Abstract
We present efficient algorithms for computing optimal or approximately optimal strategies in a zero-sum game for which player I has n pure strategies and player II has an arbitrary number of pure strategies. We assume that for any given mixed strategy of player I, a best response, or “approximate” best response, of player II can be found by an oracle in time polynomial in n. We then show how our algorithms may be applied to several search games with applications to security and counterterrorism. We evaluate our main algorithm experimentally on a prototypical search game. Our results show that it performs well compared with existing well-known algorithms for solving zero-sum games that can also be used to solve search games given a best-response oracle.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 731-743 |
| Number of pages | 13 |
| Journal | Operations Research |
| Volume | 67 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jan 1 2019 |
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Keywords
- Games/group decisions
- Learning
- Networks/graphs
- Search/surveillance
- Tree algorithms
ASJC Scopus subject areas
- Computer Science Applications
- Management Science and Operations Research
Cite this
Solving zero-sum games using best-response oracles with applications to search games. / Hellerstein, Lisa; Lidbetter, Thomas; Pirutinsky, Daniel.
In: Operations Research, Vol. 67, No. 3, 01.01.2019, p. 731-743.Research output: Contribution to journal › Review article
}
TY - JOUR
T1 - Solving zero-sum games using best-response oracles with applications to search games
AU - Hellerstein, Lisa
AU - Lidbetter, Thomas
AU - Pirutinsky, Daniel
PY - 2019/1/1
Y1 - 2019/1/1
N2 - We present efficient algorithms for computing optimal or approximately optimal strategies in a zero-sum game for which player I has n pure strategies and player II has an arbitrary number of pure strategies. We assume that for any given mixed strategy of player I, a best response, or “approximate” best response, of player II can be found by an oracle in time polynomial in n. We then show how our algorithms may be applied to several search games with applications to security and counterterrorism. We evaluate our main algorithm experimentally on a prototypical search game. Our results show that it performs well compared with existing well-known algorithms for solving zero-sum games that can also be used to solve search games given a best-response oracle.
AB - We present efficient algorithms for computing optimal or approximately optimal strategies in a zero-sum game for which player I has n pure strategies and player II has an arbitrary number of pure strategies. We assume that for any given mixed strategy of player I, a best response, or “approximate” best response, of player II can be found by an oracle in time polynomial in n. We then show how our algorithms may be applied to several search games with applications to security and counterterrorism. We evaluate our main algorithm experimentally on a prototypical search game. Our results show that it performs well compared with existing well-known algorithms for solving zero-sum games that can also be used to solve search games given a best-response oracle.
KW - Games/group decisions
KW - Learning
KW - Networks/graphs
KW - Search/surveillance
KW - Tree algorithms
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UR - http://www.scopus.com/inward/citedby.url?scp=85068458510&partnerID=8YFLogxK
U2 - 10.1287/opre.2019.1853
DO - 10.1287/opre.2019.1853
M3 - Review article
VL - 67
SP - 731
EP - 743
JO - Operations Research
JF - Operations Research
SN - 0030-364X
IS - 3
ER -