Accumulation games on graphs

Alpern, Steve; Fokkink, Robbert

doi:10.1002/net.21555

Cited by 5 publications

(3 citation statements)

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“…Caching games are a natural ancestors of accumulation games, introduced by Kikuta and Ruckle ( [16], [17] and [18]) and further studied in [1], [2] and [5]. Accumulation games, in their most general form, take place between a Hider who accumulates resources in stages over several time periods, and a Searcher who confiscates some of the resources in every period.…”

Section: Related Literaturementioning

confidence: 99%

The solution to an open problem for a caching game

Csóka

Lidbetter

2016

Naval Research Logistics

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Section: Related Literaturementioning

confidence: 99%

The solution to an open problem for a caching game

Csóka

Lidbetter

2016

Naval Research Logistics

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“…Closely related infiltration games involve a hider who traverses a path and a seeker who chooses a set of vertices that overlap with the hider as much as possible [8]. Another closely related class of games is accumulation games, which is a game between a hider, who distributes a divisible resource among a collection of descrete locations (e.g., nodes on a graph), and a seeker, who aims to find a sufficient fraction of the resource by searching a limited number of locations [68,10]. The goal of most of this work is to bound the value of the game (as a function of the graph) and, if possible, to mathematically characterize player strategies.…”

Section: Related Workmentioning

confidence: 99%

Strategic analysis of complex security scenarios.

Vorobeychik¹

2012

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Many advanced technical tools are available to prevent attacks on national infrastructure. Nevertheless, while traditional analyses of security problems have succeeded in producing good technical solutions, they have often ignored the human factor integral to these problems. Human attackers (who may be individuals or state-level attackers) expend substantial effort to breach security because they have the incentive for doing so. People involved in implementing security follow individual incentives, which need not align with global security concerns; consequently, desired security solutions are often implemented poorly, or not at all. This complex interplay between individual incentives and global (organizational and/or national) goals can be modeled and analyzed using game theoretic techniques. By analyzing not only what is possible, but also what is motivated, a holistic approach to security problems can be developed, informing policy and providing tools to policy makers.We study game theoretic models that unify several current incentive-based approaches to security, and develop simulation-based and mathematical optimization methods for analyzing such models that exploit the high-performance computing capabilities at Sandia. Our first model studies security in interdependent settings, offering a scalable local search heuristic to approximate optimal security decisions in general, and a linear programming approach, coupled with simulations of consequences, to optimally compute security in an important special case. Our second class of models addresses security patrolling problems when an adversary gets to observe the patrol location. We present a general framework, based on stochastic games, for computing optimal security policies in such settings, and present more scalable tools that apply in the important special cases. Our third contribution is a model of security that involves many defenders, but only models nonadaptive attackers (or natural disasters, inadvertent errors, etc). In this model, we demonstrate that the security decisions of many players result in global security configuration that is not very far from optimal, and is much more resilient to environment changes that an optimal solution. This positive effect dissipates, however, when the number of decision makers becomes too large.3

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“…Games of this type were introduced by Kikuta and Ruckle ([16], [17] and [18]) who called them accumulation games, and have been furthered studied for example in [2] and [4]. In the most general de…nition of accumulation games the Hider accumulates resources in stages over several time periods, but in practice most of the work in this area has focused on single stage games, which have come to be called caching games.…”

Section: Introductionmentioning

confidence: 99%

A Caching Game with Infinitely Divisible Hidden Material

Lidbetter¹

2015

SIAM J. Control Optim.

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This document is the author's final accepted version of the journal article. There may be differences between this version and the published version. You are advised to consult the publisher's version if you wish to cite from it. AbstractWe consider a caching game in which a unit amount of in…nitely divisible material is distributed among n 2 locations. A Searcher chooses how to distribute his search e¤ort r about the locations so as to maximize the probability she will …nd a given minimum amount m = 1 m r of the material. If the search e¤ort yi invested by the Searcher in a given location i is at least as great as the amount of material xi located there she …nds all of it, otherwise the amount she …nds is only yi. In other words she …nds min fxi; yig in location i. We seek the randomized distribution of search e¤ort that maximizes the probability of success for the Searcher in the worst case, hence we model the problem as a zero-sum win-lose game between the Searcher and a malevolent Hider who wishes to keep more than m of the material. We show that in the case r = m the game has a geometric interpretation that for n = 2 corresponds to a problem posed by W. H. Ruckle in his monograph, Geometric Games and Their Applications. We give solutions for the geometric game when n = 3 for certain values of m, and bounds on the value for other values of m. In the more general case r m we show that for n = 2 the game reduces to Ruckle's game.

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Accumulation games on graphs

Cited by 5 publications

References 19 publications

The solution to an open problem for a caching game

The solution to an open problem for a caching game

Strategic analysis of complex security scenarios.

A Caching Game with Infinitely Divisible Hidden Material

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