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Existence of the uniform value in zero-sum repeated games with a more informed controller
1. | TSE (GREMAQ, Université Toulouse 1 Capitole), Manufacture des Tabacs, 21, Allée de Brienne, 31015 Toulouse Cedex 6, France |
2. | Université de Neuchâtel, Institut de Mathématiques, Emilie-Argand 11, 2000 Neuchatel, Switzerland |
3. | Department of Statistics and Operations Research, Tel-Aviv University, Ramat-Aviv, 69978 Tel-Aviv, Israel |
References:
[1] |
R. J. Aumann and M. Maschler, Repeated Games with Incomplete Information, with the collaboration of R. Stearns, MIT Press, 1995. |
[2] |
D. Blackwell and T. S. Fergusson, The big match, The Annals of Mathematical Statistics, 39 (1968), 159-163.
doi: 10.1214/aoms/1177698513. |
[3] |
D. Blackwell and L. E. Dubins, An extension of Skorohod's almost sure representation theorem, Proceedings of the American Mathematical Society, 89 (1983), 691-692.
doi: 10.2307/2044607. |
[4] |
K. Fan, Minimax theorems, Proceedings of the National Academy of Sciences of the United States of America, 39 (1953), 42-47.
doi: 10.1073/pnas.39.1.42. |
[5] |
L. Kantorovich and G. S. Rubinstein, On a space of totally additive functions, Vestnik Leningrad. Univ, 13 (1958), 52-59. |
[6] |
J. F. Mertens, Repeated games, in Proceedings of the International Congress of Mathematicians, Vol. 1 (Berkeley, Calif., 1986), Amer. Math. Soc., Providence, RI, 1986, 1528-1577. |
[7] |
J. F. Mertens and A. Neyman, Stochastic games, International Journal of Game Theory, 10 (1981), 53-66.
doi: 10.1007/BF01769259. |
[8] |
J. F. Mertens, S. Sorin and S. Zamir, Repeated Games, CORE Discussion Papers 9420, 9421 and 9422, Université Catholique De Louvain, Belgium, 1994. |
[9] |
J. F. Mertens and S. Zamir, The value of two-person zero-sum repeated games with lack of information on both sides, International Journal of Game Theory, 1 (1971), 39-64.
doi: 10.1007/BF01753433. |
[10] |
A. Neyman and S. Sorin, Repeated games with public uncertain duration process, International Journal of Game Theory 39 (2010), 29-52.
doi: 10.1007/s00182-009-0197-y. |
[11] |
A. Neyman, Existence of optimal strategies in Markov games with incomplete information, International Journal of Game Theory, 37 (2008), 581-596.
doi: 10.1007/s00182-008-0134-5. |
[12] |
J. Renault, The value of Markov chain games with lack of information on one side, Mathematics of Operations Research, 31 (2006), 490-512.
doi: 10.1287/moor.1060.0199. |
[13] |
J. Renault, Uniform value in Dynamic Programming, Journal of the European Mathematical Society, 13 (2011), 309-330.
doi: 10.4171/JEMS/254. |
[14] |
J. Renault, The value of repeated games with an informed controller, Mathematics of Operations Research, 37 (2012), 154-179.
doi: 10.1287/moor.1110.0518. |
[15] |
D. Rosenberg, E. Solan and N. Vieille, Blackwell optimality in Markov decision processes with partial observation, Annals of Statistics, 30 (2002), 1178-1193.
doi: 10.1214/aos/1031689022. |
[16] |
D. Rosenberg, E. Solan and N. Vieille, Stochastic games with a single controller and incomplete information, SIAM Journal on Control and Optimization, 43 (2004), 86-110.
doi: 10.1137/S0363012902407107. |
[17] |
S. Sorin, "Big Match'' with lack of information on one side (part I), International Journal of Game Theory, 13 (1984), 201-255.
doi: 10.1007/BF01769463. |
[18] |
S. Sorin, A First Course on Zero-Sum Repeated games, Mathématiques & Applications, Springer, 2002. |
show all references
References:
[1] |
R. J. Aumann and M. Maschler, Repeated Games with Incomplete Information, with the collaboration of R. Stearns, MIT Press, 1995. |
[2] |
D. Blackwell and T. S. Fergusson, The big match, The Annals of Mathematical Statistics, 39 (1968), 159-163.
doi: 10.1214/aoms/1177698513. |
[3] |
D. Blackwell and L. E. Dubins, An extension of Skorohod's almost sure representation theorem, Proceedings of the American Mathematical Society, 89 (1983), 691-692.
doi: 10.2307/2044607. |
[4] |
K. Fan, Minimax theorems, Proceedings of the National Academy of Sciences of the United States of America, 39 (1953), 42-47.
doi: 10.1073/pnas.39.1.42. |
[5] |
L. Kantorovich and G. S. Rubinstein, On a space of totally additive functions, Vestnik Leningrad. Univ, 13 (1958), 52-59. |
[6] |
J. F. Mertens, Repeated games, in Proceedings of the International Congress of Mathematicians, Vol. 1 (Berkeley, Calif., 1986), Amer. Math. Soc., Providence, RI, 1986, 1528-1577. |
[7] |
J. F. Mertens and A. Neyman, Stochastic games, International Journal of Game Theory, 10 (1981), 53-66.
doi: 10.1007/BF01769259. |
[8] |
J. F. Mertens, S. Sorin and S. Zamir, Repeated Games, CORE Discussion Papers 9420, 9421 and 9422, Université Catholique De Louvain, Belgium, 1994. |
[9] |
J. F. Mertens and S. Zamir, The value of two-person zero-sum repeated games with lack of information on both sides, International Journal of Game Theory, 1 (1971), 39-64.
doi: 10.1007/BF01753433. |
[10] |
A. Neyman and S. Sorin, Repeated games with public uncertain duration process, International Journal of Game Theory 39 (2010), 29-52.
doi: 10.1007/s00182-009-0197-y. |
[11] |
A. Neyman, Existence of optimal strategies in Markov games with incomplete information, International Journal of Game Theory, 37 (2008), 581-596.
doi: 10.1007/s00182-008-0134-5. |
[12] |
J. Renault, The value of Markov chain games with lack of information on one side, Mathematics of Operations Research, 31 (2006), 490-512.
doi: 10.1287/moor.1060.0199. |
[13] |
J. Renault, Uniform value in Dynamic Programming, Journal of the European Mathematical Society, 13 (2011), 309-330.
doi: 10.4171/JEMS/254. |
[14] |
J. Renault, The value of repeated games with an informed controller, Mathematics of Operations Research, 37 (2012), 154-179.
doi: 10.1287/moor.1110.0518. |
[15] |
D. Rosenberg, E. Solan and N. Vieille, Blackwell optimality in Markov decision processes with partial observation, Annals of Statistics, 30 (2002), 1178-1193.
doi: 10.1214/aos/1031689022. |
[16] |
D. Rosenberg, E. Solan and N. Vieille, Stochastic games with a single controller and incomplete information, SIAM Journal on Control and Optimization, 43 (2004), 86-110.
doi: 10.1137/S0363012902407107. |
[17] |
S. Sorin, "Big Match'' with lack of information on one side (part I), International Journal of Game Theory, 13 (1984), 201-255.
doi: 10.1007/BF01769463. |
[18] |
S. Sorin, A First Course on Zero-Sum Repeated games, Mathématiques & Applications, Springer, 2002. |
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