrium and the standard game-theoretical rationalizability concepts. We explore the scope and limits of this connection depending on whether standard rationalizability versus point-rationalizability, or the local versus the global viewpoint, are concerned. In particular, we define and characterize the set of Point-Rationalizable States and prove its convexity. Also, we clarify the role of the heterogeneity of beliefs in general contexts of expectational coordination (see Evans and Guesnerie, 2005). Then, as in the case of strategic complementarities the study of some best response mapping is a key to the analysis, in the case of unambiguous strategic substitutabilities the study of some second iterate, and of the corresponding two-period cycles, allows to describe the point-rationalizable states. We provide application in microeconomic and macroeconomic contexts.expectational coordination ; rational expectations ; iterative expectational stability ; eductive stability ; strong rationality ; strategic complementarities ; strategic substitutabilities

Learning and Selfconfirming Equilibria in Network Games

Consider a set of agents who play a network game repeatedly. Agents may not know the network. They may even be unaware that they are interacting with other agents in a network. Possibly, they just understand that their payoffs depend on an unknown state that in reality is an aggregate of the actions of their neighbors. Each time, every agent chooses an action that maximizes her subjective expected payoff and then updates her beliefs according to what she observes. In particular, we assume that each agent only observes her realized payoff. A steady state of such dynamic is a selfconfirming equilibrium given the assumed feedback. We characterize the structure of the set of selfconfirming equilibria in network games and we relate selfconfirming and Nash equilibria. Thus, we provide conditions on the network under which the Nash equilibrium concept has a learning foundation, despite the fact that agents may have incomplete information. In particular, we show that the choice of being active or inactive in a network is crucial to determine whether agents can make correct inferences about the payoff state and hence play the best reply to the truth in a selfconfirming equilibrium. We also study learning dynamics and show how agents can get stuck in non--Nash selfconfirming equilibria. In such dynamics, the set of inactive agents can only increase in time, because once an agent finds it optimal to be inactive, she gets no feedback about the payoff state, hence she does not change her beliefs and remains inactive

Universal algebra for general aggregation theory: Many-valued propositional-attitude aggregators as MV-homomorphisms

Herzberg F. Universal algebra for general aggregation theory: Many-valued propositional-attitude aggregators as MV-homomorphisms. Journal of Logic and Computation. 2015;25(3):965-977

An Econometric Model of Network Formation with an Application to Board Interlocks between Firms

The paper provides a framework for partially identifying the parameters governing agents’ preferences in a static game of network formation with interdependent link decisions, complete information, and transferable or non-transferable payoffs. The proposed methodology attenuates the computational difficulties arising at the inference stage - due to the huge number of moment inequalities characterising the sharp identified set and the impossibility of brute-force calculating the integrals entering them - by decomposing the network formation game into local games which have a structure similar to entry games and are such that the network formation game is in equilibrium if and only if each local game is in equilibrium. As an empirical illustration of the developed procedure, the paper estimates firms’ incentives for having executives sitting on the board of competitors, using Italian data

An Econometric Model of Network Formation with an Application to Board Interlocks between Firms

The paper provides a framework for partially identifying the parameters governing agents’ preferences in a static game of network formation with interdependent link decisions, complete information, and transferable or non-transferable payoffs. The proposed methodology attenuates the computational difficulties arising at the inference stage - due to the huge number of moment inequalities characterising the sharp identified set and the impossibility of brute-force calculating the integrals entering them - by decomposing the network formation game into local games which have a structure similar to entry games and are such that the network formation game is in equilibrium if and only if each local game is in equilibrium. As an empirical illustration of the developed procedure, the paper estimates firms’ incentives for having executives sitting on the board of competitors, using Italian data

Expectational coordination in a class of economic models: Strategic substitutabilities versus strategic complementarities

We consider an economic model that features: 1. a continuum of agents 2. an aggregate state of the world over which agents have an infinitesimal influence. We first propose a review, based on work by Jara (2007), of the connections between the eductive viewpoint that puts emphasis on Strongly Rational Expectations equilibrium and the standard game-theoretical rationalizability concepts. We explore the scope and limits of this connection depending on whether standard rationalizability versus point-rationalizability, or the local versus the global viewpoint, are concerned. In particular, we define and characterize the set of Point-Rationalizable States and prove its convexity. Also, we clarify the role of the heterogeneity of beliefs in general contexts of expectational coordination (see Evans and Guesnerie, 2005). Then, as in the case of strategic complementarities the study of some best response mapping is a key to the analysis, in the case of unambiguous strategic substitutabilities the study of some second iterate, and of the corresponding two-period cycles, allows to describe the point-rationalizable states. We provide application in microeconomic and macroeconomic contexts.Nous étudions un modèle économique composé d'un continuum d'agents et d'un état agrégé du monde sur lequel les agents ont une influence négligeable. A partir du travail de Jara-Moroni (2007), nous proposons dans un premier temps un rappel des liens entre l'approche divinatoire qui met l'accent sur les équilibres à anticipations fortement rationnelles et les concepts de rationalisabilité (au sens conventionnel de la théorie de jeux). Nous explorons alors la portée et les limites de ces liens, aussi bien localement que globalement selon que la rationalisabilité est conventionnelle ou ponctuelle. En particulier, nous définissons et caractérisons l'ensemble des états ponctuellement rationalisables dont la convexité est démontrée. Le rôle de l'hétérogénéité des croyances dans les contextes généraux de coordination des anticipations est explicité (voir Evans et Guesnerie, 2005). Alors que dans le cas de complémentarités stratégiques, l'étude d'un certain opérateur des meilleures réponses est essentielle pour l'analyse, dans le cas de substituabilités stratégiques non ambigües, l'étude du deuxième itéré d'un même opérateur et des cycles d'ordre deux qui lui sont associés permettent de décrire l'ensemble des états ponctuellement rationalisables. Des applications micro et macroéconomiques sont proposées

A Negishi Approach to Recursive Contracts

In this paper, we argue that a large class of recursive contracts can be studied by means of the conventional Negishi method. A planner is responsible for prescribing current actions along with a distribution of future utility values to all agents, so as to maximize their weighted sum of utilities. Under convexity, the method yields the exact efficient frontier. Otherwise, the implementation requires contracts be contingent on publicly observable random signals uncorrelated to fundamentals. We also provide operational first-order conditions for the characterization of efficient contracts. Finally, we compare extensively our approach with the dual method established in the literature

Dynamic programming with recursive preferences

There is now a considerable amount of research on the deficiencies of additively separable preferences for effective modelling of economically meaningful behaviour. Through analysis of observational data and the design of suitable experiments, economists have constructed progressively more realistic representations of agents and their choices. For intertemporal decisions, this typically involves a departure from the additively separable benchmark. A familiar example is the recursive preference framework of Epstein and Zin (1989), which has become central to the quantitative asset pricing literature, while also finding widespread use in applications range from optimal taxation to fiscal policy and business cycles. This thesis presents three essays which examine mathematical research questions within the context of recursive preferences and dynamic programming. The focus is particularly on showing existence and uniqueness of recursive utility processes under stationary and non-stationary consumption growth specifications, and on solving the closely related problem of optimality of dynamic programs with recursive preferences. On one hand, the thesis has been motivated by the availability of new and unexploited techniques for studying the aforementioned questions. The techniques in question primarily build upon an alternative version of the theory of monotone concave operators proposed by Du (1989, 1990). They are typically well suited to analysis of dynamic optimality with a variety of recursive preference specifications. On the other hand, motivation also comes from the demand side: while many useful results for dynamic programming within the context of recursive preferences have been obtained by existing literature, suitable results are still lacking for some of the most popular specifications for applied work, such as common parameterizations of the Epstein-Zin specification, or preference specifications that incorporate loss aversion and narrow framing into the Epstein-Zin framework, or the ambiguity sensitive preference specifications. In this connection, the thesis has sought to provide a new approach to dynamic optimality suitable for recursive preference specifications commonly used in modern economic analysis. The approach to examining the problems of dynamic programming exploits the theory of monotone convex operators, which, while less familiar than that of monotone concave operators, turns out to be well suited to dynamic maximization. The intuition is that convexity is preserved under maximization, while concavity is not. Meanwhile, concavity pairs well with minimization problems, since minimization preserves concavity. By applying this idea, a parallel theory for these two cases is established and it provides sufficient conditions that are easy to verify in applications

Structure of Core-Periphery Communities

It has been experimentally shown that communities in social networks tend to have a core-periphery topology. However, there is still a limited understanding of the precise structure of core-periphery communities in social networks including the connectivity structure and interaction rates between agents. In this paper, we use a game-theoretic approach to derive a more precise characterization of the structure of core-periphery communities

Robust Comparative Statics in Large Dynamic Economies

We consider infinite horizon economies populated by a continuum of agents who are subject to idiosyncratic shocks. This framework contains models of saving and capital accumulation with incomplete markets in the spirit of works by Bewley, Aiyagari, and Huggett, and models of entry, exit and industry dynamics in the spirit of Hopenhayn's work as special cases. Robust and easy-to-apply comparative statics results are established with respect to exogenous parameters as well as various kinds of changes in the Markov processes governing the law of motion of the idiosyncratic shocks. These results complement the existing literature which uses simulations and numerical analysis to study this class of models and are illustrated using a number of examples