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Asymmetric delay in evolutionary games

Published: 22 October 2007 Publication History

Abstract

We study the effect of the time delays on the convergence of replicator dynamics to the evolutionary stable strategies in a symmetric evolutionary game in which each pure strategy is associated with its own delay. We compare the stability region to that obtained when all strategies have the same delay. Multiple Access Game and Hawk and Dove Game are studied.

References

[1]
J. Alboszta and J. Miȩkisz, Stability and evolutionary stable strategies in discrete replicator dynamics with delay, J. Theor. Biology, 2004.
[2]
E. Altman and T. Başar and N. Malouch, The role of information update in flow control, Netw., 2004.
[3]
J. Arino, L. Wang and G. Wolkowicz, An Alternate Formulation for a Delayed Logistic Equation, Journal of Theoretical Biology, 2006, 241, 1.
[4]
R. Bellman and K. L. Cooke, Differential difference equations, Academic Press, New York, 1963.
[5]
L. Berezansky and E. Braverman, On stability of some linear and nonlinear delay differential equations, J. Math. Anal. Appl., Vol. 314, No. 2 (2006), pages 391--411.
[6]
N. Bonneau, E. Altman, M. Debbah, and G. Caire, An Evolutionary Game Perspective to ALOHA with Power Control, 19th International Teletraffic Congress, Beijing, China, Aug. 29-Sep., 2005.
[7]
G. Brown and J. Von Neumann, Solutions of games by differential equations, In H. Kuhn and A. Tucker, editors, Contributions to the Theory of Games I, Annals of Mathematics Studies 24, pages 73--79. Princeton University Press, 1950.
[8]
R. Cressman, Evolutionary Dynamics and Extensive Form Games, MIT Press, Cambridge, 2003.
[9]
C. A. Desoer and Yung-Terng Wang, On the Generalized Nyquist Stability Criterion, IEEE Transactions on Automatic Control, April 1980, vol. AC-25, NO. 2, 187.
[10]
N. Dukkipati and N. McKeown, Stability Analysis of RCP for Long-lived Flows, fev 2004, available at http://yuba.stanford.edu/ñanditad/GroupMeetFeb04.pdf.
[11]
H. I. Freedman and Y. Kuang, Stability Switches in Linear Scalar Neutral Delay Equations, Funkcialaj Ekvacioj, 34 (1991) 187--209.
[12]
M. Felegyhazi and J.-P. Hubaux, Game Theory in Wireless Networks: A Tutorial, EPFL technical report, LCA-REPORT-2006-002, February, 2006.
[13]
Daniel Friedman, On economic applications of evolutionary game theory, Journal of Evolutionary Economics, 1998, 8, 1, 15--43.
[14]
H. Gintis, Game Theory Evolving, Princeton University Press, 2000.
[15]
K. Gopalsamy, Stability and Oscillation in Delay Differential Equations of Population Dynamics, Kluwer Academic Publishers, London, 1992.
[16]
J. Hofbauer and K. Sigmund, Evolutionary game dynamics, American Mathematical Society, Vol 40 No. 4, pp. 479--519, 2003.
[17]
J. Hofbauer and K. Sigmund, Evolutionary Games and Population Dynamics, Cambridge University Press, Cambridge, UK, 1998.
[18]
R. Johari and D. Tan, End-to-End Congestion Control for the Internet: Delays and Stability, IEEE/ACM Transactions on Networking, 2001, 9, 6.
[19]
X. Li and S. Ruin and J. Wei, Stability and bifurcation in delay-differential equations with two delays, Journal of math. analysis and applications, vol. 236, no2, pp. 254--280, 1999.
[20]
S. Liu, T. Başar and R. Srikant, Exponential-RED: A Stabilizing AQM Scheme for Low- and High-Speed TCP Protocols, IEEE/ACM Trans. on Networking, vol. 13, no. 5, oct., 2005.
[21]
S. J. Mason, A comment on Dr Vazsonyi's Paper: "A generalized Nyquist's stability criteria", May, 20, Journal of Applied Physics -- September 1949 -- Volume 20, Issue 9, p. 867.
[22]
F. Y. Ren and C. Lin and B. Wei, A Nonlinear Control Theoretic Analysis to TCP-RED System, Computer Networks, vol.49: 580--592, 2005.
[23]
J. B. Rosen, Existence and uniqueness of equilibrium points for concave N-person games, Econometrica 33, 520--534, 1965.
[24]
L. Samuelson, Evolutionary Games and Equilibrium Selection, MIT Press, 1997.
[25]
W. H. Sandholm, Potential games with continuous player sets, Journal of Economic Theory, 97:81--108, 2001.
[26]
S. Shakkottai, E. Altman and A. Kumar, The Case for Non-cooperative Multihoming of Users to Access Points in IEEE 802.11 WLANs, IEEE Infocom, 2006.
[27]
J. M. Smith and GR Price, The logic of animal conflict, Nature 246, 15--18, 1973.
[28]
J. M. Smith, Evolution and the theory of Games, Cambridge University Press, 1982.
[29]
P. K. Stevens, A Generalization of the Nyquist Stability Criterion, IEEE Transactions on Automatic Control, vol AC-26, no. 3, june, 1981.
[30]
Deb Supratim and R. Srikant, Global Stability of congestion controllers for the internet, Proc. of IEEE Conference on Decision and Control, Las Vegas, Dec, 2002.
[31]
P. Taylor and L. Jonker, Evolutionary Stable Strategies and Game Dynamics, Mathematical Biosciences, 1978. 16, 76--83.
[32]
G. Vinnicombe, On the stability of networks operating TCP-like congestion control, In 15th IFAC World Congress on Automatic Control, July 2002.
[33]
J. W. Weibull, Evolutionary Game Theory, Cambridge, MA: MIT Press, 1995.
[34]
T. Yi and Z. Wang, Effect of Time Delay and Evolutionary Stable Strategy, J. theor. Biol, 187, 111--116, 1997.
[35]
Y. Zheng and Z. Feng, Evolutionary game and resources competition in the Internet, Modern Communication Technologies, SIBCOM-2001, 2001.

Cited By

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  • (2011)Bio-inspired delayed evolutionary game dynamics with networking applicationsTelecommunications Systems10.1007/s11235-010-9307-147:1-2(137-152)Online publication date: 1-Jun-2011
  • (2008)A Lyapunov-Krasovskii stability analysis for game-theoretic based power control in optical networksProceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools10.4108/ICST.VALUETOOLS2008.4340(1-10)Online publication date: 20-Oct-2008
  • (2008)Bio-Inspired Approaches for Autonomic Pervasive Computing SystemsBio-Inspired Computing and Communication10.1007/978-3-540-92191-2_20(217-228)Online publication date: 27-Nov-2008
  • Show More Cited By

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cover image ACM Conferences
ValueTools '07: Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
October 2007
708 pages
ISBN:9789639799004

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ICST (Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering)

Brussels, Belgium

Publication History

Published: 22 October 2007

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Author Tags

  1. delay differential equation
  2. evolutionary stable strategy
  3. hawk and dove game
  4. multiple access game
  5. replicator dynamics

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ValueTools '07 Paper Acceptance Rate 45 of 83 submissions, 54%;
Overall Acceptance Rate 90 of 196 submissions, 46%

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Cited By

View all
  • (2011)Bio-inspired delayed evolutionary game dynamics with networking applicationsTelecommunications Systems10.1007/s11235-010-9307-147:1-2(137-152)Online publication date: 1-Jun-2011
  • (2008)A Lyapunov-Krasovskii stability analysis for game-theoretic based power control in optical networksProceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools10.4108/ICST.VALUETOOLS2008.4340(1-10)Online publication date: 20-Oct-2008
  • (2008)Bio-Inspired Approaches for Autonomic Pervasive Computing SystemsBio-Inspired Computing and Communication10.1007/978-3-540-92191-2_20(217-228)Online publication date: 27-Nov-2008
  • (2007)Multiple access game in ad-hoc networkProceedings of the 2nd international conference on Performance evaluation methodologies and tools10.5555/1345263.1345271(1-7)Online publication date: 22-Oct-2007

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