Redistribution through Market Segmentation - Slides
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About This Presentation
These are the slides Alexis used for a 20 minute presentation at EC'24
Slide Content
Redistribution Through Market Segmentation
Victor Augias
1
r⃝Alexis Ghersengorin
2
r⃝Daniel Barreto
3
University of Bonn
1
University of Oxford & Global Priorities Institute
2
University of Amsterdam
3
Victor Augias
1
r⃝Alexis Ghersengorin
2
r⃝Daniel Barreto
3
University of Bonn
1
University of Oxford & Global Priorities Institute
2
University of Amsterdam
3
Price discrimination and consumer welfare
The consequences of price discrimination ontotalconsumer surplus?
1. ⟶e.g. first-degree price discrimination.
2.. [Bergemann et al., 2015, Haghpanah and Siegel, 2023]→How? Create segments pooling high and low types (negative-assortativity).
Pooling externalities: Lower types exert a positive externality on higher types by
allowing them to obtain a strictly positive surplus.[Galperti et al., 2024]
⟹CS maximizing segmentations.
1
The consequences of price discrimination ontotalconsumer surplus?
1. ⟶e.g. first-degree price discrimination.
2.. [Bergemann et al., 2015, Haghpanah and Siegel, 2023]→How? Create segments pooling high and low types (negative-assortativity).
Pooling externalities: Lower types exert a positive externality on higher types by
allowing them to obtain a strictly positive surplus.[Galperti et al., 2024]
⟹CS maximizing segmentations.
1
Price discrimination and consumer welfare
The consequences of price discrimination ontotalconsumer surplus?
1. ⟶e.g. first-degree price discrimination.
2.. [Bergemann et al., 2015, Haghpanah and Siegel, 2023]→How? Create segments pooling high and low types (negative-assortativity).
Pooling externalities: Lower types exert a positive externality on higher types by
allowing them to obtain a strictly positive surplus.[Galperti et al., 2024]
⟹CS maximizing segmentations.
1
The consequences of price discrimination ontotalconsumer surplus?
1. ⟶e.g. first-degree price discrimination.
2.. [Bergemann et al., 2015, Haghpanah and Siegel, 2023]→How? Create segments pooling high and low types (negative-assortativity).
Pooling externalities: Lower types exert a positive externality on higher types by
allowing them to obtain a strictly positive surplus.[Galperti et al., 2024]
⟹CS maximizing segmentations.
1
Price discrimination and consumer welfare
The consequences of price discrimination ontotalconsumer surplus?
1. ⟶e.g. first-degree price discrimination.
2.. [Bergemann et al., 2015, Haghpanah and Siegel, 2023]→How? Create segments pooling high and low types (negative-assortativity).
Pooling externalities: Lower types exert a positive externality on higher types by
allowing them to obtain a strictly positive surplus.[Galperti et al., 2024]
⟹CS maximizing segmentations.
1
The consequences of price discrimination ontotalconsumer surplus?
1. ⟶e.g. first-degree price discrimination.
2.. [Bergemann et al., 2015, Haghpanah and Siegel, 2023]→How? Create segments pooling high and low types (negative-assortativity).
Pooling externalities: Lower types exert a positive externality on higher types by
allowing them to obtain a strictly positive surplus.[Galperti et al., 2024]
⟹CS maximizing segmentations.
1
Price discrimination and consumer welfare
The consequences of price discrimination ontotalconsumer surplus?
1. ⟶e.g. first-degree price discrimination.
2.. [Bergemann et al., 2015, Haghpanah and Siegel, 2023]→How? Create segments pooling high and low types (negative-assortativity).
Pooling externalities: Lower types exert a positive externality on higher types by
allowing them to obtain a strictly positive surplus.[Galperti et al., 2024]
⟹CS maximizing segmentations.
1
The consequences of price discrimination ontotalconsumer surplus?
1. ⟶e.g. first-degree price discrimination.
2.. [Bergemann et al., 2015, Haghpanah and Siegel, 2023]→How? Create segments pooling high and low types (negative-assortativity).
Pooling externalities: Lower types exert a positive externality on higher types by
allowing them to obtain a strictly positive surplus.[Galperti et al., 2024]
⟹CS maximizing segmentations.
1
Price discrimination and consumer welfare
The consequences of price discrimination ontotalconsumer surplus?
1. ⟶e.g. first-degree price discrimination.
2.. [Bergemann et al., 2015, Haghpanah and Siegel, 2023]→How? Create segments pooling high and low types (negative-assortativity).
Pooling externalities: Lower types exert a positive externality on higher types by
allowing them to obtain a strictly positive surplus.[Galperti et al., 2024]
⟹CS maximizing segmentations.
1
The consequences of price discrimination ontotalconsumer surplus?
1. ⟶e.g. first-degree price discrimination.
2.. [Bergemann et al., 2015, Haghpanah and Siegel, 2023]→How? Create segments pooling high and low types (negative-assortativity).
Pooling externalities: Lower types exert a positive externality on higher types by
allowing them to obtain a strictly positive surplus.[Galperti et al., 2024]
⟹CS maximizing segmentations.
1
Price discrimination and consumer welfare
The consequences of price discrimination ontotalconsumer surplus?
1. ⟶e.g. first-degree price discrimination.
2.. [Bergemann et al., 2015, Haghpanah and Siegel, 2023]→How? Create segments pooling high and low types (negative-assortativity).
Pooling externalities: Lower types exert a positive externality on higher types by
allowing them to obtain a strictly positive surplus.[Galperti et al., 2024]
⟹CS maximizing segmentations.
1
The consequences of price discrimination ontotalconsumer surplus?
1. ⟶e.g. first-degree price discrimination.
2.. [Bergemann et al., 2015, Haghpanah and Siegel, 2023]→How? Create segments pooling high and low types (negative-assortativity).
Pooling externalities: Lower types exert a positive externality on higher types by
allowing them to obtain a strictly positive surplus.[Galperti et al., 2024]
⟹CS maximizing segmentations.
1
This paper: redistributive segmentation
What if we care about how the surplus is
Specifically, what if we want to
lower surplus? [ redistribution]
Teaser
Redistributive segmentations exhibit
some of the created surplus to the seller – a.
2
What if we care about how the surplus is
Specifically, what if we want to
lower surplus? [ redistribution]
Teaser
Redistributive segmentations exhibit
some of the created surplus to the seller – a.
2
This paper: redistributive segmentation
What if we care about how the surplus is
Specifically, what if we want to
lower surplus? [ redistribution]
Teaser
Redistributive segmentations exhibit
some of the created surplus to the seller – a.
2
What if we care about how the surplus is
Specifically, what if we want to
lower surplus? [ redistribution]
Teaser
Redistributive segmentations exhibit
some of the created surplus to the seller – a.
2
This paper: redistributive segmentation
What if we care about how the surplus is
Specifically, what if we want to
lower surplus? [ redistribution]
Teaser
Redistributive segmentations exhibit
some of the created surplus to the seller – a.
2
What if we care about how the surplus is
Specifically, what if we want to
lower surplus? [ redistribution]
Teaser
Redistributive segmentations exhibit
some of the created surplus to the seller – a.
2
Economy
One monopolisitic seller and unit mass of buyers with unit demand.
Buyers:
•are described by a �∈ Θ={�1,…,�n}, where 0< �1<⋯< �n.
•consume at pricepif and only if�≥p.
The seller:
•has marginal costc= 0.
•sets the pricep∈ Θto maximize expected profit.
3
One monopolisitic seller and unit mass of buyers with unit demand.
Buyers:
•are described by a �∈ Θ={�1,…,�n}, where 0< �1<⋯< �n.
•consume at pricepif and only if�≥p.
The seller:
•has marginal costc= 0.
•sets the pricep∈ Θto maximize expected profit.
3
Economy
One monopolisitic seller and unit mass of buyers with unit demand.
Buyers:
•are described by a �∈ Θ={�1,…,�n}, where 0< �1<⋯< �n.
•consume at pricepif and only if�≥p.
The seller:
•has marginal costc= 0.
•sets the pricep∈ Θto maximize expected profit.
3
One monopolisitic seller and unit mass of buyers with unit demand.
Buyers:
•are described by a �∈ Θ={�1,…,�n}, where 0< �1<⋯< �n.
•consume at pricepif and only if�≥p.
The seller:
•has marginal costc= 0.
•sets the pricep∈ Θto maximize expected profit.
3
Economy
One monopolisitic seller and unit mass of buyers with unit demand.
Buyers:
•are described by a �∈ Θ={�1,…,�n}, where 0< �1<⋯< �n.
•consume at pricepif and only if�≥p.
The seller:
•has marginal costc= 0.
•sets the pricep∈ Θto maximize expected profit.
3
One monopolisitic seller and unit mass of buyers with unit demand.
Buyers:
•are described by a �∈ Θ={�1,…,�n}, where 0< �1<⋯< �n.
•consume at pricepif and only if�≥p.
The seller:
•has marginal costc= 0.
•sets the pricep∈ Θto maximize expected profit.
3
Market segmentations
Consider an aggregate market�∈ Δ(Θ)
�p(�1,�1)�
⋆
�n�2�n–1……�
⋆
�np
′
p
′′
∑
�∈Θ
�(�) = 1∑
p∈Θ
�(�,p) =�(�)p
′
∑
�≥p
′
�(�,p
′
)≥q∑
�≥q
�(�,p
′
)p
′
∙∙∙∙∙
4
Consider an aggregate market�∈ Δ(Θ)
�p(�1,�1)�
⋆
�n�2�n–1……�
⋆
�np
′
p
′′
∑
�∈Θ
�(�) = 1∑
p∈Θ
�(�,p) =�(�)p
′
∑
�≥p
′
�(�,p
′
)≥q∑
�≥q
�(�,p
′
)p
′
∙∙∙∙∙
4
Market segmentations
Denote�
⋆
the uniform price under�.
�p(�1,�1)�
⋆
�n�2�n–1……�
⋆
�np
′
p
′′
∑
�∈Θ
�(�) = 1∑
p∈Θ
�(�,p) =�(�)p
′
∑
�≥p
′
�(�,p
′
)≥q∑
�≥q
�(�,p
′
)p
′
∙∙∙∙∙
4
Denote�
⋆
the uniform price under�.
�p(�1,�1)�
⋆
�n�2�n–1……�
⋆
�np
′
p
′′
∑
�∈Θ
�(�) = 1∑
p∈Θ
�(�,p) =�(�)p
′
∑
�≥p
′
�(�,p
′
)≥q∑
�≥q
�(�,p
′
)p
′
∙∙∙∙∙
4
Market segmentations
We have a unit mass of buyers that we can move around in the grid.
�p(�1,�1)�
⋆
�n�2�n–1……�
⋆
�np
′
p
′′
∑
�∈Θ
�(�) = 1∑
p∈Θ
�(�,p) =�(�)p
′
∑
�≥p
′
�(�,p
′
)≥q∑
�≥q
�(�,p
′
)p
′
∙∙∙∙∙
4
We have a unit mass of buyers that we can move around in the grid.
�p(�1,�1)�
⋆
�n�2�n–1……�
⋆
�np
′
p
′′
∑
�∈Θ
�(�) = 1∑
p∈Θ
�(�,p) =�(�)p
′
∑
�≥p
′
�(�,p
′
)≥q∑
�≥q
�(�,p
′
)p
′
∙∙∙∙∙
4
Market segmentations
A segmentation�splits the buyers across different segments while satisfying…
�p(�1,�1)�
⋆
�n�2�n–1……�
⋆
�np
′
p
′′
∑
�∈Θ
�(�) = 1∑
p∈Θ
�(�,p) =�(�)p
′
∑
�≥p
′
�(�,p
′
)≥q∑
�≥q
�(�,p
′
)p
′
∙∙∙∙∙
4
A segmentation�splits the buyers across different segments while satisfying…
�p(�1,�1)�
⋆
�n�2�n–1……�
⋆
�np
′
p
′′
∑
�∈Θ
�(�) = 1∑
p∈Θ
�(�,p) =�(�)p
′
∑
�≥p
′
�(�,p
′
)≥q∑
�≥q
�(�,p
′
)p
′
∙∙∙∙∙
4
Market segmentations
(i) The marginal constraint.
�p(�1,�1)�
⋆
�n�2�n–1……�
⋆
�np
′
p
′′
∑
�∈Θ
�(�) = 1∑
p∈Θ
�(�,p) =�(�)p
′
∑
�≥p
′
�(�,p
′
)≥q∑
�≥q
�(�,p
′
)p
′
∙∙∙∙∙
4
(i) The marginal constraint.
�p(�1,�1)�
⋆
�n�2�n–1……�
⋆
�np
′
p
′′
∑
�∈Θ
�(�) = 1∑
p∈Θ
�(�,p) =�(�)p
′
∑
�≥p
′
�(�,p
′
)≥q∑
�≥q
�(�,p
′
)p
′
∙∙∙∙∙
4
Market segmentations
(ii) The obedience constraint.
�p(�1,�1)�
⋆
�n�2�n–1……�
⋆
�np
′
p
′′
∑
�∈Θ
�(�) = 1∑
p∈Θ
�(�,p) =�(�)p
′
∑
�≥p
′
�(�,p
′
)≥q∑
�≥q
�(�,p
′
)p
′
∙∙∙∙∙
4
(ii) The obedience constraint.
�p(�1,�1)�
⋆
�n�2�n–1……�
⋆
�np
′
p
′′
∑
�∈Θ
�(�) = 1∑
p∈Θ
�(�,p) =�(�)p
′
∑
�≥p
′
�(�,p
′
)≥q∑
�≥q
�(�,p
′
)p
′
∙∙∙∙∙
4
Redistributive social welfare functions
w(�,p) �payingp.
LetRbe the class of redistributive welfare functions.
Example 1: Decreasing Pareto weights
w(�,p) =�(�)(�–p)1
�≥p where�(⋅) is
[Condorelli, 2013, Dworczak et al., 2021, Akbarpour et al., 2023]
Example 2: Decreasing marginal surplus
w(�,p) =u((�–p)1
�≥p) whereuis.
5
w(�,p) �payingp.
LetRbe the class of redistributive welfare functions.
Example 1: Decreasing Pareto weights
w(�,p) =�(�)(�–p)1
�≥p where�(⋅) is
[Condorelli, 2013, Dworczak et al., 2021, Akbarpour et al., 2023]
Example 2: Decreasing marginal surplus
w(�,p) =u((�–p)1
�≥p) whereuis.
5
Redistributive social welfare functions
w(�,p) �payingp.
LetRbe the class of redistributive welfare functions.
Example 1: Decreasing Pareto weights
w(�,p) =�(�)(�–p)1
�≥p where�(⋅) is
[Condorelli, 2013, Dworczak et al., 2021, Akbarpour et al., 2023]
Example 2: Decreasing marginal surplus
w(�,p) =u((�–p)1
�≥p) whereuis.
5
w(�,p) �payingp.
LetRbe the class of redistributive welfare functions.
Example 1: Decreasing Pareto weights
w(�,p) =�(�)(�–p)1
�≥p where�(⋅) is
[Condorelli, 2013, Dworczak et al., 2021, Akbarpour et al., 2023]
Example 2: Decreasing marginal surplus
w(�,p) =u((�–p)1
�≥p) whereuis.
5
Redistributive social welfare functions
w(�,p) �payingp.
LetRbe the class of redistributive welfare functions.
Example 1: Decreasing Pareto weights
w(�,p) =�(�)(�–p)1
�≥p where�(⋅) is
[Condorelli, 2013, Dworczak et al., 2021, Akbarpour et al., 2023]
Example 2: Decreasing marginal surplus
w(�,p) =u((�–p)1
�≥p) whereuis.
5
w(�,p) �payingp.
LetRbe the class of redistributive welfare functions.
Example 1: Decreasing Pareto weights
w(�,p) =�(�)(�–p)1
�≥p where�(⋅) is
[Condorelli, 2013, Dworczak et al., 2021, Akbarpour et al., 2023]
Example 2: Decreasing marginal surplus
w(�,p) =u((�–p)1
�≥p) whereuis.
5
Redistributive social welfare functions
w(�,p) �payingp.
LetRbe the class of redistributive welfare functions.
Example 1: Decreasing Pareto weights
w(�,p) =�(�)(�–p)1
�≥p where�(⋅) is
[Condorelli, 2013, Dworczak et al., 2021, Akbarpour et al., 2023]
Example 2: Decreasing marginal surplus
w(�,p) =u((�–p)1
�≥p) whereuis.
5
w(�,p) �payingp.
LetRbe the class of redistributive welfare functions.
Example 1: Decreasing Pareto weights
w(�,p) =�(�)(�–p)1
�≥p where�(⋅) is
[Condorelli, 2013, Dworczak et al., 2021, Akbarpour et al., 2023]
Example 2: Decreasing marginal surplus
w(�,p) =u((�–p)1
�≥p) whereuis.
5
Preliminary: No Exclusion
�p(�1,�1)�n�nΩ:=
{
(�,p)∈ Θ × Θ|�≥p
}
Lemma (No exclusion)
WLOG to consider segmentations
supported onΩ.
Σ
⋆
(�) �with no exclusion. 6
�p(�1,�1)�n�nΩ:=
{
(�,p)∈ Θ × Θ|�≥p
}
Lemma (No exclusion)
WLOG to consider segmentations
supported onΩ.
Σ
⋆
(�) �with no exclusion. 6
Preliminary: No Exclusion
�p(�1,�1)�n�nΩ:=
{
(�,p)∈ Θ × Θ|�≥p
}
Lemma (No exclusion)
WLOG to consider segmentations
supported onΩ.
Σ
⋆
(�) �with no exclusion. 6
�p(�1,�1)�n�nΩ:=
{
(�,p)∈ Θ × Θ|�≥p
}
Lemma (No exclusion)
WLOG to consider segmentations
supported onΩ.
Σ
⋆
(�) �with no exclusion. 6
Preliminary: No Exclusion
�p(�1,�1)�n�nΩ:=
{
(�,p)∈ Θ × Θ|�≥p
}
Lemma (No exclusion)
WLOG to consider segmentations
supported onΩ.
Σ
⋆
(�) �with no exclusion. 6
�p(�1,�1)�n�nΩ:=
{
(�,p)∈ Θ × Θ|�≥p
}
Lemma (No exclusion)
WLOG to consider segmentations
supported onΩ.
Σ
⋆
(�) �with no exclusion. 6
Marginal changes that are unambiguously good
Start from a segmentation�∈ Σ
⋆
(�).
Question: which modifications on�would beunambiguously good? I.e., would
increaseanyredistributive objectivew∈R.
Downward mass transfers
Redistributive mass transfers
Theorem (Redistributive order)
�
′
performs better than�for ∈R(i.e.
more redistributive) if and only if�
′
can be
obtained from�by a finite sequence of
downward
C.f. [Meyer and Strulovici, 2015]
�p�????????????
7
Start from a segmentation�∈ Σ
⋆
(�).
Question: which modifications on�would beunambiguously good? I.e., would
increaseanyredistributive objectivew∈R.
Downward mass transfers
Redistributive mass transfers
Theorem (Redistributive order)
�
′
performs better than�for ∈R(i.e.
more redistributive) if and only if�
′
can be
obtained from�by a finite sequence of
downward
C.f. [Meyer and Strulovici, 2015]
�p�????????????
7
Marginal changes that are unambiguously good
Start from a segmentation�∈ Σ
⋆
(�).
Question: which modifications on�would beunambiguously good? I.e., would
increaseanyredistributive objectivew∈R.
Downward mass transfers
Redistributive mass transfers
Theorem (Redistributive order)
�
′
performs better than�for ∈R(i.e.
more redistributive) if and only if�
′
can be
obtained from�by a finite sequence of
downward
C.f. [Meyer and Strulovici, 2015]
�p�????????????
7
Start from a segmentation�∈ Σ
⋆
(�).
Question: which modifications on�would beunambiguously good? I.e., would
increaseanyredistributive objectivew∈R.
Downward mass transfers
Redistributive mass transfers
Theorem (Redistributive order)
�
′
performs better than�for ∈R(i.e.
more redistributive) if and only if�
′
can be
obtained from�by a finite sequence of
downward
C.f. [Meyer and Strulovici, 2015]
�p�????????????
7
Marginal changes that are unambiguously good
Start from a segmentation�∈ Σ
⋆
(�).
Question: which modifications on�would beunambiguously good? I.e., would
increaseanyredistributive objectivew∈R.
Downward mass transfers
Redistributive mass transfers
Theorem (Redistributive order)
�
′
performs better than�for ∈R(i.e.
more redistributive) if and only if�
′
can be
obtained from�by a finite sequence of
downward
C.f. [Meyer and Strulovici, 2015]
�p�????????????
7
Start from a segmentation�∈ Σ
⋆
(�).
Question: which modifications on�would beunambiguously good? I.e., would
increaseanyredistributive objectivew∈R.
Downward mass transfers
Redistributive mass transfers
Theorem (Redistributive order)
�
′
performs better than�for ∈R(i.e.
more redistributive) if and only if�
′
can be
obtained from�by a finite sequence of
downward
C.f. [Meyer and Strulovici, 2015]
�p�????????????
7
Marginal changes that are unambiguously good
Start from a segmentation�∈ Σ
⋆
(�).
Question: which modifications on�would beunambiguously good? I.e., would
increaseanyredistributive objectivew∈R.
Downward mass transfers
Redistributive mass transfers
Theorem (Redistributive order)
�
′
performs better than�for ∈R(i.e.
more redistributive) if and only if�
′
can be
obtained from�by a finite sequence of
downward
C.f. [Meyer and Strulovici, 2015]
�p�????????????
7
Start from a segmentation�∈ Σ
⋆
(�).
Question: which modifications on�would beunambiguously good? I.e., would
increaseanyredistributive objectivew∈R.
Downward mass transfers
Redistributive mass transfers
Theorem (Redistributive order)
�
′
performs better than�for ∈R(i.e.
more redistributive) if and only if�
′
can be
obtained from�by a finite sequence of
downward
C.f. [Meyer and Strulovici, 2015]
�p�????????????
7
Marginal changes that are unambiguously good
Start from a segmentation�∈ Σ
⋆
(�).
Question: which modifications on�would beunambiguously good? I.e., would
increaseanyredistributive objectivew∈R.
Downward mass transfers
Redistributive mass transfers
Theorem (Redistributive order)
�
′
performs better than�for ∈R(i.e.
more redistributive) if and only if�
′
can be
obtained from�by a finite sequence of
downward
C.f. [Meyer and Strulovici, 2015]
�p�????????????
7
Start from a segmentation�∈ Σ
⋆
(�).
Question: which modifications on�would beunambiguously good? I.e., would
increaseanyredistributive objectivew∈R.
Downward mass transfers
Redistributive mass transfers
Theorem (Redistributive order)
�
′
performs better than�for ∈R(i.e.
more redistributive) if and only if�
′
can be
obtained from�by a finite sequence of
downward
C.f. [Meyer and Strulovici, 2015]
�p�????????????
7
Marginal changes that are unambiguously good
Start from a segmentation�∈ Σ
⋆
(�).
Question: which modifications on�would beunambiguously good? I.e., would
increaseanyredistributive objectivew∈R.
Downward mass transfers
Redistributive mass transfers
Theorem (Redistributive order)
�
′
performs better than�for ∈R(i.e.
more redistributive) if and only if�
′
can be
obtained from�by a finite sequence of
downward
C.f. [Meyer and Strulovici, 2015]
�p�????????????
7
Start from a segmentation�∈ Σ
⋆
(�).
Question: which modifications on�would beunambiguously good? I.e., would
increaseanyredistributive objectivew∈R.
Downward mass transfers
Redistributive mass transfers
Theorem (Redistributive order)
�
′
performs better than�for ∈R(i.e.
more redistributive) if and only if�
′
can be
obtained from�by a finite sequence of
downward
C.f. [Meyer and Strulovici, 2015]
�p�????????????
7
Redistributive segmentations
Proposition
Fix w∈R.
Any optimal segmentation is:
∀p,p
′
∈supp(�),p<p
′
⟹max supp(�(⋅∣p))≤max supp(�(⋅∣p
′
)).
�p
(Ob) binds
8
Proposition
Fix w∈R.
Any optimal segmentation is:
∀p,p
′
∈supp(�),p<p
′
⟹max supp(�(⋅∣p))≤max supp(�(⋅∣p
′
)).
�p
(Ob) binds
8
Redistributive segmentations
Proposition
Fix w∈R.
Any optimal segmentation is:
∀p,p
′
∈supp(�),p<p
′
⟹max supp(�(⋅∣p))≤max supp(�(⋅∣p
′
)).
�p
(Ob) binds
8
Proposition
Fix w∈R.
Any optimal segmentation is:
∀p,p
′
∈supp(�),p<p
′
⟹max supp(�(⋅∣p))≤max supp(�(⋅∣p
′
)).
�p
(Ob) binds
8
Redistributive segmentations
Proposition
Fix w∈R.
Any optimal segmentation is:
∀p,p
′
∈supp(�),p<p
′
⟹max supp(�(⋅∣p))≤max supp(�(⋅∣p
′
)).
�p
(Ob) binds
8
Proposition
Fix w∈R.
Any optimal segmentation is:
∀p,p
′
∈supp(�),p<p
′
⟹max supp(�(⋅∣p))≤max supp(�(⋅∣p
′
)).
�p
(Ob) binds
8
Strongly-redistributive segmentations
Proposition
Fix w(�,p) =�(�)(�–p)1
�≥p.
There �
⋆
>1such that if
�(�
k)
�(�
k+1)
≥�
⋆
for any
�
k,�
k+1, then any optimal segmentation is:
∀p,p
′
∈supp(�),p<p
′
⟹max supp(�(⋅∣p))≤p
′
.
�p
Gives a simple algorithm to construct
strongly redistributive segmentations.
9
Proposition
Fix w(�,p) =�(�)(�–p)1
�≥p.
There �
⋆
>1such that if
�(�
k)
�(�
k+1)
≥�
⋆
for any
�
k,�
k+1, then any optimal segmentation is:
∀p,p
′
∈supp(�),p<p
′
⟹max supp(�(⋅∣p))≤p
′
.
�p
Gives a simple algorithm to construct
strongly redistributive segmentations.
9
Strongly-redistributive segmentations
Proposition
Fix w(�,p) =�(�)(�–p)1
�≥p.
There �
⋆
>1such that if
�(�
k)
�(�
k+1)
≥�
⋆
for any
�
k,�
k+1, then any optimal segmentation is:
∀p,p
′
∈supp(�),p<p
′
⟹max supp(�(⋅∣p))≤p
′
.
�p
Gives a simple algorithm to construct
strongly redistributive segmentations.
9
Proposition
Fix w(�,p) =�(�)(�–p)1
�≥p.
There �
⋆
>1such that if
�(�
k)
�(�
k+1)
≥�
⋆
for any
�
k,�
k+1, then any optimal segmentation is:
∀p,p
′
∈supp(�),p<p
′
⟹max supp(�(⋅∣p))≤p
′
.
�p
Gives a simple algorithm to construct
strongly redistributive segmentations.
9
Strongly-redistributive segmentations
Proposition
Fix w(�,p) =�(�)(�–p)1
�≥p.
There �
⋆
>1such that if
�(�
k)
�(�
k+1)
≥�
⋆
for any
�
k,�
k+1, then any optimal segmentation is:
∀p,p
′
∈supp(�),p<p
′
⟹max supp(�(⋅∣p))≤p
′
.
�p
Gives a simple algorithm to construct
strongly redistributive segmentations.
9
Proposition
Fix w(�,p) =�(�)(�–p)1
�≥p.
There �
⋆
>1such that if
�(�
k)
�(�
k+1)
≥�
⋆
for any
�
k,�
k+1, then any optimal segmentation is:
∀p,p
′
∈supp(�),p<p
′
⟹max supp(�(⋅∣p))≤p
′
.
�p
Gives a simple algorithm to construct
strongly redistributive segmentations.
9
Strongly-redistributive segmentations
Proposition
Fix w(�,p) =�(�)(�–p)1
�≥p.
There �
⋆
>1such that if
�(�
k)
�(�
k+1)
≥�
⋆
for any
�
k,�
k+1, then any optimal segmentation is:
∀p,p
′
∈supp(�),p<p
′
⟹max supp(�(⋅∣p))≤p
′
.
�p
Gives a simple algorithm to construct
strongly redistributive segmentations.
9
Proposition
Fix w(�,p) =�(�)(�–p)1
�≥p.
There �
⋆
>1such that if
�(�
k)
�(�
k+1)
≥�
⋆
for any
�
k,�
k+1, then any optimal segmentation is:
∀p,p
′
∈supp(�),p<p
′
⟹max supp(�(⋅∣p))≤p
′
.
�p
Gives a simple algorithm to construct
strongly redistributive segmentations.
9
Redistributive rents
Definition (Rent markets)
We say that�∈ Δ(Θ) is a
redistributive objectivew, optimal segmentation gives additional profit to the
seller. LetΓbe the set of rent markets.�p�
⋆
�
⋆
If obedient,̄��is the
monotone segmentation that does
not
10
Definition (Rent markets)
We say that�∈ Δ(Θ) is a
redistributive objectivew, optimal segmentation gives additional profit to the
seller. LetΓbe the set of rent markets.�p�
⋆
�
⋆
If obedient,̄��is the
monotone segmentation that does
not
10
Redistributive rents
Definition (Rent markets)
We say that�∈ Δ(Θ) is a
redistributive objectivew, optimal segmentation gives additional profit to the
seller. LetΓbe the set of rent markets.�p�
⋆
�
⋆
If obedient,̄��is the
monotone segmentation that does
not
10
Definition (Rent markets)
We say that�∈ Δ(Θ) is a
redistributive objectivew, optimal segmentation gives additional profit to the
seller. LetΓbe the set of rent markets.�p�
⋆
�
⋆
If obedient,̄��is the
monotone segmentation that does
not
10
Redistributive rents
Definition (Rent markets)
We say that�∈ Δ(Θ) is a
redistributive objectivew, optimal segmentation gives additional profit to the
seller. LetΓbe the set of rent markets.�p�
⋆
�
⋆
If obedient,̄��is the
monotone segmentation that does
not
10
Definition (Rent markets)
We say that�∈ Δ(Θ) is a
redistributive objectivew, optimal segmentation gives additional profit to the
seller. LetΓbe the set of rent markets.�p�
⋆
�
⋆
If obedient,̄��is the
monotone segmentation that does
not
10
Redistributive rents
Definition (Rent markets)
We say that�∈ Δ(Θ) is a
redistributive objectivew, optimal segmentation gives additional profit to the
seller. LetΓbe the set of rent markets.�p�
⋆
�
⋆
If obedient,̄��is the
monotone segmentation that does
not
10
Definition (Rent markets)
We say that�∈ Δ(Θ) is a
redistributive objectivew, optimal segmentation gives additional profit to the
seller. LetΓbe the set of rent markets.�p�
⋆
�
⋆
If obedient,̄��is the
monotone segmentation that does
not
10
Redistributive rents
Definition (Rent markets)
We say that�∈ Δ(Θ) is a
redistributive objectivew, optimal segmentation gives additional profit to the
seller. LetΓbe the set of rent markets.�p�
⋆
�
⋆
If obedient,̄��is the
monotone segmentation that does
not
Theorem
The set of rent marketsΓis
non-empty. Moreover,�∈ Γif, and
only if,̄��does not satisfy (Ob).
10
Definition (Rent markets)
We say that�∈ Δ(Θ) is a
redistributive objectivew, optimal segmentation gives additional profit to the
seller. LetΓbe the set of rent markets.�p�
⋆
�
⋆
If obedient,̄��is the
monotone segmentation that does
not
Theorem
The set of rent marketsΓis
non-empty. Moreover,�∈ Γif, and
only if,̄��does not satisfy (Ob).
10
Redistributive rents
Definition (Rent markets)
We say that�∈ Δ(Θ) is a
redistributive objectivew, optimal segmentation gives additional profit to the
seller. LetΓbe the set of rent markets.�p�
⋆
�
⋆
If obedient,̄��is the
monotone segmentation that does
not
Corollary
Let�∉ Γ. The segmentation̄��is the
unique �for
any w∈R.
10
Definition (Rent markets)
We say that�∈ Δ(Θ) is a
redistributive objectivew, optimal segmentation gives additional profit to the
seller. LetΓbe the set of rent markets.�p�
⋆
�
⋆
If obedient,̄��is the
monotone segmentation that does
not
Corollary
Let�∉ Γ. The segmentation̄��is the
unique �for
any w∈R.
10
Review of results
Results
1.
2.positive-assortative).
3.
4.(Not today)Redistributive segmentations are implementable by
regulation.
11
Results
1.
2.positive-assortative).
3.
4.(Not today)Redistributive segmentations are implementable by
regulation.
11
Related literature
•Welfare effects of market segmentation:
[Bergemann et al., 2015], [Dub´e and Misra, 2023],,
[Buchholz et al., 2024].
•Market-design-based redistribution:
[Condorelli, 2012],.
•Optimality of monotone information structures:
[Kolotilin, 2018], [Dworczak and Martini, 2019], [Ivanov, 2021],
[Mensch, 2021], [Kolotilin et al., 2022]…
12
•Welfare effects of market segmentation:
[Bergemann et al., 2015], [Dub´e and Misra, 2023],,
[Buchholz et al., 2024].
•Market-design-based redistribution:
[Condorelli, 2012],.
•Optimality of monotone information structures:
[Kolotilin, 2018], [Dworczak and Martini, 2019], [Ivanov, 2021],
[Mensch, 2021], [Kolotilin et al., 2022]…
12
References
Akbarpour, M., Dworczak, P., and Kominers, S. D. (2023).
Redistributive allocation mechanisms.
Journal of Political Economy.
Bergemann, D., Brooks, B., and Morris, S. (2015).
The limits of price discrimination.
American Economic Review, 105(3):921–57.
Buchholz, N., Doval, L., Kastl, J., Matejka, F., and Salz, T. (2024).
Personalized pricing and the value of time: Evidence from auctioned
cab rides.
Unpublished.
12
Akbarpour, M., Dworczak, P., and Kominers, S. D. (2023).
Redistributive allocation mechanisms.
Journal of Political Economy.
Bergemann, D., Brooks, B., and Morris, S. (2015).
The limits of price discrimination.
American Economic Review, 105(3):921–57.
Buchholz, N., Doval, L., Kastl, J., Matejka, F., and Salz, T. (2024).
Personalized pricing and the value of time: Evidence from auctioned
cab rides.
Unpublished.
12
References
Condorelli, D. (2012).
What money can’t buy: Efficient mechanism design with costly
signals.
Games & Economic Behavior, 75(2):613–624.
Condorelli, D. (2013).
Market and non-market mechanisms for the optimal allocation of
scarce resources.
Games & Economic Behavior, 82:582–591.
Doval, L. and Smolin, A. (2023).
Persuasion and welfare.
Journal of Political Economy.
12
Condorelli, D. (2012).
What money can’t buy: Efficient mechanism design with costly
signals.
Games & Economic Behavior, 75(2):613–624.
Condorelli, D. (2013).
Market and non-market mechanisms for the optimal allocation of
scarce resources.
Games & Economic Behavior, 82:582–591.
Doval, L. and Smolin, A. (2023).
Persuasion and welfare.
Journal of Political Economy.
12
References
Dub´e, J.-P. and Misra, S. (2023).
Personalized pricing and consumer welfare.
Journal of Political Economy, 131(1):131–189.
Dworczak, P., Kominers, S. D., and Akbarpour, M. (2021).
Redistribution Through Markets.
Econometrica, 89(4):1665–1698.
Dworczak, P. and Martini, G. (2019).
The simple economics of optimal persuasion.
Journal of Political Economy, 127(5):1993–2048.
12
Dub´e, J.-P. and Misra, S. (2023).
Personalized pricing and consumer welfare.
Journal of Political Economy, 131(1):131–189.
Dworczak, P., Kominers, S. D., and Akbarpour, M. (2021).
Redistribution Through Markets.
Econometrica, 89(4):1665–1698.
Dworczak, P. and Martini, G. (2019).
The simple economics of optimal persuasion.
Journal of Political Economy, 127(5):1993–2048.
12
References
Galperti, S., Levkun, A., and Perego, J. (2024).
The value of data records.
Review of Economic Studies, 91(2):1007–1038.
Haghpanah, N. and Siegel, R. (2023).
Pareto-improving segmentation of multiproduct markets.
Journal of Political Economy, 131(6):1546–1575.
Ivanov, M. (2021).
Optimal monotone signals in bayesian persuasion mechanisms.
Economic Theory, 72(3):955–1000.
12
Galperti, S., Levkun, A., and Perego, J. (2024).
The value of data records.
Review of Economic Studies, 91(2):1007–1038.
Haghpanah, N. and Siegel, R. (2023).
Pareto-improving segmentation of multiproduct markets.
Journal of Political Economy, 131(6):1546–1575.
Ivanov, M. (2021).
Optimal monotone signals in bayesian persuasion mechanisms.
Economic Theory, 72(3):955–1000.
12
References
Kolotilin, A. (2018).
Optimal information disclosure: A linear programming approach.
Theoretical Economics, 13(2):607–635.
Kolotilin, A., Mylovanov, T., and Zapechelnyuk, A. (2022).
Censorship as optimal persuasion.
Theoretical Economics, 17(2):561–585.
Mensch, J. (2021).
Monotone persuasion.
Games & Economic Behavior, 130:521–542.
12
Kolotilin, A. (2018).
Optimal information disclosure: A linear programming approach.
Theoretical Economics, 13(2):607–635.
Kolotilin, A., Mylovanov, T., and Zapechelnyuk, A. (2022).
Censorship as optimal persuasion.
Theoretical Economics, 17(2):561–585.
Mensch, J. (2021).
Monotone persuasion.
Games & Economic Behavior, 130:521–542.
12
References
Meyer, M. and Strulovici, B. (2015).
Beyond correlation: Measuring interdependence through
complementarities.
Unpublished.
12
Meyer, M. and Strulovici, B. (2015).
Beyond correlation: Measuring interdependence through
complementarities.
Unpublished.
12
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