# An idempotent algorithm for a class of network-disruption games

William M. McEneaney; Amit Pandey

Kybernetika (2016)

- Volume: 52, Issue: 5, page 666-695
- ISSN: 0023-5954

## Access Full Article

top## Abstract

top## How to cite

topM. McEneaney, William, and Pandey, Amit. "An idempotent algorithm for a class of network-disruption games." Kybernetika 52.5 (2016): 666-695. <http://eudml.org/doc/287528>.

@article{M2016,

abstract = {A game is considered where the communication network of the first player is explicitly modelled. The second player may induce delays in this network, while the first player may counteract such actions. Costs are modelled through expectations over idempotent probability measures. The idempotent probabilities are conditioned by observational data, the arrival of which may have been delayed along the communication network. This induces a game where the state space consists of the network delays. Even for small networks, the state-space dimension is high. Idempotent algebra-based methods are used to generate an algorithm not subject to the curse-of-dimensionality. An example is included.},

author = {M. McEneaney, William, Pandey, Amit},

journal = {Kybernetika},

keywords = {idempotent; max-plus; tropical; network; dynamic programming; game theory; command and control; idempotent; max-plus; tropical; network; dynamic programming; game theory; command and control},

language = {eng},

number = {5},

pages = {666-695},

publisher = {Institute of Information Theory and Automation AS CR},

title = {An idempotent algorithm for a class of network-disruption games},

url = {http://eudml.org/doc/287528},

volume = {52},

year = {2016},

}

TY - JOUR

AU - M. McEneaney, William

AU - Pandey, Amit

TI - An idempotent algorithm for a class of network-disruption games

JO - Kybernetika

PY - 2016

PB - Institute of Information Theory and Automation AS CR

VL - 52

IS - 5

SP - 666

EP - 695

AB - A game is considered where the communication network of the first player is explicitly modelled. The second player may induce delays in this network, while the first player may counteract such actions. Costs are modelled through expectations over idempotent probability measures. The idempotent probabilities are conditioned by observational data, the arrival of which may have been delayed along the communication network. This induces a game where the state space consists of the network delays. Even for small networks, the state-space dimension is high. Idempotent algebra-based methods are used to generate an algorithm not subject to the curse-of-dimensionality. An example is included.

LA - eng

KW - idempotent; max-plus; tropical; network; dynamic programming; game theory; command and control; idempotent; max-plus; tropical; network; dynamic programming; game theory; command and control

UR - http://eudml.org/doc/287528

ER -

## References

top- Akian, M., 10.1090/s0002-9947-99-02153-4, Trans. Amer. Math. Soc. 351 (1999), 4515-4543. Zbl0934.28005MR1466943DOI10.1090/s0002-9947-99-02153-4
- Akian, M., Gaubert, S., Lakhoua, A., 10.1137/060655286, SIAM J. Control Optim. 47 (2008), 817-848. Zbl1157.49034MR2385864DOI10.1137/060655286
- Baccelli, F. L., Cohen, G., Olsder, G. J., Quadrat, J.-P., Synchronization and Linearity., Wiley, New York 1992. Zbl0824.93003MR1204266
- Cohen, G., Gaubert, S., Quadrat, J.-P., 10.1016/j.laa.2003.08.010, Linear Algebra Appl. 379 (2004), 395-422. Zbl1042.46004MR2039751DOI10.1016/j.laa.2003.08.010
- Elliot, N. J., Kalton, N. J., 10.1090/memo/0126, Mem. Amer. Math. Soc. 126 (1972). MR0359845DOI10.1090/memo/0126
- Fleming, W. H., 10.1007/s00245-003-0785-3, Appl. Math. Optim. 49 (2004), 159-181. Zbl1138.93379MR2033833DOI10.1007/s00245-003-0785-3
- Fleming, W. H., Kaise, H., Sheu, S.-J., 10.1007/s00245-010-9097-6, Applied Math. Optim. 62 (2010), 81-144. Zbl1197.49029MR2653896DOI10.1007/s00245-010-9097-6
- Gaubert, S., McEneaney, W. M., 10.1007/s00245-011-9158-5, Applied Math. Optim. 65 (2012), 315-348. Zbl1244.93051MR2902695DOI10.1007/s00245-011-9158-5
- Gaubert, S., Qu, Z., Sridharan, S., Bundle-based pruning in the max-plus curse of dimensionality free method., In: Proc. 21st Int. Symp. Math. Theory of Networks and Systems 2014.
- Heidergott, B., Olsder, G. J., Woude, J. van der, 10.1515/9781400865239, Princeton Univ. Press 2006. MR2188299DOI10.1515/9781400865239
- Kolokoltsov, V. N., Maslov, V. P., 10.1007/978-94-015-8901-7, Kluwer 1997. Zbl0941.93001MR1447629DOI10.1007/978-94-015-8901-7
- Litvinov, G. L., Maslov, V. P., Shpiz, G. B., 10.1023/a:1010266012029, Math. Notes 69 (2001), 696-729. Zbl1017.46034MR1846814DOI10.1023/a:1010266012029
- McEneaney, W. M., 10.1016/j.automatica.2010.10.006, Automatica 47 (2011), 443-451. Zbl1219.93146MR2878297DOI10.1016/j.automatica.2010.10.006
- McEneaney, W. M., 10.1007/0-8176-4453-9, Birkhauser, Boston 2006. Zbl1103.93005MR2189436DOI10.1007/0-8176-4453-9
- McEneaney, W. M., 10.1137/040610830, SIAM J. Control Optim. 46 (2007), 1239-1276. Zbl1251.65168MR2346381DOI10.1137/040610830
- McEneaney, W. M., 10.1109/acc.2011.5990870, In: Proc. 2011 Amer. Control Conf., pp. 4051-4056. DOI10.1109/acc.2011.5990870
- McEneaney, W. M., Desir, A., Games of network disruption and idempotent algorithms., In: Proc. European Control Conf. 2013, pp. 702-709.
- McEneaney, W. M., 10.1109/cdc.2009.5400306, In: Proc. IEEE CDC 2009, pp. 1569-1574. DOI10.1109/cdc.2009.5400306
- McEneaney, W. M., Charalambous, C. D., Large deviations theory, induced log-plus and max-plus measures and their applications., In: Proc. Math. Theory Networks and Sys. 2000.
- Nitica, V., Singer, I., 10.1080/02331930600819852, Optimization 56 (2007) 171-205. Zbl1121.52002MR2288512DOI10.1080/02331930600819852
- Puhalskii, A., 10.1201/9781420035803, Chapman and Hall/CRC Press 2001. Zbl0983.60003MR1851048DOI10.1201/9781420035803
- Qu, Z., 10.1109/cdc.2014.7039624, In: Proc. 53rd IEEE Conf. on Dec. and Control 2014. DOI10.1109/cdc.2014.7039624
- Rubinov, A. M., Singer, I., 10.1080/02331930108844567, Optimization 50 (2001), 307-351. Zbl1007.26010MR1892908DOI10.1080/02331930108844567
- Singer, I., Abstract Convex Analysis., Wiley-Interscience, New York 1997. Zbl0941.49020MR1461544

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.