dynamic mechanism design without transferspages.cs.wisc.edu/~yw/files/thesis_slides.pdf · 2019. 4....
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Chapter 1 Chapter 2 Chapter 3
Dynamic Mechanism Design without Transfers
Young WuAdvisors: Marcin Peski, Colin Stewart, Xianwen Shi
August 17, 2018
Chapter 1 Chapter 2 Chapter 3
Chapters
1 Design of Committee Search
2 School Choice with Observable Characteristics
3 Mechanism Design for Stopping Problems with Two Actions
Chapter 1 Chapter 2 Chapter 3
Chapter 1Design of Committee Search
Committee search problems that have,
1 Sequential decision,
2 Irreversible decision,
3 Private value,
4 Public allocation, and
5 No transfers.
Chapter 1 Chapter 2 Chapter 3
Static ProblemBinary Mechanisms
v2
v v̄v
v̄
v�1
v�2
v2
v v̄v
v̄
v�2
v�1v1v v̄
v
v̄
v v̄v
v̄
v�1v v̄
v
v̄
v�2
v1v v̄v
v̄
Chapter 1 Chapter 2 Chapter 3
Two-Period ProblemTernary Mechanisms
v1,T�1
v2,T�1
v v̄v
v̄
a1
r2
r1
a2
Inside each region:continuationmechanismfrom T
Chapter 1 Chapter 2 Chapter 3
Three-Period ProblemMore Ternary Mechanisms
v1,T�2
v2,T�2
v v̄v
v̄
a1
r2
r1
a2
Inside each region:continuationmechanismfrom T � 1
Chapter 1 Chapter 2 Chapter 3
Pareto Optimal Mechanisms
Chapter 1 Chapter 2 Chapter 3
Other Boundary MechanismsWorse for 1, Better for 2
Chapter 1 Chapter 2 Chapter 3
Other Boundary MechanismsBetter for 1, Worse for 2
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Other Boundary MechanismsWorse for Both
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Chapter 2: School Choice with Observable Characteristics
School choice problem where,
1 Students have observable characteristics (groups), and
2 Maybe planer knows something about students’ preferences.
Focus on ordinal mechanisms that have,
1 Efficiency,
2 Within-group Envy-freeness, and
3 Within-group Symmetry.
Chapter 1 Chapter 2 Chapter 3
Probabilistic Serial Mechanism1 School
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Modified Probabilistic Serial Mechanism3 Schools
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Sub-capacities
To find an ordinal mechanism that maximizes cardinalutilities, the planner
1 Chooses sub-capacities (convex programming problem),
2 Runs modified probabilistic serial mechanism.
Chapter 1 Chapter 2 Chapter 3
Chapter 3Mechanism Design for Stopping Problems with Two Actions
Principal-agent problem in which,
1 Agent observes Markov stochastic process,
2 Agent chooses when to stop and one of two actions, and
3 Principal uses transfers to implement stopping decision rules.
Chapter 1 Chapter 2 Chapter 3
A Threshold Stopping Decision Rule
Chapter 1 Chapter 2 Chapter 3
An Implementable Stopping Decision RuleExample 1
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An Implementable Stopping Decision RuleExample 2
Chapter 1 Chapter 2 Chapter 3
An Implementable Stopping Decision RuleExample 3
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Conditions Required
On the stochastic process,
1 Monotonic transition,
2 Continuous transition, and
3 Full support.
On the utility functions,
1 Spence-Mirrlees Condition (monotonicity), and
2 Modified Pavan-Segal-Toikka (single-crossing).
Chapter 1 Chapter 2 Chapter 3
Single Crossing ConditionsExample 1
Chapter 1 Chapter 2 Chapter 3
Single Crossing ConditionsExample 2
Chapter 1 Chapter 2 Chapter 3
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