January  2015, 2(1): 33-49. doi: 10.3934/jdg.2015.2.33

Hamiltonian evolutionary games

1. 

Departamento de Matemática and CAMGSD, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

2. 

Departamento de Matemática and CMAF, Faculdade de Ciências,Universidade de Lisboa, Campo Grande, Edi ficio C6, Piso 2, 1749-016 Lisboa, Portugal

Received  May 2014 Revised  February 2015 Published  June 2015

We introduce a class of o.d.e.'s that generalizes to polymatrix games the replicator equations on symmetric and asymmetric games. We also introduce a new class of Poisson structures on the phase space of these systems, and characterize the corresponding subclass of Hamiltonian polymatrix replicator systems. This extends known results for symmetric and asymmetric replicator systems.
Citation: Hassan Najafi Alishah, Pedro Duarte. Hamiltonian evolutionary games. Journal of Dynamics & Games, 2015, 2 (1) : 33-49. doi: 10.3934/jdg.2015.2.33
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show all references

References:
[1]

J. Math. Biol., 20 (1984), 231-258. doi: 10.1007/BF00275987.  Google Scholar

[2]

J. Differential Equations, 149 (1998), 143-189. doi: 10.1006/jdeq.1998.3443.  Google Scholar

[3]

Progress in Mathematics, 242, Birkhäuser Verlag, Basel, 2005.  Google Scholar

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J. Math. Biol., 18 (1983), 123-133. doi: 10.1007/BF00280661.  Google Scholar

[5]

Amer. J. Math., 131 (2009), 1261-1310. doi: 10.1353/ajm.0.0068.  Google Scholar

[6]

J. Math. Biol., 34 (1996), 675-688. doi: 10.1007/BF02409754.  Google Scholar

[7]

Nonlinear Anal., 5 (1981), 1003-1007. doi: 10.1016/0362-546X(81)90059-6.  Google Scholar

[8]

Cambridge University Press, Cambridge, 1998. doi: 10.1017/CBO9781139173179.  Google Scholar

[9]

J. T. Howson, Jr., Equilibria of polymatrix games,, Management Sci., 18 (): 312.   Google Scholar

[10]

Cambridge University Press, 1982. Google Scholar

[11]

Ann. of Math. (2), 54 (1951), 286-295. doi: 10.2307/1969529.  Google Scholar

[12]

J. Math. Biol., 19 (1984), 329-334. doi: 10.1007/BF00277103.  Google Scholar

[13]

Birkhäuser Verlag, Basel, 1990. doi: 10.1007/978-3-0348-9257-5.  Google Scholar

[14]

Nonlinearity, 9 (1996), 887-896. doi: 10.1088/0951-7715/9/4/004.  Google Scholar

[15]

J. Math. Phys., 36 (1995), 3520-3534. doi: 10.1063/1.530978.  Google Scholar

[16]

Nonlinear Anal., 30 (1997), 1411-1417. doi: 10.1016/S0362-546X(97)00202-2.  Google Scholar

[17]

J. Differential Equations, 82 (1989), 251-268. doi: 10.1016/0022-0396(89)90133-2.  Google Scholar

[18]

J. Differential Equations, 52 (1984), 245-263. doi: 10.1016/0022-0396(84)90179-7.  Google Scholar

[19]

Econometrica, 63 (1995), 1371-1399. doi: 10.2307/2171774.  Google Scholar

[20]

MIT Press, Cambridge, MA, 2010.  Google Scholar

[21]

Biol. Cybernet., 40 (1981), 17-25. doi: 10.1007/BF00326677.  Google Scholar

[22]

Éditions Jacques Gabay, Sceaux, 1990.  Google Scholar

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