Stability with one-sided incomplete information

Bikhchandani, Sushil

doi:10.1016/j.jet.2017.01.004

Cited by 38 publications

(17 citation statements)

References 26 publications

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“…Consider a Bayesian setting in which we fix the firms' common prior λ , which has full support on

normalΩ

. Given an allocation

false(μ, boldp false)

, let

D_{i j p}^{false(μ, boldp false)}

denote the set of type assignments under which worker i gains after the combination

false(i, j; p false)

is satisfied, i.e.,

D_{i j p}^{false(μ, boldp false)} : = false{boldw \in normalΩ : ν_{boldw false(i false), boldf false(j false)} + p > ν_{boldw false(i false), boldf false(μ false(i false) false)} + {boldp}_{i, μ false(i false)} false} .

Drawing on Bikhchandani (), we can define a Bayesian blocking notion which accommodates heterogeneous information among firms. Given a state

false(μ, boldp, boldw, normalΠ false)

and a combination

false(i, j; p false)

, let

D_{i j p}^{false(μ, boldp, boldw, normalΠ false)}

be the set of type assignments which is consistent with firm j 's partition and under which worker i finds the combination

false(i, j; p false)

profitable, i.e.,

D_{i j p}^{false(μ, boldp, boldw, normalΠ false)} : = D_{i j p}^{false(μ, boldp false)} \cap {normalΠ}_{j} false(boldw false) .

…”

Section: Discussionmentioning

confidence: 99%

“…Bikhchandani () proposes a notion of stability that is similar to that of LMPS but which applies to a Bayesian setting with nontransferable utilities. Unlike LMPS and Bikhchandani (), Pomatto () considers a noncooperative matching game and uses forward‐induction reasoning to derive the set of stable outcomes that is identified in LMPS Anderson and Smith. () also study an employment model in which workers have unobserved abilities.…”

Section: Introductionmentioning

confidence: 99%

“…There are two notable exceptions. Bikhchandani () discusses the path to stability under a Bayesian notion of stability. In his paper, the final matching outcome of a blocking path is Bayesian stable only “conditional on the history,” i.e., agents may still block the final outcome with some of their erstwhile partners.…”

Section: Introductionmentioning

confidence: 99%

“…Lazarova and Dimitrov () study paths to stability with incomplete information under a permissive/best‐case notion of blocking. As a result, their approach is not applicable when more conservative blocking notions are adopted, such as the notions in LMPS, Bikhchandani (), and Pomatto ()…”

Section: Introductionmentioning

confidence: 99%

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Learning by matching

Chen

2020

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This paper studies a stability notion and matching processes in the job market with incomplete information on the workers' side. Each worker is associated with a type, and each firm cares about the type of her employee under a match. Moreover, firms' information structure is described by partitions over possible worker type profiles. With this firm-specific information, we propose a stability notion which, in addition to requiring individual rationality and no blocking pairs, captures the idea that the absence of rematching conveys no further information. When an allocation is not stable under the status quo information structure, a new pair of an allocation and an information structure will be derived. We show that starting from an arbitrary allocation and an arbitrary information structure, the process of allowing randomly chosen blocking pairs to rematch, accompanied by information updating, will converge with probability one to an allocation that is stable under the updated information structure. Our results are robust with respect to various alternative learning patterns.

show abstract

“…Consider a Bayesian setting in which we fix the firms' common prior λ , which has full support on

normalΩ

. Given an allocation

false(μ, boldp false)

, let

D_{i j p}^{false(μ, boldp false)}

denote the set of type assignments under which worker i gains after the combination

false(i, j; p false)

is satisfied, i.e.,

D_{i j p}^{false(μ, boldp false)} : = false{boldw \in normalΩ : ν_{boldw false(i false), boldf false(j false)} + p > ν_{boldw false(i false), boldf false(μ false(i false) false)} + {boldp}_{i, μ false(i false)} false} .

Drawing on Bikhchandani (), we can define a Bayesian blocking notion which accommodates heterogeneous information among firms. Given a state

false(μ, boldp, boldw, normalΠ false)

and a combination

false(i, j; p false)

, let

D_{i j p}^{false(μ, boldp, boldw, normalΠ false)}

be the set of type assignments which is consistent with firm j 's partition and under which worker i finds the combination

false(i, j; p false)

profitable, i.e.,

D_{i j p}^{false(μ, boldp, boldw, normalΠ false)} : = D_{i j p}^{false(μ, boldp false)} \cap {normalΠ}_{j} false(boldw false) .

…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Learning by matching

Chen

2020

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show abstract

“…Bikhchandani proposes a matching model with one-sided incomplete information in which workers and firms are matched [24]. In the model, although workers have private information about their types, firms' types are common knowledge [24]. Also, there have been experimental studies done on matching mechanisms with incomplete information [25,26].…”

Section: Introductionmentioning

confidence: 99%