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Volumn 81, Issue 4, 2012, Pages 264-272

On equilibrium properties of evolutionary multi-player games with random payoff matrices

Author keywords

Equilibrium stability; Multi player game theory; Multiple strategies; Number of equilibria

Indexed keywords

EVOLUTIONARY THEORY; GAME THEORY; MATRIX; POPULATION GENETICS; PROBABILITY; THEORETICAL STUDY;

EID: 84859266166     PISSN: 00405809     EISSN: 10960325     Source Type: Journal    
DOI: 10.1016/j.tpb.2012.02.004     Document Type: Article
Times cited : (56)

References (74)
  • 1
    • 84941385097 scopus 로고
    • Beweis der Unmöglichkeit algebraische Gleichungen von höheren Graden als dem vierten allgemein aufzulösen
    • Abel N.H. Beweis der Unmöglichkeit algebraische Gleichungen von höheren Graden als dem vierten allgemein aufzulösen. Journal für die reine und angewandte Mathematik 1826, 1:65-84.
    • (1826) Journal für die reine und angewandte Mathematik , vol.1 , pp. 65-84
    • Abel, N.H.1
  • 2
    • 77951206995 scopus 로고    scopus 로고
    • Proof of the Feldman-Karlin conjecture on the maximum number of equilibria in an evolutionary system
    • Altenberg L. Proof of the Feldman-Karlin conjecture on the maximum number of equilibria in an evolutionary system. Theor. Popul. Biol. 2010, 77(4):263-269.
    • (2010) Theor. Popul. Biol. , vol.77 , Issue.4 , pp. 263-269
    • Altenberg, L.1
  • 3
    • 0001111015 scopus 로고    scopus 로고
    • Matrix games, mixed strategies, and statistical mechanics
    • Berg J., Engel A. Matrix games, mixed strategies, and statistical mechanics. Phys. Rev. Lett. 1998, 81:4999-5002.
    • (1998) Phys. Rev. Lett. , vol.81 , pp. 4999-5002
    • Berg, J.1    Engel, A.2
  • 4
    • 42349099550 scopus 로고
    • Princeton University Press, Princeton, (2006 Translation by Eric Feron)
    • Bézout E. General Theory of Algebraic Equations 1779, Princeton University Press, Princeton, (2006 Translation by Eric Feron).
    • (1779) General Theory of Algebraic Equations
    • Bézout, E.1
  • 7
    • 16244396159 scopus 로고    scopus 로고
    • Evolutionary games with variable payoffs
    • Broom M. Evolutionary games with variable payoffs. C. R. Biol. 2005, 328.
    • (2005) C. R. Biol. , vol.328
    • Broom, M.1
  • 8
    • 0007778691 scopus 로고
    • On the number of local maxima of a constrained quadratic form
    • Broom M., Cannings C., Vickers G.T. On the number of local maxima of a constrained quadratic form. Proc. R. Soc. Lond. Ser. A 1993, 443:573-584.
    • (1993) Proc. R. Soc. Lond. Ser. A , vol.443 , pp. 573-584
    • Broom, M.1    Cannings, C.2    Vickers, G.T.3
  • 9
    • 0007828790 scopus 로고
    • Sequential methods for generating patterns of ESS's
    • Broom M., Cannings C., Vickers G. Sequential methods for generating patterns of ESS's. J. Math. Biol. 1994, 32:597-615.
    • (1994) J. Math. Biol. , vol.32 , pp. 597-615
    • Broom, M.1    Cannings, C.2    Vickers, G.3
  • 11
    • 12144262737 scopus 로고    scopus 로고
    • Evolutionary and asymptotic stability in symmetric multi-player games
    • Bukowski M., Miekisz J. Evolutionary and asymptotic stability in symmetric multi-player games. Internat. J. Game Theory 2004, 33:41-54.
    • (2004) Internat. J. Game Theory , vol.33 , pp. 41-54
    • Bukowski, M.1    Miekisz, J.2
  • 14
    • 78650770483 scopus 로고    scopus 로고
    • Evolving cooperation in the spatial n-player snowdrift game
    • Springer, Berlin, Heidelberg, J. Li (Ed.) AI 2010: Advances in Artificial Intelligence
    • Chiong R., Kirley M. Evolving cooperation in the spatial n-player snowdrift game. Lecture Notes in Computer Science 2011, vol. 6464:263-272. Springer, Berlin, Heidelberg. J. Li (Ed.).
    • (2011) Lecture Notes in Computer Science , vol.6464 , pp. 263-272
    • Chiong, R.1    Kirley, M.2
  • 15
    • 38949107449 scopus 로고    scopus 로고
    • Cyclic dominance and biodiversity in well-mixed populations
    • Claussen J.C., Traulsen A. Cyclic dominance and biodiversity in well-mixed populations. Phys. Rev. Lett. 2008, 100:058104.
    • (2008) Phys. Rev. Lett. , vol.100 , pp. 058104
    • Claussen, J.C.1    Traulsen, A.2
  • 17
    • 0023933627 scopus 로고
    • Frequency-dependent viability selection (a single-locus, multi-phenotype model)
    • Cressman R. Frequency-dependent viability selection (a single-locus, multi-phenotype model). J. Theoret. Biol. 1988, 130:147-165.
    • (1988) J. Theoret. Biol. , vol.130 , pp. 147-165
    • Cressman, R.1
  • 18
    • 0346231340 scopus 로고
    • The Stability Concept of Evolutionary Game Theory
    • Cressman R. The Stability Concept of Evolutionary Game Theory. Lecture Notes in Biomathematics 1992, vol. 94.
    • (1992) Lecture Notes in Biomathematics , vol.94
    • Cressman, R.1
  • 21
    • 14844342838 scopus 로고    scopus 로고
    • Cooperation in an unpredictable environment
    • MIT Press, Standish, Abbas, Bedau (Eds.)
    • Eriksson A., Lindgren K. Cooperation in an unpredictable environment. Artificial Life VIII 2002, 394-399. MIT Press. Standish, Abbas, Bedau (Eds.).
    • (2002) Artificial Life VIII , pp. 394-399
    • Eriksson, A.1    Lindgren, K.2
  • 22
    • 67349101670 scopus 로고    scopus 로고
    • Sam Karlin and multi-locus population genetics
    • Feldman M.W. Sam Karlin and multi-locus population genetics. Theor. Popul. Biol. 2009, 75:233-235.
    • (2009) Theor. Popul. Biol. , vol.75 , pp. 233-235
    • Feldman, M.W.1
  • 24
    • 0001129788 scopus 로고
    • Evolutionary dynamics with aggregate shocks
    • Fudenberg D., Harris C. Evolutionary dynamics with aggregate shocks. J. Econom. Theory 1992, 57:420-441.
    • (1992) J. Econom. Theory , vol.57 , pp. 420-441
    • Fudenberg, D.1    Harris, C.2
  • 25
    • 77950453747 scopus 로고    scopus 로고
    • Evolutionary games in the multiverse
    • Gokhale C.S., Traulsen A. Evolutionary games in the multiverse. Proc. Natl. Acad. Sci. USA 2010, 107(12):5500-5504.
    • (2010) Proc. Natl. Acad. Sci. USA , vol.107 , Issue.12 , pp. 5500-5504
    • Gokhale, C.S.1    Traulsen, A.2
  • 28
    • 68449104875 scopus 로고    scopus 로고
    • Generalized models reveal stabilizing factors in food webs
    • Gross T., Rudolf L., Levin S.A., Dieckmann U. Generalized models reveal stabilizing factors in food webs. Science 2009, 325.
    • (2009) Science , vol.325
    • Gross, T.1    Rudolf, L.2    Levin, S.A.3    Dieckmann, U.4
  • 29
    • 0006554546 scopus 로고    scopus 로고
    • Springer Publishing Company, Incorporated (Chapter 1)
    • Gut A. An Intermediate Course in Probability 2009, Springer Publishing Company, Incorporated (Chapter 1). second ed.
    • (2009) An Intermediate Course in Probability
    • Gut, A.1
  • 30
    • 53349178563 scopus 로고
    • The distribution of evolutionarily stable strategies
    • Haigh J. The distribution of evolutionarily stable strategies. J. Appl. Probab. 1988, 25:233-246.
    • (1988) J. Appl. Probab. , vol.25 , pp. 233-246
    • Haigh, J.1
  • 31
    • 0001712411 scopus 로고
    • How large is the support of an ESS?
    • Haigh J. How large is the support of an ESS?. J. Appl. Probab. 1989, 26:164-170.
    • (1989) J. Appl. Probab. , vol.26 , pp. 164-170
    • Haigh, J.1
  • 32
    • 0014413249 scopus 로고
    • The tragedy of the commons
    • Hardin G. The tragedy of the commons. Science 1968, 162:1243-1248.
    • (1968) Science , vol.162 , pp. 1243-1248
    • Hardin, G.1
  • 34
    • 33748964132 scopus 로고    scopus 로고
    • Evolutionary games and population dynamics:maintenance of cooperation in public goods games
    • Hauert C., Holmes M., Doebeli M. Evolutionary games and population dynamics:maintenance of cooperation in public goods games. Proc. R. Soc. Lond. Ser. B 2006, 273:2565-2570.
    • (2006) Proc. R. Soc. Lond. Ser. B , vol.273 , pp. 2565-2570
    • Hauert, C.1    Holmes, M.2    Doebeli, M.3
  • 35
    • 33644622609 scopus 로고    scopus 로고
    • Synergy and discounting of cooperation in social dilemmas
    • Hauert C., Michor F., Nowak M.A., Doebeli M. Synergy and discounting of cooperation in social dilemmas. J. Theoret. Biol. 2006, 239:195-202.
    • (2006) J. Theoret. Biol. , vol.239 , pp. 195-202
    • Hauert, C.1    Michor, F.2    Nowak, M.A.3    Doebeli, M.4
  • 37
    • 77649340407 scopus 로고    scopus 로고
    • Fixation probabilities of random mutants under frequency dependent selection
    • Huang W., Traulsen A. Fixation probabilities of random mutants under frequency dependent selection. J. Theoret. Biol. 2010, 263:262-268.
    • (2010) J. Theoret. Biol. , vol.263 , pp. 262-268
    • Huang, W.1    Traulsen, A.2
  • 39
    • 0018820975 scopus 로고
    • The number of stable equilibria for the classical one-locus multiallele slection model
    • Karlin S. The number of stable equilibria for the classical one-locus multiallele slection model. J. Math. Biol. 1980, 9:189-192.
    • (1980) J. Math. Biol. , vol.9 , pp. 189-192
    • Karlin, S.1
  • 40
    • 0014777969 scopus 로고
    • Linkage and selection: two locus symmetric viability model
    • Karlin S., Feldman M.W. Linkage and selection: two locus symmetric viability model. Theor. Popul. Biol. 1970, 1:39-71.
    • (1970) Theor. Popul. Biol. , vol.1 , pp. 39-71
    • Karlin, S.1    Feldman, M.W.2
  • 41
    • 84971187073 scopus 로고
    • A mathematical problem in population genetics
    • Kingman J.F.C. A mathematical problem in population genetics. Proc. Cambridge Philos. Soc. 1961, 57(3):574-582.
    • (1961) Proc. Cambridge Philos. Soc. , vol.57 , Issue.3 , pp. 574-582
    • Kingman, J.F.C.1
  • 42
    • 84925003253 scopus 로고    scopus 로고
    • Algebraic geometry
    • Princeton University Press, Princeton, (Chapter IV).4, T. Gowers, J. Barrow-Green, I. Leader (Eds.)
    • Kollár J. Algebraic geometry. The Princeton Companion To Mathematics 2008, vol. 77:363-372. Princeton University Press, Princeton, (Chapter IV).4. T. Gowers, J. Barrow-Green, I. Leader (Eds.).
    • (2008) The Princeton Companion To Mathematics , vol.77 , pp. 363-372
    • Kollár, J.1
  • 43
    • 64849113193 scopus 로고    scopus 로고
    • Emergence of cooperation in public goods games
    • Kurokawa S., Ihara Y. Emergence of cooperation in public goods games. Proc. R. Soc. Ser. B 2009, 276:1379-1384.
    • (2009) Proc. R. Soc. Ser. B , vol.276 , pp. 1379-1384
    • Kurokawa, S.1    Ihara, Y.2
  • 44
    • 84859268850 scopus 로고    scopus 로고
    • On the robustness of the extension of the one-third law of evolution to the multi-player game
    • Lessard S. On the robustness of the extension of the one-third law of evolution to the multi-player game. Dynam. Games Appl. 2011, 1:408-418.
    • (2011) Dynam. Games Appl. , vol.1 , pp. 408-418
    • Lessard, S.1
  • 45
    • 0034494487 scopus 로고    scopus 로고
    • Multiple scales and the maintenance of biodiversity
    • Levin S.A. Multiple scales and the maintenance of biodiversity. Ecosystems 2000, 3:498-506.
    • (2000) Ecosystems , vol.3 , pp. 498-506
    • Levin, S.A.1
  • 46
    • 77249167781 scopus 로고    scopus 로고
    • Games, Groups and the Global Good
    • Springer, S.A. Levin (Ed.)
    • Games, Groups and the Global Good. Springer Series in Game Theory 2009, Springer. S.A. Levin (Ed.).
    • (2009) Springer Series in Game Theory
  • 48
    • 0000643605 scopus 로고
    • Stability in randomly fluctuating versus deterministic environments
    • May R.M. Stability in randomly fluctuating versus deterministic environments. Am. Nat. 1973, 107(957).
    • (1973) Am. Nat. , vol.107 , Issue.957
    • May, R.M.1
  • 50
    • 34548719708 scopus 로고
    • The logic of animal conflict
    • Maynard Smith J., Price G.R. The logic of animal conflict. Nature 1973, 246:15-18.
    • (1973) Nature , vol.246 , pp. 15-18
    • Maynard Smith, J.1    Price, G.R.2
  • 51
    • 0002021736 scopus 로고
    • Equilibrium points in n-person games
    • Nash J.F. Equilibrium points in n-person games. Proc. Natl. Acad. Sci. USA 1950, 36:48-49.
    • (1950) Proc. Natl. Acad. Sci. USA , vol.36 , pp. 48-49
    • Nash, J.F.1
  • 52
    • 58149234977 scopus 로고    scopus 로고
    • Evolutionary dynamics of collective action in n-person stag hunt dilemmas
    • Pacheco J.M., Santos F.C., Souza M.O., Skyrms B. Evolutionary dynamics of collective action in n-person stag hunt dilemmas. Proc. R. Soc. Ser. B 2009, 276:315-321.
    • (2009) Proc. R. Soc. Ser. B , vol.276 , pp. 315-321
    • Pacheco, J.M.1    Santos, F.C.2    Souza, M.O.3    Skyrms, B.4
  • 53
    • 0036426078 scopus 로고    scopus 로고
    • Unifying evolutionary dynamics
    • Page K.M., Nowak M.A. Unifying evolutionary dynamics. J. Theoret. Biol. 2002, 219:93-98.
    • (2002) J. Theoret. Biol. , vol.219 , pp. 93-98
    • Page, K.M.1    Nowak, M.A.2
  • 54
    • 34548305141 scopus 로고    scopus 로고
    • Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games
    • Reichenbach T., Mobilia M., Frey E. Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games. Nature 2007, 448:1046-1049.
    • (2007) Nature , vol.448 , pp. 1046-1049
    • Reichenbach, T.1    Mobilia, M.2    Frey, E.3
  • 55
    • 36849066945 scopus 로고    scopus 로고
    • Noise and correlations in a spatial population model with cyclic competition
    • Reichenbach T., Mobilia M., Frey E. Noise and correlations in a spatial population model with cyclic competition. Phys. Rev. Lett. 2007, 99:238105.
    • (2007) Phys. Rev. Lett. , vol.99 , pp. 238105
    • Reichenbach, T.1    Mobilia, M.2    Frey, E.3
  • 57
    • 0024282834 scopus 로고
    • To each genotype a separate strategy-a dynamic game theory model of a general diploid system
    • Rowe G.W. To each genotype a separate strategy-a dynamic game theory model of a general diploid system. J. Theoret. Biol. 1988, 134:89-101.
    • (1988) J. Theoret. Biol. , vol.134 , pp. 89-101
    • Rowe, G.W.1
  • 59
    • 47049124531 scopus 로고    scopus 로고
    • Social diversity promotes the emergence of cooperation in public goods games
    • Santos F.C., Santos M.D., Pacheco J.M. Social diversity promotes the emergence of cooperation in public goods games. Nature 2008, 454:213-216.
    • (2008) Nature , vol.454 , pp. 213-216
    • Santos, F.C.1    Santos, M.D.2    Pacheco, J.M.3
  • 61
    • 38249034409 scopus 로고
    • A maximum principle for frequency dependent selection
    • Sigmund K. A maximum principle for frequency dependent selection. Math. Biosci. 1987, 84:189-195.
    • (1987) Math. Biosci. , vol.84 , pp. 189-195
    • Sigmund, K.1
  • 63
    • 70249145392 scopus 로고    scopus 로고
    • Evolution of cooperation undern-person snowdrift games
    • Souza M.O., Pacheco J.M., Santos F.C. Evolution of cooperation undern-person snowdrift games. J. Theoret. Biol. 2009, 260:581-588.
    • (2009) J. Theoret. Biol. , vol.260 , pp. 581-588
    • Souza, M.O.1    Pacheco, J.M.2    Santos, F.C.3
  • 64
  • 65
    • 45849156108 scopus 로고    scopus 로고
    • Phase transitions and volunteering in spatial public goods games
    • Szabó G., Hauert C. Phase transitions and volunteering in spatial public goods games. Phys. Rev. Lett. 2002, 89:118101.
    • (2002) Phys. Rev. Lett. , vol.89 , pp. 118101
    • Szabó, G.1    Hauert, C.2
  • 66
    • 0017819644 scopus 로고
    • Evolutionary stable strategies and game dynamics
    • Taylor P.D., Jonker L. Evolutionary stable strategies and game dynamics. Math. Biosci. 1978, 40:145-156.
    • (1978) Math. Biosci. , vol.40 , pp. 145-156
    • Taylor, P.D.1    Jonker, L.2
  • 67
    • 81455138715 scopus 로고    scopus 로고
    • From genes to games: cooperation and cyclic dominance in meiotic drive
    • Traulsen A., Reed F.A. From genes to games: cooperation and cyclic dominance in meiotic drive. J. Theoret. Biol. 2011, 10.1016/j.jtbi.2011.04.032.
    • (2011) J. Theoret. Biol.
    • Traulsen, A.1    Reed, F.A.2
  • 68
    • 34247564630 scopus 로고    scopus 로고
    • Hamilton's missing link
    • van Veelen M. Hamilton's missing link. J. Theoret. Biol. 2007, 246:551-554.
    • (2007) J. Theoret. Biol. , vol.246 , pp. 551-554
    • van Veelen, M.1
  • 69
    • 0007728509 scopus 로고
    • On the number of equilibria in a one-locus, multi allelic system
    • Vickers G.T., Cannings C. On the number of equilibria in a one-locus, multi allelic system. J. Theoret. Biol. 1988, 131:273-277.
    • (1988) J. Theoret. Biol. , vol.131 , pp. 273-277
    • Vickers, G.T.1    Cannings, C.2
  • 73
    • 0035544909 scopus 로고    scopus 로고
    • Selection and segregation distortion in a sex-differentiated population
    • Weissing F.J., van Boven M. Selection and segregation distortion in a sex-differentiated population. Theor. Popul. Biol. 2001, 60:327-341.
    • (2001) Theor. Popul. Biol. , vol.60 , pp. 327-341
    • Weissing, F.J.1    van Boven, M.2
  • 74
    • 0003288597 scopus 로고
    • Population dynamics from game theory
    • Zeeman E.C. Population dynamics from game theory. Lecture Notes in Math. 1980, 819:471-497.
    • (1980) Lecture Notes in Math. , vol.819 , pp. 471-497
    • Zeeman, E.C.1


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