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Strategic substitutes for A ≡ [0, a max ] ⊂ R. There exists a unique equilibrium and multiple fixed points for 2
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We consider an economic model that features (1) a continuum of agents and (2) an aggregate state of the world over which agents
have an infinitesimal influence. We first review the connections between the “eductive” viewpoint on expectational stability
and standard game-theoretical rationalizability concepts. The “eductive” reasoning selects diffe...
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Citations
... eletos and Pavan (2004), Angeletos and Pavan (2007), Hellwig (2005), Cornand and Heinemann (2010)). We depart from the literature by assuming that uncertainty bears on the sensitivity parameter. Our equivalence between instability and existence of sunspot equilibrium is reminiscent of equivalence results found in dynamic models in Guesnerie (1993). Guesnerie (2011) discuss the links between various concepts based on CK ideas. The paper is organized as follows. The benchmark setup is presented in Section 2. The case of complete information is briefly described in Section 3. In Section 4, the analysis is extended to the case of asymmetric information, and the main results are given. In Section 5, we ...
... Our equivalence between instability and existence of sunspot equilibrium is reminiscent of equivalence results found in dynamic models in Guesnerie (1993). Guesnerie (2011) discuss the links between various concepts based on CK ideas. The paper is organized as follows. ...
We study how asymmetric information affects the set of rationalizable solutions in a linear setup where the outcome is determined by forecasts about this same outcome. The unique rational expectations equilibrium is also the unique rationalizable solution when the sensitivity of the outcome to agents’ forecasts is less than one, provided that this sensitivity is common knowledge. Relaxing this common knowledge assumption, multiple rationalizable solutions arise when the proportion of agents who know the sensitivity is large, and the uninformed agents believe it is possible that the sensitivity is greater than one. Instability is equivalent to existence of some kind of sunspot equilibria.
... That is, we discuss examples in which players take into account the whole distribution τ in order to evaluate their payoffs. Nevertheless, there are numerous applications in which agents interact with each other via an aggregate (e.g., see Acemoglu and Jensen, 2010; Guesnerie and Jara-Moroni, 2011 ). The results presented in this paper are still applicable to this subclass of games. ...
We study the existence and computation of equilibrium in large games with strategic complementarities. Using monotone operators (in stochastic dominance orders) defined on the space of distributions, we first prove existence of the greatest and least distributional Nash equilibrium in the sense of Mas-Colell (1984) under different set of assumptions than those in the existing literature. In addition, we provide results on computable monotone distributional equilibrium comparative statics relative to ordered perturbations of the parameters of our games. We then provide similar results for Nash/Schmeidler (1973) equilibria (defined by strategies) in our large games. We conclude by discussing the question of equilibrium uniqueness, as well as presenting applications of our results to models of Bertrand competition, "beauty contests," and existence of equilibrium in large economies.
The paper puts emphasis on the so-called “eductive” approach for a critical assessment of the Rational Expectations hypothesis. Section 2 makes an intuitive unformal presentation, aimed at comparing the approach and the results of “eductive” learning and “real time” learning in two polar models, (a two period partial equilibrium model and a simple Real Business Cycle mode). A segment of theoretical literature, taking an eductive view of stability in the fields of finance, trade, general equilibrium, short term or long term macroeconomics, is reviewed in Section 3.
We study global games with strategic substitutes. Specifically, for a class of binary‐action, N‐player games with strategic substitutes, we prove that under payoff asymmetry, as incomplete information vanishes, the global games approach selects a unique equilibrium. We characterize this equilibrium profile; players employ switching strategies at different cutoff signals, the order of which is directly determined by payoff asymmetry. We provide examples that illustrate our result and its connection with dominance solvability. We extend the global game literature, which has thus far been developed for games with strategic complementarities, to new applications in industrial organization, collective action problems, finance, etc.
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This paper proposes a solution concept called the type-symmetric randomized equilibrium (TSRE), where agents with the same type of characteristics take the same randomized choice. It is shown that this solution concept provides a micro-foundation for the macro notion of equilibrium distribution for economies and games with many agents. In particular, any Walrasian (resp. Nash) equilibrium distribution in a large economy (resp. game) is shown to be uniquely determined by one TSRE if the agent space is modelled by the classical Lebesgue unit interval. The relationship of TSRE with other equilibrium notions is also established.
The theory of large one-shot simultaneous-play games with a biosocial typology has been presented in both the individualized and distributionalized forms—large individualized games (LIG) and large distributionalized games (LDG), respectively. Using an example of an LDG with two actions and a single trait in which some Nash equilibrium distributions cannot be induced by the Nash equilibria of the representing LIG, this paper offers three equivalence results that delineate a relationship between the two game forms. Our analysis also reveals the different roles that the Lebesgue unit interval and a saturated space play in the theory.
This paper offers a resolution to an extensively studied question in theoretical economics: which measure spaces are suitable for modeling many economic agents? We propose the condition of “nowhere equivalence” to characterize those measure spaces that can be effectively used to model the space of many agents. In particular, this condition is shown to be more general than various approaches that have been proposed to handle the shortcoming of the Lebesgue unit interval as an agent space. We illustrate the minimality of the nowhere equivalence condition by showing its necessity in deriving the determinateness property, the existence of equilibria, and the closed graph property for equilibrium correspondences in general equilibrium theory and game theory.
We show that if every large game with a given player space and any given uncountable trait space (or action set) is a proper idealized limit, then the player space must be saturated. When the player space is allowed to be an arbitrary atomless probability space, even a non-saturated one such as the classical Lebesgue unit interval, we establish the following: (i) If a large game has a countable action set and a countable trait space, then the game has a closed Nash equilibrium correspondence, and is thus proper as an idealized limit; (ii) If every large game having a given action set and a given trait space is proper as an idealized limit, then both the action set and the trait space must be countable.
The eductive approach consists of finding solutions consistent with common knowledge of individual rationality and the model. An equilibrium is stable whenever it is the unique outcome consistent with these assumptions. This is a strong stability criterion as it relies on no assumption of prior knowledge of others expectations. This review presents various (in)stability results. It focuses on the following method: Rewrite the model as a temporary equilibrium map in which the current economic outcome is determined by expectations and characterize stability by contracting properties of this map. The main insight suggested by these results is due to Guesnerie (2002): Stability is obtained when the actual outcome is not very sensitive to expectations. Additional insights include that agents heterogeneity is a source of instability; the ability of prices to transmit information is limited by the quality of private information; and coordination when agents are infinitely lived is difficult because of the large effect of long-run expectations.
