Uncertainty about Uncertainty and Delay in Bargaining

Feinberg, Yossi; Skrzypacz, and Andrzej

doi:10.1111/j.1468-0262.2005.00565.x

Cited by 55 publications

(34 citation statements)

References 28 publications

(67 reference statements)

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“…Thus, the subset of BDP priors is small in both geometric and measure-theoretic senses. In relation to our discussion of Feinberg and Skrzypacz (2005), we will see that it is quite common that the same property is generic at the lower order space but is non-generic at the higher order ones.…”

Section: Literature Review Of Order-2 Bayesian Gamesmentioning

confidence: 80%

“…Once again, allowing a payoff type to have two different order-1 beliefs leads to altered bidding strategies so that the outcome in the first-price auction is no longer efficient, and revenue equivalence to the Second-Price Auction is not valid. Feinberg and Skrzypacz (2005) show that the Coase conjecture fails and delay occurs 2 Given a convex family of priors containing at least one non-BDP prior, Heifetz and Neeman (2006) show that the subset of BDP priors is contained in a proper face of and finitely shy in the convex family of priors. Thus, the subset of BDP priors is small in both geometric and measure-theoretic senses.…”

Section: Literature Review Of Order-2 Bayesian Gamesmentioning

confidence: 99%

“…Indeed, several recent studies show that deviations from naive type spaces may lead to qualitatively different conclusions in well-known models (see for example, Neeman 2004, Feinberg andSkrzypacz, 2005). There is, however, a great deal of additional complexity attached to type spaces beyond the naive ones.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Feinberg and Skrzypacz (2005) showed that introducing higher-order uncertainty dramatically changes the outcomes. Specifically, the presence of the buyer's (second-order) uncertainties about seller's (first-order) beliefs can lead to the failure of the Coase property, if the seller is considered by the buyer to entertain a certainty belief.…”

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confidence: 99%

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An Explicit Approach to Modeling Finite-Order Type Spaces and Applications

Qin

Yang

2010

SSRN Journal

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Every abstract type of a belief-closed type space corresponds to an infinite belief hierarchy. But only finite order of beliefs is necessary for most applications.As we demonstrate, many important insights from recent development in the theory of Bayesian games with higher-order uncertainty involve belief hierarchies of order 2.We start with characterizing order-2 "consistent priors" and show that they form a convex set and contain the convex hull of both the naive and completeinformation type spaces. We establish conditions for private-value heterogeneous naive priors to be embedded in order-2 consistent priors, so as to retro-fit the Harsanyi doctrine of having nature generate all fundamental uncertainties in a game at the very beginning.We then extend the notion of consistent priors to arbitrary finite order k. We define an abstract belief-closed type space to be of order k if it can be mapped via a type morphism into the "canonical representation" of an order-k consistent prior. We show that order-k type spaces are those in which any two types of each player must be either identical implying one of them is redundant or separable by their order-(k-1) belief hierarchies. Finite type spaces are always of finite orders. We consider "finite-order projections" of a type space and show that they are finite-order type spaces themselves. The condition of global stability * We thank Yi-Chun Chen, Kim-Sau Chung, Qingmin Liu, Dov Monderer, and seminar participants at UCR for helpful discussions, comments, and references during the development of this paper.† Contact: Cheng-Zhong Qin, Department of Economics, University of California at Santa Barbara; qin@econ.ucsb.edu; Chun-Lei Yang, Research Center for Humanity and Social Sciences, Academia Sinica, Taipei, Taiwan; cly@gate.sinica.edu.tw 1 under uncertainty ensures the convergence of the Bayesian-Nash equilibria with the projection type spaces to those with the original type space.By defining a total variation norm based on finite-order projections, we generalize Kajii and Morris's (1997) idea of equilibrium robustness to Bayesian games.We then establish the robustness of Bayesian-Nash equilibria that generalizes the robustness results of Monderer and Samet (1989) for complete-information games.We apply our framework of finite-order type spaces or consistent priors to review several important models in the literature and illustrate some new insights.

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Section: Literature Review Of Order-2 Bayesian Gamesmentioning

confidence: 80%

Section: Literature Review Of Order-2 Bayesian Gamesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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An Explicit Approach to Modeling Finite-Order Type Spaces and Applications

Qin

Yang

2010

SSRN Journal

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“…Whether a player is willing to invest in a project, for example, may depend on what he or she thinks that his or her opponent thinks about the economic fundamentals, what he or she thinks that his or her opponent thinks that he or she thinks, and so on, up to arbitrarily high order (e.g., [1]). Higher-order beliefs can also affect economic conclusions in settings ranging from bargaining [2,3] and speculative trade [4] to mechanism design [5] . Higher-order beliefs about actions are central to epistemic characterizations, for example, of rationalizability [6,7], Nash equilibrium [8,9] and forward induction reasoning [10].…”

Section: Introductionmentioning

confidence: 99%

When Do Types Induce the Same Belief Hierarchy?

Perea

Kets

2016

Games

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Type structures are a simple device to describe higher-order beliefs. However, how can we check whether two types generate the same belief hierarchy? This paper generalizes the concept of a type morphism and shows that one type structure is contained in another if and only if the former can be mapped into the other using a generalized type morphism. Hence, every generalized type morphism is a hierarchy morphism and vice versa. Importantly, generalized type morphisms do not make reference to belief hierarchies. We use our results to characterize the conditions under which types generate the same belief hierarchy.

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