Implementation without commitment in moral hazard environments Bruno Salcedo Pennsylvania State University LAMES – November 2013
1 Introduction 2 Interdependent-choice equilibrium 3 Nash implementation without commitment 4 Equilibrium refinements
Coordination • Coordination or interdependent choices – the choices of some agents depending on the choices of others • e.g. others will be good to me if and only if I am good to them • Standard settings: repeated games or games with contracts • A player might be willing to choose some alternative today (or sign a contract) only because of the way his opponents will react in the future to his current choice • This paper investigates coordination in single-shot interactions without commitment
Coordination • Coordination or interdependent choices – the choices of some agents depending on the choices of others • e.g. others will be good to me if and only if I am good to them • Standard settings: repeated games or games with contracts • A player might be willing to choose some alternative today (or sign a contract) only because of the way his opponents will react in the future to his current choice • This paper investigates coordination in single-shot interactions without commitment
Coordination • Coordination or interdependent choices – the choices of some agents depending on the choices of others • e.g. others will be good to me if and only if I am good to them • Standard settings: repeated games or games with contracts • A player might be willing to choose some alternative today (or sign a contract) only because of the way his opponents will react in the future to his current choice • This paper investigates coordination in single-shot interactions without commitment
Moral hazard • Moral hazard – individual and social incentives are misaligned, e.g. Nash equilibria are Pareto inefficient • Moral hazard disappears with complete contracts (Coase’s theorem) or with repetition and patience (folk theorems) Question Which outcomes can be sustained as equilibria with the help of a non-strategic mediator but without repetition, monetary transfers or binding contracts? • Different literatures ask related questions, e.g. Aumann (1974, 1987); Forges (1986); Myerson (1986)
Moral hazard • Moral hazard – individual and social incentives are misaligned, e.g. Nash equilibria are Pareto inefficient • Moral hazard disappears with complete contracts (Coase’s theorem) or with repetition and patience (folk theorems) Question Which outcomes can be sustained as equilibria with the help of a non-strategic mediator but without repetition, monetary transfers or binding contracts? • Different literatures ask related questions, e.g. Aumann (1974, 1987); Forges (1986); Myerson (1986)
Moral hazard • Moral hazard – individual and social incentives are misaligned, e.g. Nash equilibria are Pareto inefficient • Moral hazard disappears with complete contracts (Coase’s theorem) or with repetition and patience (folk theorems) Question Which outcomes can be sustained as equilibria with the help of a non-strategic mediator but without repetition, monetary transfers or binding contracts? • Different literatures ask related questions, e.g. Aumann (1974, 1987); Forges (1986); Myerson (1986)
Moral hazard • Moral hazard – individual and social incentives are misaligned, e.g. Nash equilibria are Pareto inefficient • Moral hazard disappears with complete contracts (Coase’s theorem) or with repetition and patience (folk theorems) Question Which outcomes can be sustained as equilibria with the help of a non-strategic mediator but without repetition, monetary transfers or binding contracts? • Different literatures ask related questions, e.g. Aumann (1974, 1987); Forges (1986); Myerson (1986)
A prisoner’s dilemma – Nishihara (1997, 1999) • Two suspects of a crime are arrested • The DA has enough information to convict them for a misdemeanor but needs a signed confession to charge them for the alleged crime • Each prisoner is offered a sentence reduction in exchange for such confession C D C 1 , 1 − k , 1 + g D 1 + g , − k 0 , 0 k, g > 0 , g < 1
. . . managed by a trusted lawyer • The prisoners have a constitutional right to hire the services of a lawyer (she) who will schedule and be present in all their interactions with the DA • They could hire the same lawyer and instruct her as follows: • You must uniformly randomize the order of our appointments, so that each of us will be the first one to receive the offer with probability 1 / 2 • You must always recommend that we not confess, unless our accomplice has already confessed • In that case you should instruct us to also confess • Other than that, you must not reveal any additional information
. . . managed by a trusted lawyer • The prisoners have a constitutional right to hire the services of a lawyer (she) who will schedule and be present in all their interactions with the DA • They could hire the same lawyer and instruct her as follows: • You must uniformly randomize the order of our appointments, so that each of us will be the first one to receive the offer with probability 1 / 2 • You must always recommend that we not confess, unless our accomplice has already confessed • In that case you should instruct us to also confess • Other than that, you must not reveal any additional information
. . . managed by a trusted lawyer • The prisoners have a constitutional right to hire the services of a lawyer (she) who will schedule and be present in all their interactions with the DA • They could hire the same lawyer and instruct her as follows: • You must uniformly randomize the order of our appointments, so that each of us will be the first one to receive the offer with probability 1 / 2 • You must always recommend that we not confess, unless our accomplice has already confessed • In that case you should instruct us to also confess • Other than that, you must not reveal any additional information
b b b b b b b b b b b bc b b b Extensive form mechanism 0 1 0 1 D C 1 2 1 + g 1 + g C D C D − k − k � 1 0 � 2 2 � 1 � 1 2 − k − k 1 + g C D 1 + g D C 1 2 1 C D 0 1 0
Outline of the paper 1 Interdependent-choice equilibrium • Mediated games in which a trusted mediator manages the play • ICE are Nash outcomes of mediated games 2 Revelation principle • Large class of mechanisms consistent with no commitment, no transfers, and no repetition • Corresponding equilibrium outcomes are ICE • These restrictions rule out a folk theorem 3 Subgame perfection [not in this talk]
Outline of the paper 1 Interdependent-choice equilibrium • Mediated games in which a trusted mediator manages the play • ICE are Nash outcomes of mediated games 2 Revelation principle • Large class of mechanisms consistent with no commitment, no transfers, and no repetition • Corresponding equilibrium outcomes are ICE • These restrictions rule out a folk theorem 3 Subgame perfection [not in this talk]
Outline of the paper 1 Interdependent-choice equilibrium • Mediated games in which a trusted mediator manages the play • ICE are Nash outcomes of mediated games 2 Revelation principle • Large class of mechanisms consistent with no commitment, no transfers, and no repetition • Corresponding equilibrium outcomes are ICE • These restrictions rule out a folk theorem 3 Subgame perfection [not in this talk]
1 Introduction 2 Interdependent-choice equilibrium 3 Nash implementation without commitment 4 Equilibrium refinements
Environment • Strategic environment partially characterized by: • Players I = { 1 , 2 } • Finite sets of actions A i , A = × i ∈ I A i • Utility functions u i : A → R • NOT a simultaneous move game!! • Remain agnostic about the sequential and informational structures • Do not assume that choices are “simultaneous” nor independent
Environment • Strategic environment partially characterized by: • Players I = { 1 , 2 } • Finite sets of actions A i , A = × i ∈ I A i • Utility functions u i : A → R • NOT a simultaneous move game!! • Remain agnostic about the sequential and informational structures • Do not assume that choices are “simultaneous” nor independent
Mediated games • A non-strategic mediator “manages” the play through sequential private recommendations � � • A mediated game is characterized by a tuple α, θ, B = × i B i • α ( a ) is the probability that the mediator chooses to implement a • θ ( i | a ) is the probability that the mediator chooses i to move first, conditional on choosing to implement a • B i is the set of additional punishments that i can use as credible threats, the set of actual punishments is B ∗ i = B i ∪ supp( α i )
Mediated games • A non-strategic mediator “manages” the play through sequential private recommendations � � • A mediated game is characterized by a tuple α, θ, B = × i B i • α ( a ) is the probability that the mediator chooses to implement a • θ ( i | a ) is the probability that the mediator chooses i to move first, conditional on choosing to implement a • B i is the set of additional punishments that i can use as credible threats, the set of actual punishments is B ∗ i = B i ∪ supp( α i )
Recommend
More recommend
