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On noncooperative $n$-player principal eigenvalue games
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Nash Equilibrium in evolutionary competitive models of firms and workers under external regulation
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, Edificio C6, Piso 2, 1749-016 Lisboa, Portugal |
References:
[1] |
E. Akin and V. Losert, Evolutionary dynamics of zero-sum games, J. Math. Biol., 20 (1984), 231-258.
doi: 10.1007/BF00275987. |
[2] |
P. Duarte, R. L. Fernandes and W. M. Oliva, Dynamics of the attractor in the Lotka-Volterra equations, J. Differential Equations, 149 (1998), 143-189.
doi: 10.1006/jdeq.1998.3443. |
[3] |
J.-P. Dufour and N. T. Zung, Poisson Structures and Their Normal Forms, Progress in Mathematics, 242, Birkhäuser Verlag, Basel, 2005. |
[4] |
I. Eshel and E. Akin, Coevolutionary instability and mixed Nash solutions, J. Math. Biol., 18 (1983), 123-133.
doi: 10.1007/BF00280661. |
[5] |
R. L. Fernandes, J.-P. Oretga and T. S. Ratiu, The momentum map in Poisson geometry, Amer. J. Math., 131 (2009), 1261-1310.
doi: 10.1353/ajm.0.0068. |
[6] |
J. Hofbauer, Evolutionary dynamics for bimatrix games: A Hamiltonian system?, J. Math. Biol., 34 (1996), 675-688.
doi: 10.1007/BF02409754. |
[7] |
J. Hofbauer, On the occurrence of limit cycles in the Volterra-Lotka equation, Nonlinear Anal., 5 (1981), 1003-1007.
doi: 10.1016/0362-546X(81)90059-6. |
[8] |
J. Hofbauer and K. Sigmund, Evolutionary games and population dynamics, Cambridge University Press, Cambridge, 1998.
doi: 10.1017/CBO9781139173179. |
[9] |
J. T. Howson, Jr., Equilibria of polymatrix games,, Management Sci., 18 (): 312.
|
[10] |
J. Maynard Smith, Evolution and the Theory of Games, Cambridge University Press, 1982. |
[11] |
J. Nash, Non-cooperative games, Ann. of Math. (2), 54 (1951), 286-295.
doi: 10.2307/1969529. |
[12] |
G. Palm, Evolutionary stable strategies and game dynamics for $n$-person games, J. Math. Biol., 19 (1984), 329-334.
doi: 10.1007/BF00277103. |
[13] |
A. M. Perelomov, Integrable Systems of Classical Mechanics and Lie algebras. Vol. I, Birkhäuser Verlag, Basel, 1990.
doi: 10.1007/978-3-0348-9257-5. |
[14] |
M. Plank, Bi-Hamiltonian systems and Lotka-Volterra equations: A three-dimensional classification, Nonlinearity, 9 (1996), 887-896.
doi: 10.1088/0951-7715/9/4/004. |
[15] |
M. Plank, Hamiltonian structures for the $n$-dimensional Lotka-Volterra equations, J. Math. Phys., 36 (1995), 3520-3534.
doi: 10.1063/1.530978. |
[16] |
M. Plank, Some qualitative differences between the replicator dynamics of two player and $n$ player games, Nonlinear Anal., 30 (1997), 1411-1417.
doi: 10.1016/S0362-546X(97)00202-2. |
[17] |
R. Redheffer, A new class of Volterra differential equations for which the solutions are globally asymptotically stable, J. Differential Equations, 82 (1989), 251-268.
doi: 10.1016/0022-0396(89)90133-2. |
[18] |
R. Redheffer and W. Walter, Solution of the stability problem for a class of generalized Volterra prey-predator systems, J. Differential Equations, 52 (1984), 245-263.
doi: 10.1016/0022-0396(84)90179-7. |
[19] |
K. Ritzberger and J. Weibull, Evolutionary selection in normal-form games, Econometrica, 63 (1995), 1371-1399.
doi: 10.2307/2171774. |
[20] |
W. H. Sandholm, Population Games and Evolutionary Dynamics, MIT Press, Cambridge, MA, 2010. |
[21] |
P. Schuster , K. Sigmund, J. Hofbauer, R. Gottlieb and P. Merz, Self-regulation of behaviour in animal societies. III. Games between two populations with self-interaction, Biol. Cybernet., 40 (1981), 17-25.
doi: 10.1007/BF00326677. |
[22] |
V. Volterra, Leçons Sur La Théorie Mathématique de la Lutte Pour La Vie, Éditions Jacques Gabay, Sceaux, 1990. |
show all references
References:
[1] |
E. Akin and V. Losert, Evolutionary dynamics of zero-sum games, J. Math. Biol., 20 (1984), 231-258.
doi: 10.1007/BF00275987. |
[2] |
P. Duarte, R. L. Fernandes and W. M. Oliva, Dynamics of the attractor in the Lotka-Volterra equations, J. Differential Equations, 149 (1998), 143-189.
doi: 10.1006/jdeq.1998.3443. |
[3] |
J.-P. Dufour and N. T. Zung, Poisson Structures and Their Normal Forms, Progress in Mathematics, 242, Birkhäuser Verlag, Basel, 2005. |
[4] |
I. Eshel and E. Akin, Coevolutionary instability and mixed Nash solutions, J. Math. Biol., 18 (1983), 123-133.
doi: 10.1007/BF00280661. |
[5] |
R. L. Fernandes, J.-P. Oretga and T. S. Ratiu, The momentum map in Poisson geometry, Amer. J. Math., 131 (2009), 1261-1310.
doi: 10.1353/ajm.0.0068. |
[6] |
J. Hofbauer, Evolutionary dynamics for bimatrix games: A Hamiltonian system?, J. Math. Biol., 34 (1996), 675-688.
doi: 10.1007/BF02409754. |
[7] |
J. Hofbauer, On the occurrence of limit cycles in the Volterra-Lotka equation, Nonlinear Anal., 5 (1981), 1003-1007.
doi: 10.1016/0362-546X(81)90059-6. |
[8] |
J. Hofbauer and K. Sigmund, Evolutionary games and population dynamics, Cambridge University Press, Cambridge, 1998.
doi: 10.1017/CBO9781139173179. |
[9] |
J. T. Howson, Jr., Equilibria of polymatrix games,, Management Sci., 18 (): 312.
|
[10] |
J. Maynard Smith, Evolution and the Theory of Games, Cambridge University Press, 1982. |
[11] |
J. Nash, Non-cooperative games, Ann. of Math. (2), 54 (1951), 286-295.
doi: 10.2307/1969529. |
[12] |
G. Palm, Evolutionary stable strategies and game dynamics for $n$-person games, J. Math. Biol., 19 (1984), 329-334.
doi: 10.1007/BF00277103. |
[13] |
A. M. Perelomov, Integrable Systems of Classical Mechanics and Lie algebras. Vol. I, Birkhäuser Verlag, Basel, 1990.
doi: 10.1007/978-3-0348-9257-5. |
[14] |
M. Plank, Bi-Hamiltonian systems and Lotka-Volterra equations: A three-dimensional classification, Nonlinearity, 9 (1996), 887-896.
doi: 10.1088/0951-7715/9/4/004. |
[15] |
M. Plank, Hamiltonian structures for the $n$-dimensional Lotka-Volterra equations, J. Math. Phys., 36 (1995), 3520-3534.
doi: 10.1063/1.530978. |
[16] |
M. Plank, Some qualitative differences between the replicator dynamics of two player and $n$ player games, Nonlinear Anal., 30 (1997), 1411-1417.
doi: 10.1016/S0362-546X(97)00202-2. |
[17] |
R. Redheffer, A new class of Volterra differential equations for which the solutions are globally asymptotically stable, J. Differential Equations, 82 (1989), 251-268.
doi: 10.1016/0022-0396(89)90133-2. |
[18] |
R. Redheffer and W. Walter, Solution of the stability problem for a class of generalized Volterra prey-predator systems, J. Differential Equations, 52 (1984), 245-263.
doi: 10.1016/0022-0396(84)90179-7. |
[19] |
K. Ritzberger and J. Weibull, Evolutionary selection in normal-form games, Econometrica, 63 (1995), 1371-1399.
doi: 10.2307/2171774. |
[20] |
W. H. Sandholm, Population Games and Evolutionary Dynamics, MIT Press, Cambridge, MA, 2010. |
[21] |
P. Schuster , K. Sigmund, J. Hofbauer, R. Gottlieb and P. Merz, Self-regulation of behaviour in animal societies. III. Games between two populations with self-interaction, Biol. Cybernet., 40 (1981), 17-25.
doi: 10.1007/BF00326677. |
[22] |
V. Volterra, Leçons Sur La Théorie Mathématique de la Lutte Pour La Vie, Éditions Jacques Gabay, Sceaux, 1990. |
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