Course-allocation mechanisms currently used have flaws in fairness and efficiency (Budish and Cantillon, 2009).
For the case of simple additive-separable preferences, the HZ generalization is attractive: efficient, interim envy free, and strategy-proof in the large economy.
Even nonlinear preferences, such as diminishing marginal utilities, can be encoded by the judicious design of message spaces: Milgrom (2010)’s assignment messages:
Suppose an agent has preference
V({a}) = 8,V({b}) = 7,V({a,b}) = 12. How do you express this nonlinear preferences via linear preferences?
Create the good contingent on usage: a1 :aconsumed alone,
a2 :aconsumed as a second item (along withb). The agent can reportva1= 8,va2= 5,andvb= 7, along with the constraint that she can consume at most one out of{a1,a2} and at most one out of{a1,b}.
The trick doesn’t work for complementary goods (e.g., supposeV({a,b}) = 20).
Application: Course Allocation
Course-allocation mechanisms currently used have flaws in fairness and efficiency (Budish and Cantillon, 2009).
For the case of simple additive-separable preferences, the HZ generalization is attractive: efficient, interim envy free, and strategy-proof in the large economy.
Even nonlinear preferences, such as diminishing marginal utilities, can be encoded by the judicious design of message spaces: Milgrom (2010)’s assignment messages:
Suppose an agent has preference
V({a}) = 8,V({b}) = 7,V({a,b}) = 12. How do you express this nonlinear preferences via linear preferences?
Create the good contingent on usage: a1 :aconsumed alone,
a2 :aconsumed as a second item (along withb). The agent can reportva1= 8,va2= 5,andvb= 7, along with the constraint that she can consume at most one out of{a1,a2} and at most one out of{a1,b}.
The trick doesn’t work for complementary goods (e.g., supposeV({a,b}) = 20).
Application: Course Allocation
Course-allocation mechanisms currently used have flaws in fairness and efficiency (Budish and Cantillon, 2009).
For the case of simple additive-separable preferences, the HZ generalization is attractive: efficient, interim envy free, and strategy-proof in the large economy.
Even nonlinear preferences, such as diminishing marginal utilities, can be encoded by the judicious design of message spaces: Milgrom (2010)’s assignment messages:
Suppose an agent has preference
V({a}) = 8,V({b}) = 7,V({a,b}) = 12. How do you express this nonlinear preferences via linear preferences?
Create the good contingent on usage: a1 :aconsumed alone,
a2 :aconsumed as a second item (along withb). The agent can reportva1= 8,va2= 5,andvb= 7, along with the constraint that she can consume at most one out of{a1,a2} and at most one out of{a1,b}.
The trick doesn’t work for complementary goods (e.g., supposeV({a,b}) = 20).
Application: Course Allocation
Course-allocation mechanisms currently used have flaws in fairness and efficiency (Budish and Cantillon, 2009).
For the case of simple additive-separable preferences, the HZ generalization is attractive: efficient, interim envy free, and strategy-proof in the large economy.
Even nonlinear preferences, such as diminishing marginal utilities, can be encoded by the judicious design of message spaces: Milgrom (2010)’s assignment messages:
Suppose an agent has preference
V({a}) = 8,V({b}) = 7,V({a,b}) = 12. How do you express this nonlinear preferences via linear preferences?
Create the good contingent on usage: a1 :aconsumed alone,
a2 :aconsumed as a second item (along withb). The agent can reportva1= 8,va2= 5,andvb= 7, along with the constraint that she can consume at most one out of{a1,a2} and at most one out of{a1,b}.
The trick doesn’t work for complementary goods (e.g., supposeV({a,b}) = 20).
Application: Course Allocation
Course-allocation mechanisms currently used have flaws in fairness and efficiency (Budish and Cantillon, 2009).
For the case of simple additive-separable preferences, the HZ generalization is attractive: efficient, interim envy free, and strategy-proof in the large economy.
Even nonlinear preferences, such as diminishing marginal utilities, can be encoded by the judicious design of message spaces: Milgrom (2010)’s assignment messages:
Suppose an agent has preference
V({a}) = 8,V({b}) = 7,V({a,b}) = 12. How do you express this nonlinear preferences via linear preferences?
Create the good contingent on usage: a1 :aconsumed alone,
a2 :aconsumed as a second item (along withb). The agent can reportva1= 8,va2= 5,andvb= 7, along with the
constraint that she can consume at most one out of{a1,a2} and at most one out of{a1,b}.
The trick doesn’t work for complementary goods (e.g., supposeV({a,b}) = 20).
Application: Course Allocation
Course-allocation mechanisms currently used have flaws in fairness and efficiency (Budish and Cantillon, 2009).
For the case of simple additive-separable preferences, the HZ generalization is attractive: efficient, interim envy free, and strategy-proof in the large economy.
Even nonlinear preferences, such as diminishing marginal utilities, can be encoded by the judicious design of message spaces: Milgrom (2010)’s assignment messages:
Suppose an agent has preference
V({a}) = 8,V({b}) = 7,V({a,b}) = 12. How do you express this nonlinear preferences via linear preferences?
Create the good contingent on usage: a1 :aconsumed alone,
a2 :aconsumed as a second item (along withb). The agent can reportva1= 8,va2= 5,andvb= 7, along with the
constraint that she can consume at most one out of{a1,a2} and at most one out of{a1,b}.
The trick doesn’t work for complementary goods (e.g., supposeV({a,b}) = 20).