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Volumn 3, Issue , 2002, Pages 1723-1759

Chapter 45 Computing equilibria for two-person games

Author keywords

degenerate game; equilibrium computation; extensive game; Lemke Howson algorithm; perfect equilibrium; pivoting

Indexed keywords


EID: 67649370955     PISSN: 15740005     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1574-0005(02)03008-4     Document Type: Review
Times cited : (172)

References (89)
  • 1
    • 0007093587 scopus 로고
    • On the generation of all equilibrium points for bimatrix games through the Lemke-Howson algorithm
    • Aggarwal V. On the generation of all equilibrium points for bimatrix games through the Lemke-Howson algorithm. Mathematical Programming 4 (1973) 233-234
    • (1973) Mathematical Programming , vol.4 , pp. 233-234
    • Aggarwal, V.1
  • 3
    • 34249842390 scopus 로고
    • A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra
    • Avis D., and Fukuda K. A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra. Discrete and Computational Geometry 8 (1992) 295-313
    • (1992) Discrete and Computational Geometry , vol.8 , pp. 295-313
    • Avis, D.1    Fukuda, K.2
  • 4
    • 34250381325 scopus 로고
    • Another note on bimatrix games
    • Bastian M. Another note on bimatrix games. Mathematical Programming 11 (1976) 299-300
    • (1976) Mathematical Programming , vol.11 , pp. 299-300
    • Bastian, M.1
  • 8
  • 11
    • 0008723917 scopus 로고
    • A program for finding Nash equilibria
    • Dickhaut J., and Kaplan T. A program for finding Nash equilibria. The Mathematica Journal 1 4 (1991) 87-93
    • (1991) The Mathematica Journal , vol.1 , Issue.4 , pp. 87-93
    • Dickhaut, J.1    Kaplan, T.2
  • 12
    • 0001159656 scopus 로고
    • The linear complementarity problem
    • Eaves B.C. The linear complementarity problem. Management Science 17 (1971) 612-634
    • (1971) Management Science , vol.17 , pp. 612-634
    • Eaves, B.C.1
  • 13
  • 17
    • 45249127547 scopus 로고
    • Nash and correlated equilibria: Some complexity considerations
    • Gilboa I., and Zemel E. Nash and correlated equilibria: Some complexity considerations. Games and Economic Behavior 1 (1989) 80-93
    • (1989) Games and Economic Behavior , vol.1 , pp. 80-93
    • Gilboa, I.1    Zemel, E.2
  • 19
    • 70350097614 scopus 로고
    • Games in extensive and strategic forms
    • Chapter 2. Aumann R.J., and Hart S. (Eds), North-Holland, Cambridge
    • Chapter 2. Hart S. Games in extensive and strategic forms. In: Aumann R.J., and Hart S. (Eds). Handbook of Game Theory Vol. 1 (1992), North-Holland, Cambridge 19-40
    • (1992) Handbook of Game Theory , vol.1 , pp. 19-40
    • Hart, S.1
  • 21
    • 67649342399 scopus 로고    scopus 로고
    • Foundations of strategic equilibrium
    • Chapter 42. Aumann R.J., and Hart S. (Eds), North-Holland, Amsterdam
    • Chapter 42. Hillas J., and Kohlberg E. Foundations of strategic equilibrium. In: Aumann R.J., and Hart S. (Eds). Handbook of Game Theory Vol. 3 (2002), North-Holland, Amsterdam 1597-1663
    • (2002) Handbook of Game Theory , vol.3 , pp. 1597-1663
    • Hillas, J.1    Kohlberg, E.2
  • 22
    • 0011697387 scopus 로고
    • Equilibria of polymatrix games
    • Howson Jr. J.T. Equilibria of polymatrix games. Management Science 18 (1972) 312-318
    • (1972) Management Science , vol.18 , pp. 312-318
    • Howson Jr., J.T.1
  • 23
    • 0011697387 scopus 로고
    • Bayesian equilibria of finite two-person games with incomplete information
    • Howson Jr. J.T., and Rosenthal R.W. Bayesian equilibria of finite two-person games with incomplete information. Management Science 21 (1974) 313-315
    • (1974) Management Science , vol.21 , pp. 313-315
    • Howson Jr., J.T.1    Rosenthal, R.W.2
  • 26
    • 0035530138 scopus 로고    scopus 로고
    • On the computation of stable sets and strictly perfect equilibria
    • Jansen M.J.M., and Vermeulen A.J. On the computation of stable sets and strictly perfect equilibria. Economic Theory 17 (2001) 325-344
    • (2001) Economic Theory , vol.17 , pp. 325-344
    • Jansen, M.J.M.1    Vermeulen, A.J.2
  • 27
    • 0031256798 scopus 로고    scopus 로고
    • On the maximal number of Nash equilibria in an n × n bimatrix game
    • Keiding H. On the maximal number of Nash equilibria in an n × n bimatrix game. Games and Economic Behavior 21 (1997) 148-160
    • (1997) Games and Economic Behavior , vol.21 , pp. 148-160
    • Keiding, H.1
  • 29
    • 0000292804 scopus 로고
    • On the strategic stability of equilibria
    • Kohlberg E., and Mertens J.-F. On the strategic stability of equilibria. Econometrica 54 (1986) 1003-1037
    • (1986) Econometrica , vol.54 , pp. 1003-1037
    • Kohlberg, E.1    Mertens, J.-F.2
  • 30
    • 0003212154 scopus 로고
    • A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems
    • Springer, Amsterdam
    • Kojima M., Megiddo N., Noma T., and Yoshise A. A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems. Lecture Notes in Computer Science Vol. 538 (1991), Springer, Amsterdam
    • (1991) Lecture Notes in Computer Science , vol.538
    • Kojima, M.1    Megiddo, N.2    Noma, T.3    Yoshise, A.4
  • 31
    • 0000979731 scopus 로고
    • The complexity of two-person zero-sum games in extensive form
    • Koller D., and Megiddo N. The complexity of two-person zero-sum games in extensive form. Games and Economic Behavior 4 (1992) 528-552
    • (1992) Games and Economic Behavior , vol.4 , pp. 528-552
    • Koller, D.1    Megiddo, N.2
  • 32
    • 0030535025 scopus 로고    scopus 로고
    • Finding mixed strategies with small supports in extensive form games
    • Koller D., and Megiddo N. Finding mixed strategies with small supports in extensive form games. International Journal of Game Theory 25 (1996) 73-92
    • (1996) International Journal of Game Theory , vol.25 , pp. 73-92
    • Koller, D.1    Megiddo, N.2
  • 34
    • 0030170957 scopus 로고    scopus 로고
    • Efficient computation of equilibria for extensive two-person games
    • Koller D., Megiddo N., and von Stengel B. Efficient computation of equilibria for extensive two-person games. Games and Economic Behavior 14 (1996) 247-259
    • (1996) Games and Economic Behavior , vol.14 , pp. 247-259
    • Koller, D.1    Megiddo, N.2    von Stengel, B.3
  • 35
    • 0031192989 scopus 로고    scopus 로고
    • Representations and solutions for game-theoretic problems
    • Koller D., and Pfeffer A. Representations and solutions for game-theoretic problems. Artificial Intelligence 94 (1997) 167-215
    • (1997) Artificial Intelligence , vol.94 , pp. 167-215
    • Koller, D.1    Pfeffer, A.2
  • 37
    • 0000619048 scopus 로고
    • Extensive games and the problem of information
    • Contributions to the Theory of Games II. Kuhn H.W., and Tucker A.W. (Eds), Princeton Univ. Press, Berlin
    • Kuhn H.W. Extensive games and the problem of information. In: Kuhn H.W., and Tucker A.W. (Eds). Contributions to the Theory of Games II. Annals of Mathematics Studies Vol. 28 (1953), Princeton Univ. Press, Berlin 193-216
    • (1953) Annals of Mathematics Studies , vol.28 , pp. 193-216
    • Kuhn, H.W.1
  • 39
    • 0001644591 scopus 로고
    • Bimatrix equilibrium points and mathematical programming
    • Lemke C.E. Bimatrix equilibrium points and mathematical programming. Management Science 11 (1965) 681-689
    • (1965) Management Science , vol.11 , pp. 681-689
    • Lemke, C.E.1
  • 41
    • 70350100693 scopus 로고
    • Game-theoretic aspects of computing
    • Chapter 38. Aumann R.J., and Hart S. (Eds), North-Holland, Princeton
    • Chapter 38. Linial N. Game-theoretic aspects of computing. In: Aumann R.J., and Hart S. (Eds). Handbook of Game Theory Vol. 2 (1994), North-Holland, Princeton 1339-1395
    • (1994) Handbook of Game Theory , vol.2 , pp. 1339-1395
    • Linial, N.1
  • 42
    • 0011574297 scopus 로고
    • An overview of the mathematical theory of games
    • Appendix P
    • Appendix P. Lucas W.F. An overview of the mathematical theory of games. Management Science 18 (1972) 3-19
    • (1972) Management Science , vol.18 , pp. 3-19
    • Lucas, W.F.1
  • 45
    • 70350102387 scopus 로고    scopus 로고
    • Computation of equilibria in finite games
    • Amman H.M., Kendrick D.A., and Rust J. (Eds), Elsevier, Amsterdam
    • McKelvey R.D., and McLennan A. Computation of equilibria in finite games. In: Amman H.M., Kendrick D.A., and Rust J. (Eds). Handbook of Computational Economics Vol. I (1996), Elsevier, Amsterdam 87-142
    • (1996) Handbook of Computational Economics , vol.I , pp. 87-142
    • McKelvey, R.D.1    McLennan, A.2
  • 46
    • 0042204039 scopus 로고    scopus 로고
    • Generic 4 × 4 two person games have at most 15 Nash equilibria
    • McLennan A., and Park I.-U. Generic 4 × 4 two person games have at most 15 Nash equilibria. Games and Economic Behavior 26 (1999) 111-130
    • (1999) Games and Economic Behavior , vol.26 , pp. 111-130
    • McLennan, A.1    Park, I.-U.2
  • 47
    • 84976163829 scopus 로고
    • The maximum number of faces of a convex polytope
    • McMullen P. The maximum number of faces of a convex polytope. Mathematika 17 (1970) 179-184
    • (1970) Mathematika , vol.17 , pp. 179-184
    • McMullen, P.1
  • 48
    • 0042558387 scopus 로고
    • A note on the complexity of p-matrix LCP and computing an equilibrium
    • IBM Almaden Research Center, Amsterdam
    • Megiddo N. A note on the complexity of p-matrix LCP and computing an equilibrium. Research Report RJ 6439 (1988), IBM Almaden Research Center, Amsterdam
    • (1988) Research Report RJ 6439
    • Megiddo, N.1
  • 49
    • 0026142122 scopus 로고
    • On total functions, existence theorems and computational complexity (Note)
    • Megiddo N., and Papadimitriou C.H. On total functions, existence theorems and computational complexity (Note). Theoretical Computer Science 81 (1989) 317-324
    • (1989) Theoretical Computer Science , vol.81 , pp. 317-324
    • Megiddo, N.1    Papadimitriou, C.H.2
  • 50
  • 51
    • 0000829832 scopus 로고
    • Stable equilibria - a reformulation, Part II
    • Mertens J.-F. Stable equilibria - a reformulation, Part II. Mathematics of Operations Research 16 (1991) 694-753
    • (1991) Mathematics of Operations Research , vol.16 , pp. 694-753
    • Mertens, J.-F.1
  • 54
    • 49349132229 scopus 로고
    • The solution of bilinear programming problems and finding the equilibrium situations in bimatrix games
    • Mukhamediev B.M. The solution of bilinear programming problems and finding the equilibrium situations in bimatrix games. Computational Mathematics and Mathematical Physics 18 (1978) 60-66
    • (1978) Computational Mathematics and Mathematical Physics , vol.18 , pp. 60-66
    • Mukhamediev, B.M.1
  • 57
    • 0001730497 scopus 로고
    • Non-cooperative games
    • Nash J.F. Non-cooperative games. Annals of Mathematics 54 (1951) 286-295
    • (1951) Annals of Mathematics , vol.54 , pp. 286-295
    • Nash, J.F.1
  • 58
    • 0028459906 scopus 로고
    • On the complexity of the parity argument and other inefficient proof of existence
    • Papadimitriou C.H. On the complexity of the parity argument and other inefficient proof of existence. Journal of Computer and System Sciences 48 (1994) 498-532
    • (1994) Journal of Computer and System Sciences , vol.48 , pp. 498-532
    • Papadimitriou, C.H.1
  • 60
    • 0040747444 scopus 로고    scopus 로고
    • A theorem on the number of Nash equilibria in a bimatrix game
    • Quint T., and Shubik M. A theorem on the number of Nash equilibria in a bimatrix game. International Journal of Game Theory 26 (1997) 353-359
    • (1997) International Journal of Game Theory , vol.26 , pp. 353-359
    • Quint, T.1    Shubik, M.2
  • 61
    • 70350123267 scopus 로고
    • Zero-sum two-person games
    • Chapter 20. Aumann R.J., and Hart S. (Eds), North-Holland, New York
    • Chapter 20. Raghavan T.E.S. Zero-sum two-person games. In: Aumann R.J., and Hart S. (Eds). Handbook of Game Theory Vol. 2 (1994), North-Holland, New York 735-768
    • (1994) Handbook of Game Theory , vol.2 , pp. 735-768
    • Raghavan, T.E.S.1
  • 62
    • 67649365851 scopus 로고    scopus 로고
    • Non-zero-sum two-person games
    • Chapter 44. Aumann R.J., and Hart S. (Eds), North-Holland, Amsterdam
    • Chapter 44. Raghavan T.E.S. Non-zero-sum two-person games. In: Aumann R.J., and Hart S. (Eds). Handbook of Game Theory Vol. 3 (2002), North-Holland, Amsterdam 1687-1721
    • (2002) Handbook of Game Theory , vol.3 , pp. 1687-1721
    • Raghavan, T.E.S.1
  • 63
    • 0008787431 scopus 로고
    • Reduction of a game with complete memory to a matrix game
    • Romanovskii I.V. Reduction of a game with complete memory to a matrix game. Soviet Mathematics 3 (1962) 678-681
    • (1962) Soviet Mathematics , vol.3 , pp. 678-681
    • Romanovskii, I.V.1
  • 65
    • 33747856809 scopus 로고
    • Reexamination of the perfectness concept for equilibrium points in extensive games
    • Selten R. Reexamination of the perfectness concept for equilibrium points in extensive games. International Journal of Game Theory 4 (1975) 22-55
    • (1975) International Journal of Game Theory , vol.4 , pp. 22-55
    • Selten, R.1
  • 66
    • 0000861465 scopus 로고
    • Evolutionary stability in extensive two-person games - correction and further development
    • Selten R. Evolutionary stability in extensive two-person games - correction and further development. Mathematical Social Sciences 16 (1988) 223-266
    • (1988) Mathematical Social Sciences , vol.16 , pp. 223-266
    • Selten, R.1
  • 68
    • 18844461316 scopus 로고
    • On the accessibility of fixed points
    • Moeschlin O., and Pallaschke D. (Eds), North-Holland, Chichester
    • Shapley L.S. On the accessibility of fixed points. In: Moeschlin O., and Pallaschke D. (Eds). Game Theory and Mathematical Economics (1981), North-Holland, Chichester 367-377
    • (1981) Game Theory and Mathematical Economics , pp. 367-377
    • Shapley, L.S.1
  • 69
    • 67649349256 scopus 로고
    • Comments on a note by Aggarwal
    • Todd M.J. Comments on a note by Aggarwal. Mathematical Programming 10 (1976) 130-133
    • (1976) Mathematical Programming , vol.10 , pp. 130-133
    • Todd, M.J.1
  • 70
    • 33646993070 scopus 로고
    • Bimatrix games - an addendum
    • Todd M.J. Bimatrix games - an addendum. Mathematical Programming 14 (1978) 112-115
    • (1978) Mathematical Programming , vol.14 , pp. 112-115
    • Todd, M.J.1
  • 73
    • 67649370958 scopus 로고    scopus 로고
    • Strategic equilibrium
    • Chapter 41. Aumann R.J., and Hart S. (Eds), North-Holland, Berlin
    • Chapter 41. van Damme E. Strategic equilibrium. In: Aumann R.J., and Hart S. (Eds). Handbook of Game Theory Vol. 3 (2002), North-Holland, Berlin 1521-1596
    • (2002) Handbook of Game Theory , vol.3 , pp. 1521-1596
    • van Damme, E.1
  • 74
    • 0003245591 scopus 로고
    • Adjustment Processes for Exchange Economies and Noncooperative Games
    • Springer, Amsterdam
    • van den Elzen A. Adjustment Processes for Exchange Economies and Noncooperative Games. Lecture Notes in Economics and Mathematical Systems Vol. 402 (1993), Springer, Amsterdam
    • (1993) Lecture Notes in Economics and Mathematical Systems , vol.402
    • van den Elzen, A.1
  • 76
    • 0001116149 scopus 로고    scopus 로고
    • An algorithmic approach toward the tracing procedure for bi-matrix games
    • van den Elzen A.H., and Talman A.J.J. An algorithmic approach toward the tracing procedure for bi-matrix games. Games and Economic Behavior 28 (1999) 130-145
    • (1999) Games and Economic Behavior , vol.28 , pp. 130-145
    • van den Elzen, A.H.1    Talman, A.J.J.2
  • 77
    • 84989726716 scopus 로고
    • On the set of (perfect) equilibria of a bimatrix game
    • Vermeulen A.J., and Jansen M.J.M. On the set of (perfect) equilibria of a bimatrix game. Naval Research Logistics 41 (1994) 295-302
    • (1994) Naval Research Logistics , vol.41 , pp. 295-302
    • Vermeulen, A.J.1    Jansen, M.J.M.2
  • 79
    • 0030167455 scopus 로고    scopus 로고
    • Efficient computation of behavior strategies
    • von Stengel B. Efficient computation of behavior strategies. Games and Economic Behavior 14 (1996) 220-246
    • (1996) Games and Economic Behavior , vol.14 , pp. 220-246
    • von Stengel, B.1
  • 80
    • 67649314870 scopus 로고    scopus 로고
    • Computing equilibria for two-person games
    • Dept. of Computer Science, ETH Zürich, Berlin
    • von Stengel B. Computing equilibria for two-person games. Technical Report 253 (1996), Dept. of Computer Science, ETH Zürich, Berlin
    • (1996) Technical Report 253
    • von Stengel, B.1
  • 81
    • 0033463683 scopus 로고    scopus 로고
    • New maximal numbers of equilibria in bimatrix games
    • von Stengel B. New maximal numbers of equilibria in bimatrix games. Discrete and Computational Geometry 21 (1999) 557-568
    • (1999) Discrete and Computational Geometry , vol.21 , pp. 557-568
    • von Stengel, B.1
  • 82
    • 0036212395 scopus 로고    scopus 로고
    • Computing normal form perfect equilibria for extensive two-person games
    • to appear
    • to appear. von Stengel B., van den Elzen A.H., and Talman A.J.J. Computing normal form perfect equilibria for extensive two-person games. Econometrica (2002)
    • (2002) Econometrica
    • von Stengel, B.1    van den Elzen, A.H.2    Talman, A.J.J.3
  • 84
    • 0000002344 scopus 로고
    • Computing equilibria of two-person games from the extensive form
    • Wilson R. Computing equilibria of two-person games from the extensive form. Management Science 18 (1972) 448-460
    • (1972) Management Science , vol.18 , pp. 448-460
    • Wilson, R.1
  • 85
    • 0000438471 scopus 로고
    • Computing simply stable equilibria
    • Wilson R. Computing simply stable equilibria. Econometrica 60 (1992) 1039-1070
    • (1992) Econometrica , vol.60 , pp. 1039-1070
    • Wilson, R.1
  • 86
    • 0002705049 scopus 로고
    • An algorithm to determine all equilibrium points of a bimatrix game
    • Moeschlin O., and Pallaschke D. (Eds), North-Holland
    • Winkels H.-M. An algorithm to determine all equilibrium points of a bimatrix game. In: Moeschlin O., and Pallaschke D. (Eds). Game Theory and Related Topics (1979), North-Holland 137-148
    • (1979) Game Theory and Related Topics , pp. 137-148
    • Winkels, H.-M.1
  • 87
    • 0009711392 scopus 로고
    • Equilibrium points in polymatrix games
    • (in Russian). [Math. Reviews 39 #3831]
    • (in Russian). Yanovskaya E.B. Equilibrium points in polymatrix games. [Math. Reviews 39 #3831]. Litovskii Matematicheskii Sbornik 8 (1968) 381-384
    • (1968) Litovskii Matematicheskii Sbornik , vol.8 , pp. 381-384
    • Yanovskaya, E.B.1
  • 88
    • 67649323406 scopus 로고
    • Quasistrategies in position games
    • Yanovskaya E.B. Quasistrategies in position games. Engineering Cybernetics 1 (1970) 11-19
    • (1970) Engineering Cybernetics , vol.1 , pp. 11-19
    • Yanovskaya, E.B.1


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