0
$\begingroup$

Thomson's How to Divide When There Isn’t Enough is a textbook on allocation problems (aka bankruptcy problems). I have a trouble understanding the following excerpt from it (p. 13):

[I]n various theories of resource allocation, one may ask that a rule always provide each agent the incentive to be truthful about the information the agent holds pri- vately [...],17 but this requirement is often incompatible with very minimal demands of efficiency and fairness in distribution.

where footnote 17 is

[...] This property of a rule known as “strategy-proofness” is the requirement that, for each economy and each agent, truth-telling be a dominant strategy in the manipulation game associated with the rule.

Here's how I tried to figure out that passage. I understood that this property was what Sprumont (1991) called strategy-proofness. Now, it is true that Sprumont's models are not bankruptcy problems, but I believe that some translations between results on both kinds of models are possible. In fact, what Sprumont calls the uniform allocation rule is what Thomson calls constrained equal awards rule (up to restriction and scaling).

Then I do not understand why that rule violates any reasonable basic requirement.

What does Thomson mean here?

Improve this question
$\endgroup$
4
  • $\begingroup$ Under the constrained equal rewards rule, someone who gets constrained has an incentive to state having a bigger claim. $\endgroup$ Commented Sep 14 at 10:37
  • $\begingroup$ @MichaelGreinecker Are you saying that, contrary to my believe stated above, the uniform allocation rule is not (the restriction of) constrained equal awards rule? $\endgroup$ Commented Sep 14 at 11:18
  • $\begingroup$ That I don't know; I'm saying that the constrained equal rewards rule is not strategy-proof. $\endgroup$ Commented Sep 14 at 11:43
  • $\begingroup$ They are not the same. The uniform rule very much relies on the single-peaked domain. In the claims problem, your claim might be $c_i$ but thats not the maximum of your preferences. You would prefer to get more than your claim if possible. That the entire problem, in the uniform, lying will possibly push you past your peak which is bad. In the constrained equal it might push you past which is good. $\endgroup$ Commented Sep 14 at 15:48

0

Reset to default

Start asking to get answers

Find the answer to your question by asking.

Ask question

Explore related questions

See similar questions with these tags.