Three-part partition games on rectangles

A partition game on a rectangle is a two-person zero-sum game in which the rectangle is partitioned into a finite number of regions and the payoff function is constant in each region. A special case with four regions is essentially Silverman's game, which has been extensively studied in recent...

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Bibliographic Details
Published inTheoretical computer science Vol. 259; no. 1-2; pp. 639 - 661
Main Author Heuer, Gerald A.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 28.05.2001
Elsevier
Subjects
Applied sciences
Exact sciences and technology
Game theory
Games on intervals
Operational research and scientific management
Operational research. Management science
Partition games
Partition games
Games on intervals
Partition
Optimal strategy
Existence theorem
interval fgame
Colonel Blotto game
Mixed strategy
partition game
Game theory
Interval
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Summary:A partition game on a rectangle is a two-person zero-sum game in which the rectangle is partitioned into a finite number of regions and the payoff function is constant in each region. A special case with four regions is essentially Silverman's game, which has been extensively studied in recent years. In this paper, we examine three-part partition games where the boundaries separating the regions are the graphs of two continuous functions. Various conditions under which optimal mixed strategies and game value do or do not exist are found, as are optimal strategies and value in case they exist. Some games of this type have in the classical game theory literature been interpreted as continuous Colonel Blotto games.
Bibliography:ObjectType-Article-2
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ISSN:0304-3975
1879-2294
DOI:10.1016/S0304-3975(00)00404-7