Bidding for envy-freeness
749
Table 8. Players’ valuations of bundles after the second round of compensations
B4 B1 B3 B2
|
P1 |
[50 |
50 |
50 |
45 |
|
P2 |
40 |
[6Ô] |
55 |
65 |
|
P3 |
65 |
0 |
[65] |
65 |
|
P4 |
60 |
50 |
50 |
[60] |
|
30 |
0 |
40 |
25 |
Graph G~
3)
4)
1)2!4
tion all compensations must be returned, and the compensation procedure is
restarted. Note that the bid matrix after the required permutation of columns
is now given by Table 1. As we know this new assignment is utilitarian and the
compensation procedure with ex-post payments will lead to an envy-free out-
come.
References
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Brams SJ,Kilgour DM (2001) Competitive fair division. J Political Econ (forthcoming)
Brams SJ, Taylor AD (1996) Fair division - from cake-cutting to dispute resolution.
Cambridge University Press, Cambridge, MA
Foley DK (1967) Resource allocation and the public sector. Yale Econ Essays 7: 45-98
Klijn F (2000) An algorithm for envy-free allocations in an economy with indivisible
objects and money. Soc Choice Welfare 17: 201-216
Knaster B (1946) Sur le proble`me du partage pragmatique de H Steinhaus. Ann Soc
Polonaise Math 19: 228-230
Steinhaus H (1948) The problem of fair division. Econometrica 16: 101-104
Su FE (1999) Rental harmony: Sperner’s lemma in fair division. Am Math Monthly
106: 930-942
Svensson LG (1983) Large indivisibles: An analysis with respect to price equilibrium
and fairness. Econometrica 51: 939-954
Tadenuma K, Thomson W (1991) No-envy and consistency in economies with indi-
visible goods. Econometrica 59: 1755-1767
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