ASSA 2024 slides on mechanism design approach

ASSA 2024 slides on mechanism design approach

1. A mechanism-design approach to property rights
Piotr Dworczak
?
Ellen Muir
(Northwestern; GRAPE) (Harvard)
January 6, 2024
ASSA Annual Meeting
Session: Advances in Mechanism and Information Design
?
Co-funded by the European Union (ERC, IMD-101040122). Views and opinions expressed are those of the authors
only and do not necessarily reect those of the European Union or the European Research Council.

2. Motivation
Assignment of property rightsmatters, particularly in the
presence of transaction costs (Coase, 1960; Williamson, 1979).
There aretrade-offsin the design of property rights:
Investment incentives;
Efciency of reallocation;
Market power and distribution of surplus.
Example: How to optimally design spectrum licenses?

3. Motivation
Assignment of property rightsmatters, particularly in the
presence of transaction costs (Coase, 1960; Williamson, 1979).
There aretrade-offsin the design of property rights:
Investment incentives;
Efciency of reallocation;
Market power and distribution of surplus.
Example: How to optimally design spectrum licenses?

4. Motivation
Assignment of property rightsmatters, particularly in the
presence of transaction costs (Coase, 1960; Williamson, 1979).
There aretrade-offsin the design of property rights:
Investment incentives;
Efciency of reallocation;
Market power and distribution of surplus.
Example: How to optimally design spectrum licenses?

5. Our framework
Property rightsdetermine the holder's outside options(with
regard to the underlying good) in economic interactions:
Full property right: Holder can always keep the good;
No right: Outside option is (normalized to) zero;Option to own: Holder can keep the good at a price....
Key modeling idea: Designerdoesn't control the allocation
directly but shecan design an agent's outside option.
This perspective allows us to characterize theoptimal property
rightusing a mechanism-design approach.
Result: The optimal property right is simple but more exible than
a conventional property right, often featuring anoption to own.

6. Our framework
Property rightsdetermine the holder's outside options(with
regard to the underlying good) in economic interactions:
Full property right: Holder can always keep the good;
No right: Outside option is (normalized to) zero;Option to own: Holder can keep the good at a price....
Key modeling idea: Designerdoesn't control the allocation
directly but shecan design an agent's outside option.
This perspective allows us to characterize theoptimal property
rightusing a mechanism-design approach.
Result: The optimal property right is simple but more exible than
a conventional property right, often featuring anoption to own.

7. Our framework
Property rightsdetermine the holder's outside options(with
regard to the underlying good) in economic interactions:
Full property right: Holder can always keep the good;
No right: Outside option is (normalized to) zero;Option to own: Holder can keep the good at a price....
Key modeling idea: Designerdoesn't control the allocation
directly but shecan design an agent's outside option.
This perspective allows us to characterize theoptimal property
rightusing a mechanism-design approach.
Result: The optimal property right is simple but more exible than
a conventional property right, often featuring anoption to own.

8. Our framework
Property rightsdetermine the holder's outside options(with
regard to the underlying good) in economic interactions:
Full property right: Holder can always keep the good;
No right: Outside option is (normalized to) zero;Option to own: Holder can keep the good at a price....
Key modeling idea: Designerdoesn't control the allocation
directly but shecan design an agent's outside option.
This perspective allows us to characterize theoptimal property
rightusing a mechanism-design approach.
Result: The optimal property right is simple but more exible than
a conventional property right, often featuring anoption to own.

9. Our framework
Property rightsdetermine the holder's outside options(with
regard to the underlying good) in economic interactions:
Full property right: Holder can always keep the good;
No right: Outside option is (normalized to) zero;Option to own: Holder can keep the good at a price....
Key modeling idea: Designerdoesn't control the allocation
directly but shecan design an agent's outside option.
This perspective allows us to characterize theoptimal property
rightusing a mechanism-design approach.
Result: The optimal property right is simple but more exible than
a conventional property right, often featuring anoption to own.

10. Our framework
Property rightsdetermine the holder's outside options(with
regard to the underlying good) in economic interactions:
Full property right: Holder can always keep the good;
No right: Outside option is (normalized to) zero;Option to own: Holder can keep the good at a price....
Key modeling idea: Designerdoesn't control the allocation
directly but shecan design an agent's outside option.
This perspective allows us to characterize theoptimal property
rightusing a mechanism-design approach.
Result: The optimal property right is simple but more exible than
a conventional property right, often featuring anoption to own.

11. Our framework
Property rightsdetermine the holder's outside options(with
regard to the underlying good) in economic interactions:
Full property right: Holder can always keep the good;
No right: Outside option is (normalized to) zero;Option to own: Holder can keep the good at a price....
Key modeling idea: Designerdoesn't control the allocation
directly but shecan design an agent's outside option.
This perspective allows us to characterize theoptimal property
rightusing a mechanism-design approach.
Result: The optimal property right is simple but more exible than
a conventional property right, often featuring anoption to own.

12. Our framework
Property rightsdetermine the holder's outside options(with
regard to the underlying good) in economic interactions:
Full property right: Holder can always keep the good;
No right: Outside option is (normalized to) zero;Option to own: Holder can keep the good at a price....
Key modeling idea: Designerdoesn't control the allocation
directly but shecan design an agent's outside option.
This perspective allows us to characterize theoptimal property
rightusing a mechanism-design approach.
Result: The optimal property right is simple but more exible than
a conventional property right, often featuring anoption to own.

13. Marginal contribution
Two large literatures studying property rights in the presence of
transaction costs:
Property rights affectefciencyunder private information:
Myerson and Satterthwaite (1983), Cramton, Gibbons and
Klemperer (1987),Che (2006), Segal and Whinston (2016), ...
Property rights affectinvestment incentives:
Grossman and Hart (1986), Hart and Moore (1990), Aghion,
Dewatripont and Rey (1994),Hart (1995), N¨oldeke and Schmidt
(1995, 1998), Maskin and Tirole (1999b), ...
Attractive properties of options to own were recognized.
We provide anoptimality foundation(in a “refreshed”
framework, allowing for market-design applications).

14. Marginal contribution
Two large literatures studying property rights in the presence of
transaction costs:
Property rights affectefciencyunder private information:
Myerson and Satterthwaite (1983), Cramton, Gibbons and
Klemperer (1987),Che (2006), Segal and Whinston (2016), ...
Property rights affectinvestment incentives:
Grossman and Hart (1986), Hart and Moore (1990), Aghion,
Dewatripont and Rey (1994),Hart (1995), N¨oldeke and Schmidt
(1995, 1998), Maskin and Tirole (1999b), ...
Attractive properties of options to own were recognized.
We provide anoptimality foundation(in a “refreshed”
framework, allowing for market-design applications).

15. Marginal contribution
Two large literatures studying property rights in the presence of
transaction costs:
Property rights affectefciencyunder private information:
Myerson and Satterthwaite (1983), Cramton, Gibbons and
Klemperer (1987),Che (2006), Segal and Whinston (2016), ...
Property rights affectinvestment incentives:
Grossman and Hart (1986), Hart and Moore (1990), Aghion,
Dewatripont and Rey (1994),Hart (1995), N¨oldeke and Schmidt
(1995, 1998), Maskin and Tirole (1999b), ...
Attractive properties of options to own were recognized.
We provide anoptimality foundation(in a “refreshed”
framework, allowing for market-design applications).

16. Marginal contribution
Two large literatures studying property rights in the presence of
transaction costs:
Property rights affectefciencyunder private information:
Myerson and Satterthwaite (1983), Cramton, Gibbons and
Klemperer (1987),Che (2006), Segal and Whinston (2016), ...
Property rights affectinvestment incentives:
Grossman and Hart (1986), Hart and Moore (1990), Aghion,
Dewatripont and Rey (1994),Hart (1995), N¨oldeke and Schmidt
(1995, 1998), Maskin and Tirole (1999b), ...
Attractive properties of options to own were recognized.
We provide anoptimality foundation(in a “refreshed”
framework, allowing for market-design applications).

17. Other related papers
Allocation mechanisms versus efcient investment:
Rogerson (1992), Bergemann and V¨alim¨aki (2002), Milgrom
(2017), Hateld, Kojima, and Kominers (2019), Gershkov,
Moldovanu, Strack, and Zhang (2021), Akbarpour, Kominers, Li,
Li, and Milgrom (2023), ...
Related techniques:Jullien (2000), Kleiner, Moldovanu, and
Strack (2021), Loertscher and Muir (2022), Kang (2023),
Akbarpour
R
Dworczak
R
Kominers (2023),...
Spectrum license design:Posner and Weyl (2017), Milgrom,
Weyl and Zhang (2017), Weyl and Zhang (2017), ...
Optimal patent design:Wright (1983), Klemperer (1990),
Gilbert and Shapiro (1990), Gallini (1992), Kremer (1998),
Hopenhayn, Llobet and Mitchell (2006), Weyl and Tirole (2012)...

18. Model
Model

19. Timeline

20. Timeline

21. Timeline

22. Timeline

23. Timeline

24. Timeline

25. Timeline

26. Timeline

27. Timeline

28. Timeline

29. Timeline

30. Timeline

31. Timeline

32. Model
Timet=2:
The agent's (private) typeand a (public) state!are drawn from
a joint distribution that depends on whether the agent invested.
Principal chooses a trading mechanism(x!();t!()), where
x2[0;1]denotes an allocation, andt2Rdenotes a transfer;
Mechanism is chosen subject to IC and IR constraints, and must
respect the rights that the agent holds.
Principal maximizesV(; !)x+t, where >0.
Agent's utility isxt.

33. Model
Agent's problem att=1
The agent decides whether to pay the costc>0 to invest.
If the agent invests:
!G,F!.
Otherwise:
!G,F
!, withF!
FOSD
F
!, for every!.
In thenon-contractible case, the mechanism att=2 and the
agent's rights do not depend on the investment decision.
In thecontractible case, the mechanism att=2 and the
agent's rights are contingent on the investment decision.

34. Model
Agent's problem att=1
The agent decides whether to pay the costc>0 to invest.
If the agent invests:
!G,F!.
Otherwise:
!G,F
!, withF!
FOSD
F
!, for every!.
In thenon-contractible case, the mechanism att=2 and the
agent's rights do not depend on the investment decision.
In thecontractible case, the mechanism att=2 and the
agent's rights are contingent on the investment decision.

35. Model
Designer's problem att=0
Designer chooses a menu of “rights”
M=f(x
i;t
i)g
i2I;
wherex
i2[0;1],t
i2R, and setIis arbitrary (Mis compact).
The agent can “execute” any one of these rights att=2.
Designer maximizesV
?
(; !)x+
?
t, where
?
0.
Assume: Investment is preferred by the designer to no investment;
investment can be induced by some rights; but it is not induced if the
agent holds no rights.

36. Model
Designer's problem att=0
Designer chooses a menu of “rights”
M=f(x
i;t
i)g
i2I;
wherex
i2[0;1],t
i2R, and setIis arbitrary (Mis compact).
The agent can “execute” any one of these rights att=2.
Designer maximizesV
?
(; !)x+
?
t, where
?
0.
Assume: Investment is preferred by the designer to no investment;
investment can be induced by some rights; but it is not induced if the
agent holds no rights.

37. Model
Designer's problem att=0
Designer chooses a menu of “rights”
M=f(x
i;t
i)g
i2I;
wherex
i2[0;1],t
i2R, and setIis arbitrary (Mis compact).
The agent can “execute” any one of these rights att=2.
Designer maximizesV
?
(; !)x+
?
t, where
?
0.
Technicalities:[;

]is a compact subset ofR;VandV
?
are
continuous in(and measurable in!),Fhas a continuous positive
density on.

38. Comments about the model

39. Comments about the model

40. Comments about the model

41. Comments about the model

42. Comments about the model
Rights create anoutside optionfor the agent: principal must
guarantee that the agent's type-utility from participating in the
mechanism is not lower thanmax
i2Ifx
it
ig.
The framework captures many conventional rights:Property right:M=f(x=1;t=0)g;
Cash payment:M=f(0;p)g;Property right with a resale option:M=f(1;0);(0;p)g;Renewable lease/ option to own:M=f(1;p)g;Partial property right:M=f(y;0)g, wherey2(0;1);Flexible property right:M=fs;p(s))g
s2[0;1].

43. Comments about the model
Rights create anoutside optionfor the agent: principal must
guarantee that the agent's type-utility from participating in the
mechanism is not lower thanmax
i2Ifx
it
ig.
The framework captures many conventional rights:Property right:M=f(x=1;t=0)g;
Cash payment:M=f(0;p)g;Property right with a resale option:M=f(1;0);(0;p)g;Renewable lease/ option to own:M=f(1;p)g;Partial property right:M=f(y;0)g, wherey2(0;1);Flexible property right:M=fs;p(s))g
s2[0;1].

44. Comments about the model
Rights create anoutside optionfor the agent: principal must
guarantee that the agent's type-utility from participating in the
mechanism is not lower thanmax
i2Ifx
it
ig.
The framework captures many conventional rights:Property right:M=f(x=1;t=0)g;
Cash payment:M=f(0;p)g;Property right with a resale option:M=f(1;0);(0;p)g;Renewable lease/ option to own:M=f(1;p)g;Partial property right:M=f(y;0)g, wherey2(0;1);Flexible property right:M=fs;p(s))g
s2[0;1].

45. Comments about the model
Rights create anoutside optionfor the agent: principal must
guarantee that the agent's type-utility from participating in the
mechanism is not lower thanmax
i2Ifx
it
ig.
The framework captures many conventional rights:Property right:M=f(x=1;t=0)g;
Cash payment:M=f(0;p)g;Property right with a resale option:M=f(1;0);(0;p)g;Renewable lease/ option to own:M=f(1;p)g;Partial property right:M=f(y;0)g, wherey2(0;1);Flexible property right:M=fs;p(s))g
s2[0;1].

46. Comments about the model
Rights create anoutside optionfor the agent: principal must
guarantee that the agent's type-utility from participating in the
mechanism is not lower thanmax
i2Ifx
it
ig.
The framework captures many conventional rights:Property right:M=f(x=1;t=0)g;
Cash payment:M=f(0;p)g;Property right with a resale option:M=f(1;0);(0;p)g;Renewable lease/ option to own:M=f(1;p)g;Partial property right:M=f(y;0)g, wherey2(0;1);Flexible property right:M=fs;p(s))g
s2[0;1].

47. Comments about the model
Rights create anoutside optionfor the agent: principal must
guarantee that the agent's type-utility from participating in the
mechanism is not lower thanmax
i2Ifx
it
ig.
The framework captures many conventional rights:Property right:M=f(x=1;t=0)g;
Cash payment:M=f(0;p)g;Property right with a resale option:M=f(1;0);(0;p)g;Renewable lease/ option to own:M=f(1;p)g;Partial property right:M=f(y;0)g, wherey2(0;1);Flexible property right:M=fs;p(s))g
s2[0;1].

48. Comments about the model
Rights create anoutside optionfor the agent: principal must
guarantee that the agent's type-utility from participating in the
mechanism is not lower thanmax
i2Ifx
it
ig.
The framework captures many conventional rights:Property right:M=f(x=1;t=0)g;
Cash payment:M=f(0;p)g;Property right with a resale option:M=f(1;0);(0;p)g;Renewable lease/ option to own:M=f(1;p)g;Partial property right:M=f(y;0)g, wherey2(0;1);Flexible property right:M=fs;p(s))g
s2[0;1].

49. Comments about the model
Rights create anoutside optionfor the agent: principal must
guarantee that the agent's type-utility from participating in the
mechanism is not lower thanmax
i2Ifx
it
ig.
The framework captures many conventional rights:Property right:M=f(x=1;t=0)g;
Cash payment:M=f(0;p)g;Property right with a resale option:M=f(1;0);(0;p)g;Renewable lease/ option to own:M=f(1;p)g;Partial property right:M=f(y;0)g, wherey2(0;1);Flexible property right:M=fs;p(s))g
s2[0;1].

50. Analysis and results
Analysis and results

51. Main result
Theorem
There exists an optimal menu of rights that takes the form
M
?
=f(1;p);(y;p
0
)gfor some p;p
0
2Rand y2[0;1).
Comments:
The optimal menu is simple in that it consists ofat most two
types of rights.
One of the rights can be taken to be anoption to own.

52. Main result
Theorem
There exists an optimal menu of rights that takes the form
M
?
=f(1;p);(y;p
0
)gfor some p;p
0
2Rand y2[0;1).
Comments:
The optimal menu is simple in that it consists ofat most two
types of rights.
One of the rights can be taken to be anoption to own.

53. Main result
Theorem
There exists an optimal menu of rights that takes the form
M
?
=f(1;p);(y;p
0
)gfor some p;p
0
2Rand y2[0;1).
Comments:
The optimal menu is simple in that it consists ofat most two
types of rights.
One of the rights can be taken to be anoption to own.

54. Proof outline
1. Mis equivalent to an outside-option functionR()for the
agent in the second-period mechanism, by setting
R() = maxf0;max
i2Ifx
it
igg.
2.
additional constraint:U()R()(as in Jullien, 2000).
3.
(Myerson, 1981), showing that the set of types at which the
outside-option constraint binds is independent ofR.
More
4.
optimally att=2 arelinearinR.
5.6.
which takes the form(1;p).

55. Proof outline
1. Mis equivalent to an outside-option functionR()for the
agent in the second-period mechanism, by setting
R() = maxf0;max
i2Ifx
it
igg.
2.
additional constraint:U()R()(as in Jullien, 2000).
3.
(Myerson, 1981), showing that the set of types at which the
outside-option constraint binds is independent ofR.
More
4.
optimally att=2 arelinearinR.
5.6.
which takes the form(1;p).

56. Proof outline
1. Mis equivalent to an outside-option functionR()for the
agent in the second-period mechanism, by setting
R() = maxf0;max
i2Ifx
it
igg.
2.
additional constraint:U()R()(as in Jullien, 2000).
3.
(Myerson, 1981), showing that the set of types at which the
outside-option constraint binds is independent ofR.
More
4.
optimally att=2 arelinearinR.
5.6.
which takes the form(1;p).

57. Proof outline
1. Mis equivalent to an outside-option functionR()for the
agent in the second-period mechanism, by setting
R() = maxf0;max
i2Ifx
it
igg.
2.
additional constraint:U()R()(as in Jullien, 2000).
3.
(Myerson, 1981), showing that the set of types at which the
outside-option constraint binds is independent ofR.
More
4.
optimally att=2 arelinearinR.
5.6.
which takes the form(1;p).

58. Proof outline
1. Mis equivalent to an outside-option functionR()for the
agent in the second-period mechanism, by setting
R() = maxf0;max
i2Ifx
it
igg.
2.
additional constraint:U()R()(as in Jullien, 2000).
3.
(Myerson, 1981), showing that the set of types at which the
outside-option constraint binds is independent ofR.
More
4.
optimally att=2 arelinearinR.
5.6.
which takes the form(1;p).

59. Proof outline
1. Mis equivalent to an outside-option functionR()for the
agent in the second-period mechanism, by setting
R() = maxf0;max
i2Ifx
it
igg.
2.
additional constraint:U()R()(as in Jullien, 2000).
3.
(Myerson, 1981), showing that the set of types at which the
outside-option constraint binds is independent ofR.
More
4.
optimally att=2 arelinearinR.
5.6.
which takes the form(1;p).

60. Corollaries of the proof
With no constraint, the problem is to maximize a linear objective
=)solution is an extreme point
=)option to ownis optimal.
Easy extension toKlinear constraints
=)We need at mostK+1 options in the optimal menu.
Extension tocontinuous investment:
Suppose agent choosese2[0;1]at strictly convex cost
c(e), andeis the probability thatis drawn fromF!.
Satisfying FOC at the target investment levele
?
is sufcient
for obedience.
FOC is linear inR() =)we needtwo options in the
optimal menu.

61. Corollaries of the proof
With no constraint, the problem is to maximize a linear objective
=)solution is an extreme point
=)option to ownis optimal.
Easy extension toKlinear constraints
=)We need at mostK+1 options in the optimal menu.
Extension tocontinuous investment:
Suppose agent choosese2[0;1]at strictly convex cost
c(e), andeis the probability thatis drawn fromF!.
Satisfying FOC at the target investment levele
?
is sufcient
for obedience.
FOC is linear inR() =)we needtwo options in the
optimal menu.

62. Corollaries of the proof
With no constraint, the problem is to maximize a linear objective
=)solution is an extreme point
=)option to ownis optimal.
Easy extension toKlinear constraints
=)We need at mostK+1 options in the optimal menu.
Extension tocontinuous investment:
Suppose agent choosese2[0;1]at strictly convex cost
c(e), andeis the probability thatis drawn fromF!.
Satisfying FOC at the target investment levele
?
is sufcient
for obedience.
FOC is linear inR() =)we needtwo options in the
optimal menu.

63. The monotone case
Assumethat:
Buyer and seller virtual surpluses aremonotone:
B()
1F()
f()
and
S()+
F()
f()
are non-decreasing in;
Both thedesigner's and the principal's objectivefunctions
V
?
(; !)andV(; !)arenon-decreasingin the agent's type.
The cost of investmentcis sufciently high.

64. The monotone case
Proposition
When the investment decision of the agent is contractible, the
designer optimally chooses a menu of the form
M
?
=f(1;p);(0;p
0
)gfor some p2Rand p
0
2R+.
When the investment decision of the agent is not contractible, the
designer optimally chooses a menu of the form M
?
=f(1;p);(y;0)g
for some p2Rand y2[0;1).
When investment is contractible,offering a cash paymentfor
investment is effective.
When investment is not contractible, the designer can incentivize
investment only byshifting more rents to higher types.

65. The monotone case
Proposition
When the investment decision of the agent is contractible, the
designer optimally chooses a menu of the form
M
?
=f(1;p);(0;p
0
)gfor some p2Rand p
0
2R+.
When the investment decision of the agent is not contractible, the
designer optimally chooses a menu of the form M
?
=f(1;p);(y;0)g
for some p2Rand y2[0;1).
When investment is contractible,offering a cash paymentfor
investment is effective.
When investment is not contractible, the designer can incentivize
investment only byshifting more rents to higher types.

66. The monotone case
Proposition
When the investment decision of the agent is contractible, the
designer optimally chooses a menu of the form
M
?
=f(1;p);(0;p
0
)gfor some p2Rand p
0
2R+.
When the investment decision of the agent is not contractible, the
designer optimally chooses a menu of the form M
?
=f(1;p);(y;0)g
for some p2Rand y2[0;1).
When investment is contractible,offering a cash paymentfor
investment is effective.
When investment is not contractible, the designer can incentivize
investment only byshifting more rents to higher types.

67. Applications
In the paper, we look at severalapplications:
1.
2.
3.
4.
5.

68. Summary and future directions
Summary and future directions

69. Summary
We introduced a simple but exible framework for analyzing
optimal design of (property) rights.
Property rightspartially restore commitmentto future trading
mechanisms.
We used a mechanism-design approach to characterizeoptimal
property rights.
The optimal right often features anoption to own.

70. Future directions
Can the designer do better byconditioning rights on the state
in an incentive-compatible way?
Consider designing a menu of menusM=fM
jg
jsuch that the
principal selects a menuM
jbased on realized state and the
agent chooses an option fromM
j.
This can help!
What if both parties (att=2) haveprivate information and
bargaining poweris not exogenous?
Allocate rights to both
parties?
What if the designer can prohibit the usage of certain
allocation-transfer pairs by the principal?
Optimalallocation of rights att=0 to multiple agents?

71. Future directions
Can the designer do better byconditioning rights on the state
in an incentive-compatible way?
Consider designing a menu of menusM=fM
jg
jsuch that the
principal selects a menuM
jbased on realized state and the
agent chooses an option fromM
j.
This can help!
What if both parties (att=2) haveprivate information and
bargaining poweris not exogenous?
Allocate rights to both
parties?
What if the designer can prohibit the usage of certain
allocation-transfer pairs by the principal?
Optimalallocation of rights att=0 to multiple agents?

72. Future directions
Can the designer do better byconditioning rights on the state
in an incentive-compatible way?
Consider designing a menu of menusM=fM
jg
jsuch that the
principal selects a menuM
jbased on realized state and the
agent chooses an option fromM
j.
This can help!
What if both parties (att=2) haveprivate information and
bargaining poweris not exogenous?
Allocate rights to both
parties?
What if the designer can prohibit the usage of certain
allocation-transfer pairs by the principal?
Optimalallocation of rights att=0 to multiple agents?

73. Future directions
Can the designer do better byconditioning rights on the state
in an incentive-compatible way?
Consider designing a menu of menusM=fM
jg
jsuch that the
principal selects a menuM
jbased on realized state and the
agent chooses an option fromM
j.
This can help!
What if both parties (att=2) haveprivate information and
bargaining poweris not exogenous?
Allocate rights to both
parties?
What if the designer can prohibit the usage of certain
allocation-transfer pairs by the principal?
Optimalallocation of rights att=0 to multiple agents?

74. Future directions
Can the designer do better byconditioning rights on the state
in an incentive-compatible way?
Consider designing a menu of menusM=fM
jg
jsuch that the
principal selects a menuM
jbased on realized state and the
agent chooses an option fromM
j.
This can help!
What if both parties (att=2) haveprivate information and
bargaining poweris not exogenous?
Allocate rights to both
parties?
What if the designer can prohibit the usage of certain
allocation-transfer pairs by the principal?
Optimalallocation of rights att=0 to multiple agents?

75. Future directions
Can the designer do better byconditioning rights on the state
in an incentive-compatible way?
Consider designing a menu of menusM=fM
jg
jsuch that the
principal selects a menuM
jbased on realized state and the
agent chooses an option fromM
j.
This can help!
What if both parties (att=2) haveprivate information and
bargaining poweris not exogenous?
Allocate rights to both
parties?
What if the designer can prohibit the usage of certain
allocation-transfer pairs by the principal?
Optimalallocation of rights att=0 to multiple agents?

76. Future directions
Can the designer do better byconditioning rights on the state
in an incentive-compatible way?
Consider designing a menu of menusM=fM
jg
jsuch that the
principal selects a menuM
jbased on realized state and the
agent chooses an option fromM
j.
This can help!
What if both parties (att=2) haveprivate information and
bargaining poweris not exogenous?
Allocate rights to both
parties?
What if the designer can prohibit the usage of certain
allocation-transfer pairs by the principal?
Optimalallocation of rights att=0 to multiple agents?

77. Future directions
Can the designer do better byconditioning rights on the state
in an incentive-compatible way?
Consider designing a menu of menusM=fM
jg
jsuch that the
principal selects a menuM
jbased on realized state and the
agent chooses an option fromM
j. This can help!
What if both parties (att=2) haveprivate information and
bargaining poweris not exogenous? Allocate rights to both
parties?
What if the designer can prohibit the usage of certain
allocation-transfer pairs by the principal?
Optimalallocation of rights att=0 to multiple agents?

78. Appendix
Appendix

79. Ironing Jullien (2000)
Back

80. Ironing Jullien (2000)
Back

81. Ironing Jullien (2000)
Back

82. Ironing Jullien (2000)
Back

83. Ironing Jullien (2000)
Back

84. Ironing Jullien (2000)
Back
Why does ironing work?
The outside option constraint is:
u+
Z


x()dU()R()u
0
+
Z


x0()d:
This is (almost) asecond-order stochastic dominance
constraint ifxandx0are treated as CDFs.
Ironing corresponds to taking a mean-preserving spread of the
distribution—it preserves the outside-option constraint.
Related work: Kleiner, Moldovanu, and Strack (2021), Loertscher
and Muir (2022), Akbarpour
R
Dworczak
R
Kominers (2023)

85. Ironing Jullien (2000)
Back
Why does ironing work?
The outside option constraint is:
u+
Z


x()dU()R()u
0
+
Z


x0()d:
This is (almost) asecond-order stochastic dominance
constraint ifxandx0are treated as CDFs.
Ironing corresponds to taking a mean-preserving spread of the
distribution—it preserves the outside-option constraint.
Related work: Kleiner, Moldovanu, and Strack (2021), Loertscher
and Muir (2022), Akbarpour
R
Dworczak
R
Kominers (2023)

86. Ironing Jullien (2000)
Back
Why does ironing work?
The outside option constraint is:
u+
Z


x()dU()R()u
0
+
Z


x0()d:
This is (almost) asecond-order stochastic dominance
constraint ifxandx0are treated as CDFs.
Ironing corresponds to taking a mean-preserving spread of the
distribution—it preserves the outside-option constraint.
Related work: Kleiner, Moldovanu, and Strack (2021), Loertscher
and Muir (2022), Akbarpour
R
Dworczak
R
Kominers (2023)

87. Ironing Jullien (2000)
Back
Why does ironing work?
The outside option constraint is:
u+
Z


x()du
0
+
Z


x0()d:
This is (almost) asecond-order stochastic dominance
constraint ifxandx0are treated as CDFs.
Ironing corresponds to taking a mean-preserving spread of the
distribution—it preserves the outside-option constraint.
Related work: Kleiner, Moldovanu, and Strack (2021), Loertscher
and Muir (2022), Akbarpour
R
Dworczak
R
Kominers (2023)

88. Ironing Jullien (2000)
Back
Why does ironing work?
The outside option constraint is:
u+
Z


x()du
0
+
Z


x0()d:
This is (almost) asecond-order stochastic dominance
constraint ifxandx0are treated as CDFs.
Ironing corresponds to taking a mean-preserving spread of the
distribution—it preserves the outside-option constraint.
Related work: Kleiner, Moldovanu, and Strack (2021), Loertscher
and Muir (2022), Akbarpour
R
Dworczak
R
Kominers (2023)

89. Ironing Jullien (2000)
Back
Why does ironing work?
The outside option constraint is:
u+
Z


x()du
0
+
Z


x0()d:
This is (almost) asecond-order stochastic dominance
constraint ifxandx0are treated as CDFs.
Ironing corresponds to taking a mean-preserving spread of the
distribution—it preserves the outside-option constraint.
Related work: Kleiner, Moldovanu, and Strack (2021), Loertscher
and Muir (2022), Akbarpour
R
Dworczak
R
Kominers (2023)

90. Ironing Jullien (2000)
Back
Why does ironing work?
The outside option constraint is:
u+
Z


x()du
0
+
Z


x0()d:
This is (almost) asecond-order stochastic dominance
constraint ifxandx0are treated as CDFs.
Ironing corresponds to taking a mean-preserving spread of the
distribution—it preserves the outside-option constraint.
Related work: Kleiner, Moldovanu, and Strack (2021), Loertscher
and Muir (2022), Akbarpour
R
Dworczak
R
Kominers (2023)