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Payoff performance of fictitious play
1. | Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, United Kingdom |
2. | Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom |
References:
[1] |
R. J. Aumann, Subjectivity and correlation in randomized strategies, J. Math. Econom., 1 (1974), 67-96.
doi: 10.1016/0304-4068(74)90037-8. |
[2] |
R. J. Aumann, Correlated equilibrium as an expression of Bayesian rationality, Econometrica, 55 (1987), 1-18.
doi: 10.2307/1911154. |
[3] |
U. Berger, Fictitious play in $2 \times n$ games, J. Econ. Theory, 120 (2005), 139-154.
doi: 10.1016/j.jet.2004.02.003. |
[4] |
U. Berger, Two more classes of games with the continuous-time fictitious play property, Game. Econ. Behav., 60 (2007), 247-261.
doi: 10.1016/j.geb.2006.10.008. |
[5] |
U. Berger, Learning in games with strategic complementarities revisited, J. Econ. Theory, 143 (2008), 292-301.
doi: 10.1016/j.jet.2008.01.007. |
[6] |
D. Blackwell, Controlled random walks, In Proceedings of the International Congress of Mathematicians, 3 (1954), 336-338. |
[7] |
G. W. Brown, Some notes on computation of games solutions, Technical report, Report P-78, The Rand Corporation, 1949. |
[8] |
G. W. Brown, Iterative solution of games by fictitious play, In Activity Analysis of Production and Allocation, volume 13, pages 374-376. John Wiley & Sons, New York, 1951. |
[9] |
D. P. Foster and R. V. Vohra, Calibrated learning and correlated equilibrium, Game. Econ. Behav., 21 (1997), 40-55.
doi: 10.1006/game.1997.0595. |
[10] |
D. Fudenberg and D. K. Levine, Consistency and cautious fictitious play, J. Econ. Dyn. Control, 19 (1995), 1065-1089.
doi: 10.1016/0165-1889(94)00819-4. |
[11] |
D. Fudenberg and D. K. Levine, The Theory of Learning in Games, MIT Press Series on Economic Learning and Social Evolution, 2. MIT Press, Cambridge, MA, 1998. |
[12] |
A. Gaunersdorfer and J. Hofbauer, Fictitious play, Shapley polygons, and the replicator equation, Game. Econ. Behav., 11 (1995), 279-303.
doi: 10.1006/game.1995.1052. |
[13] |
I. Gilboa and A. Matsui, Social stability and equilibrium, Econometrica, 59 (1991), 859-867.
doi: 10.2307/2938230. |
[14] |
J. Hannan, Approximation to Bayes risk in repeated play, Contributions to the Theory of Games, 3 (1957), 97-139. |
[15] |
C. Harris, On the rate of convergence of continuous-time fictitious play, Game. Econ. Behav., 22 (1998), 238-259.
doi: 10.1006/game.1997.0582. |
[16] |
S. Hart, Adaptive heuristics, Econometrica, 73 (2005), 1401-1430.
doi: 10.1111/j.1468-0262.2005.00625.x. |
[17] |
S. Hart and A. Mas-Colell, A simple adaptive procedure leading to correlated equilibrium, Econometrica, 68 (2000), 1127-1150.
doi: 10.1111/1468-0262.00153. |
[18] |
S. Hart and A. Mas-Colell, A general class of adaptive strategies, J. Econ. Theory, 98 (2001), 26-54.
doi: 10.1006/jeth.2000.2746. |
[19] |
J. Hofbauer, Stability for the Best Response Dynamics, Mimeo, 1995. |
[20] |
V. Krishna and T. Sjöström, On the convergence of fictitious play, Math. Oper. Res., 23 (1998), 479-511.
doi: 10.1287/moor.23.2.479. |
[21] |
A. Matsui, Best response dynamics and socially stable strategies, J. Econ. Theory, 57 (1992), 343-362.
doi: 10.1016/0022-0531(92)90040-O. |
[22] |
D. Monderer, D. Samet and A. Sela, Belief affirming in learning processes, J. Econ. Theory, 73 (1997), 438-452.
doi: 10.1006/jeth.1996.2245. |
[23] |
S. Morris and T. Ui, Best response equivalence, Game. Econ. Behav., 49 (2004), 260-287.
doi: 10.1016/j.geb.2003.12.004. |
[24] |
H. J. Moulin and J.-P. Vial, Strategically zero-sum games: The class of games whose completely mixed equilibria cannot be improved upon, Internat. J. Game Theory, 7 (1978), 201-221.
doi: 10.1007/BF01769190. |
[25] |
G. Ostrovski and S. van Strien, Piecewise linear Hamiltonian flows associated to zero-sum games: Transition combinatorics and questions on ergodicity, Regul. Chaotic Dyn., 16 (2011), 128-153.
doi: 10.1134/S1560354711010059. |
[26] |
J. Rosenmüller, Über Periodizitätseigenschaften spieltheoretischer Lernprozesse, Z. Wahrscheinlichkeit., 17 (1971), 259-308.
doi: 10.1007/BF00536300. |
[27] |
L. S. Shapley, Some topics in two-person games, Advances in Game Theory, 52 (1964), 1-28. |
[28] |
C. Sparrow, S. van Strien and C. Harris, Fictitious play in $3\times 3$ games: The transition between periodic and chaotic behaviour, Game. Econ. Behav., 63 (2008), 259-291.
doi: 10.1016/j.geb.2007.08.005. |
[29] |
K. Sydsaeter and P. Hammond, Essential Mathematics for Economic Analysis, Prentice Hall, 3rd edition, 2008. |
[30] |
S. van Strien and C. Sparrow, Fictitious play in $3 \times 3$ games: Chaos and dithering behaviour, Game. Econ. Behav., 73 (2011), 262-286.
doi: 10.1016/j.geb.2010.12.004. |
[31] |
S. van Strien, A new class of Hamiltonian flows with random-walk behavior originating from zero-sum games and Fictitious Play, Nonlinearity, 24 (2011), 1715-1742.
doi: 10.1088/0951-7715/24/6/002. |
[32] |
H. P. Young, Strategic Learning and Its Limits (Arne Ryde Memorial Lectures Series), Oxford University Press, USA, 2005. |
show all references
References:
[1] |
R. J. Aumann, Subjectivity and correlation in randomized strategies, J. Math. Econom., 1 (1974), 67-96.
doi: 10.1016/0304-4068(74)90037-8. |
[2] |
R. J. Aumann, Correlated equilibrium as an expression of Bayesian rationality, Econometrica, 55 (1987), 1-18.
doi: 10.2307/1911154. |
[3] |
U. Berger, Fictitious play in $2 \times n$ games, J. Econ. Theory, 120 (2005), 139-154.
doi: 10.1016/j.jet.2004.02.003. |
[4] |
U. Berger, Two more classes of games with the continuous-time fictitious play property, Game. Econ. Behav., 60 (2007), 247-261.
doi: 10.1016/j.geb.2006.10.008. |
[5] |
U. Berger, Learning in games with strategic complementarities revisited, J. Econ. Theory, 143 (2008), 292-301.
doi: 10.1016/j.jet.2008.01.007. |
[6] |
D. Blackwell, Controlled random walks, In Proceedings of the International Congress of Mathematicians, 3 (1954), 336-338. |
[7] |
G. W. Brown, Some notes on computation of games solutions, Technical report, Report P-78, The Rand Corporation, 1949. |
[8] |
G. W. Brown, Iterative solution of games by fictitious play, In Activity Analysis of Production and Allocation, volume 13, pages 374-376. John Wiley & Sons, New York, 1951. |
[9] |
D. P. Foster and R. V. Vohra, Calibrated learning and correlated equilibrium, Game. Econ. Behav., 21 (1997), 40-55.
doi: 10.1006/game.1997.0595. |
[10] |
D. Fudenberg and D. K. Levine, Consistency and cautious fictitious play, J. Econ. Dyn. Control, 19 (1995), 1065-1089.
doi: 10.1016/0165-1889(94)00819-4. |
[11] |
D. Fudenberg and D. K. Levine, The Theory of Learning in Games, MIT Press Series on Economic Learning and Social Evolution, 2. MIT Press, Cambridge, MA, 1998. |
[12] |
A. Gaunersdorfer and J. Hofbauer, Fictitious play, Shapley polygons, and the replicator equation, Game. Econ. Behav., 11 (1995), 279-303.
doi: 10.1006/game.1995.1052. |
[13] |
I. Gilboa and A. Matsui, Social stability and equilibrium, Econometrica, 59 (1991), 859-867.
doi: 10.2307/2938230. |
[14] |
J. Hannan, Approximation to Bayes risk in repeated play, Contributions to the Theory of Games, 3 (1957), 97-139. |
[15] |
C. Harris, On the rate of convergence of continuous-time fictitious play, Game. Econ. Behav., 22 (1998), 238-259.
doi: 10.1006/game.1997.0582. |
[16] |
S. Hart, Adaptive heuristics, Econometrica, 73 (2005), 1401-1430.
doi: 10.1111/j.1468-0262.2005.00625.x. |
[17] |
S. Hart and A. Mas-Colell, A simple adaptive procedure leading to correlated equilibrium, Econometrica, 68 (2000), 1127-1150.
doi: 10.1111/1468-0262.00153. |
[18] |
S. Hart and A. Mas-Colell, A general class of adaptive strategies, J. Econ. Theory, 98 (2001), 26-54.
doi: 10.1006/jeth.2000.2746. |
[19] |
J. Hofbauer, Stability for the Best Response Dynamics, Mimeo, 1995. |
[20] |
V. Krishna and T. Sjöström, On the convergence of fictitious play, Math. Oper. Res., 23 (1998), 479-511.
doi: 10.1287/moor.23.2.479. |
[21] |
A. Matsui, Best response dynamics and socially stable strategies, J. Econ. Theory, 57 (1992), 343-362.
doi: 10.1016/0022-0531(92)90040-O. |
[22] |
D. Monderer, D. Samet and A. Sela, Belief affirming in learning processes, J. Econ. Theory, 73 (1997), 438-452.
doi: 10.1006/jeth.1996.2245. |
[23] |
S. Morris and T. Ui, Best response equivalence, Game. Econ. Behav., 49 (2004), 260-287.
doi: 10.1016/j.geb.2003.12.004. |
[24] |
H. J. Moulin and J.-P. Vial, Strategically zero-sum games: The class of games whose completely mixed equilibria cannot be improved upon, Internat. J. Game Theory, 7 (1978), 201-221.
doi: 10.1007/BF01769190. |
[25] |
G. Ostrovski and S. van Strien, Piecewise linear Hamiltonian flows associated to zero-sum games: Transition combinatorics and questions on ergodicity, Regul. Chaotic Dyn., 16 (2011), 128-153.
doi: 10.1134/S1560354711010059. |
[26] |
J. Rosenmüller, Über Periodizitätseigenschaften spieltheoretischer Lernprozesse, Z. Wahrscheinlichkeit., 17 (1971), 259-308.
doi: 10.1007/BF00536300. |
[27] |
L. S. Shapley, Some topics in two-person games, Advances in Game Theory, 52 (1964), 1-28. |
[28] |
C. Sparrow, S. van Strien and C. Harris, Fictitious play in $3\times 3$ games: The transition between periodic and chaotic behaviour, Game. Econ. Behav., 63 (2008), 259-291.
doi: 10.1016/j.geb.2007.08.005. |
[29] |
K. Sydsaeter and P. Hammond, Essential Mathematics for Economic Analysis, Prentice Hall, 3rd edition, 2008. |
[30] |
S. van Strien and C. Sparrow, Fictitious play in $3 \times 3$ games: Chaos and dithering behaviour, Game. Econ. Behav., 73 (2011), 262-286.
doi: 10.1016/j.geb.2010.12.004. |
[31] |
S. van Strien, A new class of Hamiltonian flows with random-walk behavior originating from zero-sum games and Fictitious Play, Nonlinearity, 24 (2011), 1715-1742.
doi: 10.1088/0951-7715/24/6/002. |
[32] |
H. P. Young, Strategic Learning and Its Limits (Arne Ryde Memorial Lectures Series), Oxford University Press, USA, 2005. |
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