CDAM: Computational, Discrete and Applicable Mathematics@LSE

 CDAM Research Report, LSE-CDAM-2008-18

September 2008

Accumulation Games on Graphs

Steve Alpern and Robbert Fokkink

Accumulation games on discrete locations were introduced by W. Ruckle and K. Kikuta. The Hider secretly distributes his total wealth h>1 over locations 1, 2,...,n. The Searcher con.scates the material from any r of these locations. The Hider wins if the wealth remaining at the n-r unsearched locations sums to at least 1; otherwise the Searcher wins. Their game models problems in which the Hider needs to have, after confiscation (or loss by natural causes), a sufficient amount of material (food, wealth, arms) to carry out some objective (survive the winter, buy a house, start an insurrection).

This paper takes the hiding locations to be the nodes of a graph and restricts the node sets the Searcher can remove to be drawn from a given family: the edges, the connected r-sets, or some other given sets of nodes. This models the case where the pilferer, or storm, is known to act only on a set of close locations. Unlike the original game, our game requires mixed strategies.

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