Ostrovski, Georg and Strien, Sebastian van, 1956-. (2011) Piecewise linear hamiltonian flows associated to zero-sum games : transition combinatorics and questions on ergodicity. Regular and Chaotic Dynamics, Vol.16 (No.1-2). pp. 128-153. ISSN 1560-3547

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Abstract

In this paper we consider a class of piecewise affine Hamiltonian vector fields whose orbits are piecewise straight lines. We give a first classification result of such systems and show that the orbit-structure of the flow of such a differential equation is surprisingly rich.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Hamiltonian systems, Piecewise linear topology, Dynamics, Vector fields
Journal or Publication Title:	Regular and Chaotic Dynamics
Publisher:	M A I K Nauka - Interperiodica
ISSN:	1560-3547
Date:	2011
Volume:	Vol.16
Number:	No.1-2
Page Range:	pp. 128-153
Identification Number:	10.1134/S1560354711010059
Status:	Peer Reviewed
Publication Status:	Published
References:	1. Aubin, J.-P. and Cellina, A., Differential Inclusions. Set-valued Maps and Viability Theory. Berlin: Springer, 1984. 2. Berger, U., Fictitious Play in 2 × n Games, J. Econom. Theory, 2005, vol. 120, pp. 139–154. 3. Brown, G.W., Iterative Solution of Games by Fictitious Play, Activity Analysis of Production and Allocation, Cowles Commission Monograph No. 13., New York: John Wiley & Sons, Inc., 1951, pp. 374– 376. 4. di Bernardo, M., Budd, C.J., Champneys, A.R., and Kowalczyk, P., Piecewise-smooth Dynamical Systems. Theory and applications., London: Springer, 2008. 5. Hofbauer, J., Stability for the Best Response Dynamics, Preprint, August 1995. 6. Kunze, M., Non-smooth Dynamical Systems, Berlin: Springer, 2000. 7. Leine, R.I. and Nijmeijer, H., Dynamics and Bifurcations of Non-smooth Mechanical Systems, Berlin: Springer, 2004. 8. Nash, J., Non-Cooperative Games, Ann. of Math. (2), 1951, vol. 54, pp. 286–295. 9. Robinson, J., An Iterative Method of Solving a Game, Ann. of Math. (2), 1951, vol. 54, pp. 296–301. 10. Rosenm¨uller, J., ¨Uber Periodizit¨atseigenschaften Spieltheoretischer Lernprozesse, Zeitschrift f¨ur Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1971, vol. 17, pp. 259–308. 11. Sparrow, C., van Strien, S., and Harris, Ch., Fictitious Play in 3 × 3 Games: the Transition Between Periodic and Chaotic Behavior, Games Econom. Behav., 2008, vol. 63, pp. 259–291. 12. van Strien, S., Hamiltonian Flows with Random-walk Behavior Originating from Zero-sum Games and Fictitious Play, Preprint, 2009. 13. van Strien, S. and Sparrow, C., Fictitious Play in 3 × 3 Games: Chaos and Dithering Behavior, Games Econom. Behav., 2009 (to appear).
URI:	http://wrap.warwick.ac.uk/id/eprint/39093

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