# Uniqueness of optimal strategies in Captain Lotto games

Uniqueness of optimal strategies in Captain Lotto games We consider the class of two-person zero-sum allocation games known as Captain Lotto games (Hart in Int J Game Theory 45:37–61, 2016). These are Colonel Blotto type games in which the players have capacity constraints. We consider the game with non-strict constraints, and with strict constraints. We show in most cases that when optimal strategies exist, they are necessarily unique. When they don’t exist, we characterize the pointwise limit of the cumulative distribution functions of $$\varepsilon$$ ε -optimal strategies. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Game Theory Springer Journals

# Uniqueness of optimal strategies in Captain Lotto games

International Journal of Game Theory, Volume 47 (1) – Jun 14, 2017
47 pages

/lp/springer_journal/uniqueness-of-optimal-strategies-in-captain-lotto-games-Ng0NxZLgnZ
Publisher
Springer Journals
Copyright © 2017 by Springer-Verlag Berlin Heidelberg
Subject
Economics; Economic Theory/Quantitative Economics/Mathematical Methods; Game Theory, Economics, Social and Behav. Sciences; Behavioral/Experimental Economics; Operations Research/Decision Theory
ISSN
0020-7276
eISSN
1432-1270
D.O.I.
10.1007/s00182-017-0578-6
Publisher site
See Article on Publisher Site

### Abstract

We consider the class of two-person zero-sum allocation games known as Captain Lotto games (Hart in Int J Game Theory 45:37–61, 2016). These are Colonel Blotto type games in which the players have capacity constraints. We consider the game with non-strict constraints, and with strict constraints. We show in most cases that when optimal strategies exist, they are necessarily unique. When they don’t exist, we characterize the pointwise limit of the cumulative distribution functions of $$\varepsilon$$ ε -optimal strategies.

### Journal

International Journal of Game TheorySpringer Journals

Published: Jun 14, 2017

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