Neighboring information and distributions of agents' characteristics under uncertainty

Allen, Beth

doi:10.1016/0304-4068(83)90051-4

Cited by 44 publications

(32 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Over the last decade several authors have studied notions of similarity of information (e.g. Allen 1983Allen , 1984Cotter 1986;VanZandt 1988;and Stinchcombe 1990). In the economic context this similarity should be defined such that agents behave similarly when information is similar.…”

mentioning

confidence: 99%

Proximity of Information in Games with Incomplete Information

Monderer

Samet

1996

Mathematics of OR

View full text Add to dashboard Cite

Existing notions of proximity of information fail to satisfy desired continuity properties of equilibria in games with incomplete information. We demonstrate this failure and propose a topology on information structures which is the minimal one that satisfies those continuity requirements. This topology is defined in terms of the common belief players have about the proximity of each player's information.

show abstract

mentioning

confidence: 99%

Proximity of Information in Games with Incomplete Information

Monderer

Samet

1996

Mathematics of OR

View full text Add to dashboard Cite

show abstract

“…We must then define a topology on information sub-σ-fields. Allen (1983) was the first to introduce such a topology into economics. She used the Boylan metric, which we shall also employ in Section 9.4.…”

Section: Application To Continuity Of the Value Of Informationmentioning

confidence: 99%

“…The Boylan metric was introduced by Boylan (1971), characterized further by Rogge (1974) and Landers and Rogge (1986), and introduced to economics by Allen (1983). It is stronger than the pointwise convergence topology and is equivalent to the topology of uniform convergence when each sub-σ-field F is viewed as a linear…”

Section: Application To the Value Of Information In Bayesian Zero-summentioning

confidence: 99%

A theorem of the maximin and applications to Bayesian zero-sum games

Zandt

Zhang

2010

Int J Game Theory

View full text Add to dashboard Cite

Consider a family of zero-sum games indexed by a parameter that determines each player's payoff function and feasible strategies. Our first main result characterizes continuity assumptions on the payoffs and the constraint correspondence such that the equilibrium value and strategies depend continuously and upper hemicontinuously (respectively) on the parameter. This characterization uses two topologies in order to overcome a topological tension that arises when players' strategy sets are infinite-dimensional. Our second main result is an application to Bayesian zero-sum games in which each player's information is viewed as a parameter. We model each player's information as a sub-σ-field, so that it determines her feasible strategies: those that are measurable with respect to the player's information. We thereby characterize conditions under which the equilibrium value and strategies depend continuously and upper hemicontinuously (respectively) on each player's information. This clarifies and extends related results of Einy et al. (2008).

show abstract

“…The previous studies on the continuity of economic behavior with respect to information (Allen (1983) and Einy et al (2004)) used the topology introduced by Boylan (1971). This topology is generated by a pseudometric d that assigns a finite distance to any pair of σ-algebras, x and y, contained in B.…”

Section: A Topology On Private Informationmentioning

confidence: 99%

“…Boylan (1971) proposed a topology that is analogous to the Hausdorff metric on closed sets. Allen (1983) studied its properties and proved convergence of consumer demand and continuity of indirect utility with respect to this topology on information. Cotter (1986Cotter ( , 1987 introduced a weaker topology, based on the pointwise convergence metric, and showed that it retains the same properties of continuity of conditional expected utility and excess demand.…”

Section: Introductionmentioning

confidence: 99%

Private Information: Similarity as Compatibility

Correia‐da‐Silva¹,

Hervés-Beloso

2006

Economic Theory

View full text Add to dashboard Cite

Abstract. We investigate the continuity of equilibrium in differential information economies with a finite number of agents. In this setting, agents can make contingent contracts based on events that are commonly observed. With private information modeled as finite partitions of a compact and metrizable space of states of nature, we introduce a topology on information that evaluates the similarity between private information fields taking into account their compatibility. This topology allows us to establish upper semicontinuity of the private core correspondence.

show abstract

Neighboring information and distributions of agents' characteristics under uncertainty

Cited by 44 publications

References 9 publications

Proximity of Information in Games with Incomplete Information

Proximity of Information in Games with Incomplete Information

A theorem of the maximin and applications to Bayesian zero-sum games

Private Information: Similarity as Compatibility

Contact Info

Product

Resources

About