Allocation Games with Caps: From Captain Lotto to All-Pay Auctions
Sergiu Hart
(*) Proof of Proposition 3 (better written and slightly more detailed)
Abstract
A Lotto game is a two-person zero-sum game where each player chooses a
distribution on nonnegative real numbers with given expectation, so as
to maximize the probability that his realized choice is higher than his
opponent's. These games arise in various competitive allocation setups
(e.g., contests, research and development races, political campaigns,
Colonel Blotto games). A Captain Lotto game is a Lotto game with
caps,
which are upper bounds on the numbers that may be chosen. First, we
solve the Captain Lotto games. Second, we show how to reduce all-pay
auctions to simpler games—expenditure games—using
the solution of
the corresponding Lotto games. As a particular application we solve
all-pay auctions with unequal caps, which yield a significant increase
in the seller's revenue (or, the players' efforts).
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First version: January 2013
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The Hebrew University of Jerusalem, Center for Rationality DP-670,
October 2014
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Revised, May 2015
- International Journal of Game Theory, 45 (2016), 1-2,
37-61
See also:
Last modified:
© Sergiu Hart