메뉴 건너뛰기




Volumn 175, Issue 1, 2010, Pages 177-211

Generalized Nash equilibrium problems

Author keywords

Coupled constraints; Existence; Nash Equilibrium Problem; Pseudo game; Social equilibrium; Solution algorithm; Stability

Indexed keywords


EID: 76749125765     PISSN: 02545330     EISSN: 15729338     Source Type: Journal    
DOI: 10.1007/s10479-009-0653-x     Document Type: Article
Times cited : (623)

References (116)
  • 3
    • 3142557595 scopus 로고    scopus 로고
    • Equilibrium games, and pricing in transportation and telecommunication networks
    • Altman, E., & Wynter, L. (2004). Equilibrium games, and pricing in transportation and telecommunication networks. Networks Spatial Economics, 4, 7-21.
    • (2004) Networks Spatial Economics , vol.4 , pp. 7-21
    • Altman, E.1    Wynter, L.2
  • 5
    • 33746555005 scopus 로고    scopus 로고
    • Solution methods for variational inequalities with coupled constraints
    • Antipin, A. S. (2000a). Solution methods for variational inequalities with coupled constraints. Computational Mathematics and Mathematical Physics, 40, 1239-1254.
    • (2000) Computational Mathematics and Mathematical Physics , vol.40 , pp. 1239-1254
    • Antipin, A.S.1
  • 6
    • 23044527747 scopus 로고    scopus 로고
    • Solving variational inequalities with coupling constraints with the use of differential equations
    • Antipin, A. S. (2000b). Solving variational inequalities with coupling constraints with the use of differential equations. Differential Equations, 36, 1587-1596.
    • (2000) Differential Equations , vol.36 , pp. 1587-1596
    • Antipin, A.S.1
  • 7
    • 0035424912 scopus 로고    scopus 로고
    • Differential equations for equilibrium problems with coupled constraints
    • Antipin, A. S. (2001). Differential equations for equilibrium problems with coupled constraints. Nonlinear Analysis, 47, 1833-1844.
    • (2001) Nonlinear Analysis , vol.47 , pp. 1833-1844
    • Antipin, A.S.1
  • 8
    • 0001436273 scopus 로고
    • Existence of an equilibrium for a competitive economy
    • Arrow, K. J., & Debreu, G. (1954). Existence of an equilibrium for a competitive economy. Econometrica, 22, 265-290.
    • (1954) Econometrica , vol.22 , pp. 265-290
    • Arrow, K.J.1    Debreu, G.2
  • 9
    • 0003836533 scopus 로고
    • Berlin, Heidelberg, New York: Springer
    • Aubin, J.-P. (1993). Optima and equilibria. Berlin, Heidelberg, New York: Springer.
    • (1993) Optima and Equilibria
    • Aubin, J.-P.1
  • 11
    • 0004071782 scopus 로고
    • 2Reprinted in SIAM Series "Classics in Applied Mathematics", 1999, London/New York: Academic Press
    • Başar, T., & Olsder, G. J. (1989). Dynamic noncooperative game theory (2nd edn.). London/New York: Academic Press. Reprinted in SIAM Series "Classics in Applied Mathematics", 1999.
    • (1989) Dynamic Noncooperative Game Theory
    • Başar, T.1    Olsder, G.J.2
  • 12
    • 34547112614 scopus 로고    scopus 로고
    • Allocation of railroad capacity under competition: A game theoretic approach to track time pricing
    • M. Gendreau and P. Marcotte (Eds.), Dordrecht: Kluwer Academic
    • Bassanini, A., La Bella, A., & Nastasi, A. (2002). Allocation of railroad capacity under competition: a game theoretic approach to track time pricing. In M. Gendreau & P. Marcotte (Eds.), Transportation and networks analysis: current trends (pp. 1-17). Dordrecht: Kluwer Academic.
    • (2002) Transportation and Networks Analysis: Current Trends , pp. 1-17
    • Bassanini, A.1    la Bella, A.2    Nastasi, A.3
  • 13
    • 0000655673 scopus 로고
    • Characterization of existence of equilibria in games with discontinuous and non-quasiconcave payoffs
    • Baye, M. R., Tian, G., & Zhou, J. (1993). Characterization of existence of equilibria in games with discontinuous and non-quasiconcave payoffs. Review of Economic Studies, 60, 935-948.
    • (1993) Review of Economic Studies , vol.60 , pp. 935-948
    • Baye, M.R.1    Tian, G.2    Zhou, J.3
  • 14
    • 0001475203 scopus 로고
    • Points de Nash dans le cas de fonctionnelles quadratiques et jeux differentiels lineaires a N personnes
    • Bensoussan, A. (1974). Points de Nash dans le cas de fonctionnelles quadratiques et jeux differentiels lineaires a N personnes. SIAM Journal of Control and Optimization, 12, 460-499.
    • (1974) SIAM Journal of Control and Optimization , vol.12 , pp. 460-499
    • Bensoussan, A.1
  • 15
    • 34247570007 scopus 로고    scopus 로고
    • Iterative approximation of fixed points
    • 2, Berlin, Heidelberg: Springer
    • Berinde, V. (2007). Iterative approximation of fixed points. In Lecture notes in mathematics: Vol. 1912 (2nd edn.). Berlin, Heidelberg: Springer.
    • (2007) Lecture Notes in Mathematics , vol.1912
    • Berinde, V.1
  • 17
    • 0000548078 scopus 로고
    • Review of "Théorie mathématique de la richesse sociale" by Léon Walras and "Recherches sur les principes mathématiques de la théorie des richesses"by Augustin Cournot
    • Bertrand, J. (1883). Review of "Théorie mathématique de la richesse sociale" by Léon Walras and "Recherches sur les principes mathématiques de la théorie des richesses" by Augustin Cournot. Journal des Savants, 499-508.
    • (1883) Journal Des Savants , pp. 499-508
    • Bertrand, J.1
  • 18
    • 16244405596 scopus 로고    scopus 로고
    • A game-theoretic formulation of joint implementation of environmental projects
    • Breton, M., Zaccour, G., & Zahaf, M. (2005). A game-theoretic formulation of joint implementation of environmental projects. European Journal of Operational Research, 168, 221-239.
    • (2005) European Journal of Operational Research , vol.168 , pp. 221-239
    • Breton, M.1    Zaccour, G.2    Zahaf, M.3
  • 21
    • 0000617544 scopus 로고
    • The generalized quasi-variational inequality problem
    • Chan, D., & Pang, J.-S. (1982). The generalized quasi-variational inequality problem. Mathematics of Operations Research, 7, 211-222.
    • (1982) Mathematics of Operations Research , vol.7 , pp. 211-222
    • Chan, D.1    Pang, J.-S.2
  • 22
    • 1442339029 scopus 로고    scopus 로고
    • Numerical solution to Nash-Cournot equilibria in coupled constraints electricity markets
    • Contreras, J., Klusch, M. K., & Krawczyk, J. B. (2004). Numerical solution to Nash-Cournot equilibria in coupled constraints electricity markets. IEEE Transactions on Power Systems, 19, 195-206.
    • (2004) IEEE Transactions on Power Systems , vol.19 , pp. 195-206
    • Contreras, J.1    Klusch, M.K.2    Krawczyk, J.B.3
  • 24
    • 0000249741 scopus 로고
    • Exchange price equilibria and variational inequalities
    • Dafermos, S. (1990). Exchange price equilibria and variational inequalities. Mathematical Programming, 46, 391-402.
    • (1990) Mathematical Programming , vol.46 , pp. 391-402
    • Dafermos, S.1
  • 25
    • 84960608031 scopus 로고
    • The existence of equilibrium in discontinuous economic games, I: Theory
    • Dasgupta, P., & Maskin, E. (1986a). The existence of equilibrium in discontinuous economic games, I: theory. Review of Economic Studies, 53, 1-26.
    • (1986) Review of Economic Studies , vol.53 , pp. 1-26
    • Dasgupta, P.1    Maskin, E.2
  • 26
    • 84960563884 scopus 로고
    • The existence of equilibrium in discontinuous economic games, II: Applications
    • Dasgupta, P., & Maskin, E. (1986b). The existence of equilibrium in discontinuous economic games, II: applications. Review of Economic Studies, 53, 27-41.
    • (1986) Review of Economic Studies , vol.53 , pp. 27-41
    • Dasgupta, P.1    Maskin, E.2
  • 28
    • 0004212232 scopus 로고
    • New Haven: Yale University Press
    • Debreu, G. (1959). Theory of values. New Haven: Yale University Press.
    • (1959) Theory of Values
    • Debreu, G.1
  • 29
    • 0000424497 scopus 로고
    • Economies with a finite set of equilibria
    • Debreu, G. (1970). Economies with a finite set of equilibria. Econometrica, 38, 387-392.
    • (1970) Econometrica , vol.38 , pp. 387-392
    • Debreu, G.1
  • 30
    • 0029423693 scopus 로고
    • The PATH solver: A non-monotone stabilization scheme for mixed complementarity problems
    • Dirkse, S. P., & Ferris, M. C. (1995). The PATH solver: a non-monotone stabilization scheme for mixed complementarity problems. Optimization Methods & Software, 5, 123-156.
    • (1995) Optimization Methods & Software , vol.5 , pp. 123-156
    • Dirkse, S.P.1    Ferris, M.C.2
  • 33
    • 34848903352 scopus 로고    scopus 로고
    • Generalized Nash equilibrium problems
    • Facchinei, F., & Kanzow, C. (2007). Generalized Nash equilibrium problems. 4OR, 5, 173-210.
    • (2007) 4OR , vol.5 , pp. 173-210
    • Facchinei, F.1    Kanzow, C.2
  • 36
    • 34848836954 scopus 로고    scopus 로고
    • Exact penalty functions for generalized Nash problems
    • G. PilloDi and M. Roma (Eds.), Berlin: Springer
    • Facchinei, F., & Pang, J.-S. (2006). Exact penalty functions for generalized Nash problems. In G. Di Pillo & M. Roma (Eds.), Large-scale nonlinear optimization (pp. 115-126). Berlin: Springer.
    • (2006) Large-Scale Nonlinear Optimization , pp. 115-126
    • Facchinei, F.1    Pang, J.-S.2
  • 37
    • 84926080626 scopus 로고    scopus 로고
    • Nash equilibria: The variational approach
    • (to appear), D. P. Palomar and Y. Eldar (Eds.), Cambridge: Cambridge University Press
    • Facchinei, F., & Pang, J.-S. (2009). Nash equilibria: the variational approach. In D. P. Palomar & Y. Eldar (Eds.), Convex optimization in signal processing and communications. Cambridge: Cambridge University Press (to appear).
    • (2009) Convex Optimization in Signal Processing and Communications
    • Facchinei, F.1    Pang, J.-S.2
  • 39
    • 46749142109 scopus 로고    scopus 로고
    • Generalized Nash equilibrium problems and Newton methods
    • Facchinei, F., Fischer, A., & Piccialli, V. (2009a). Generalized Nash equilibrium problems and Newton methods. Mathematical Programming, 117, 163-194.
    • (2009) Mathematical Programming , vol.117 , pp. 163-194
    • Facchinei, F.1    Fischer, A.2    Piccialli, V.3
  • 41
    • 0001550873 scopus 로고
    • Paths to constrained Nash equilibria
    • Flåm, S. D. (1993). Paths to constrained Nash equilibria. Applied Mathematics & Optimization, 27, 275-289.
    • (1993) Applied Mathematics & Optimization , vol.27 , pp. 275-289
    • Flåm, S.D.1
  • 42
    • 4243631874 scopus 로고
    • On variational stability in competitive economies
    • Flåm, S. D. (1994). On variational stability in competitive economies. Set-Valued Analysis, 2, 159-173.
    • (1994) Set-Valued Analysis , vol.2 , pp. 159-173
    • Flåm, S.D.1
  • 43
    • 34848898049 scopus 로고
    • Noncooperative convex games: Computing equilibrium by partial regularization
    • Flåm, S. D., & Ruszczyński, A. (1994). Noncooperative convex games: computing equilibrium by partial regularization. IIASA Working Paper, 94-42.
    • (1994) IIASA Working Paper , pp. 94-42
    • Flåm, S.D.1    Ruszczyński, A.2
  • 45
    • 34848897416 scopus 로고    scopus 로고
    • A class of gap functions for quasi-variational inequality problems
    • Fukushima, M. (2007). A class of gap functions for quasi-variational inequality problems. Journal of Industrial and Management Optimization, 3, 165-171.
    • (2007) Journal of Industrial and Management Optimization , vol.3 , pp. 165-171
    • Fukushima, M.1
  • 46
    • 20444502586 scopus 로고    scopus 로고
    • Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games
    • Fukushima, M., & Pang, J.-S. (2005). Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games. Computational Management Science, 2, 21-56.
    • (2005) Computational Management Science , vol.2 , pp. 21-56
    • Fukushima, M.1    Pang, J.-S.2
  • 47
    • 34848877684 scopus 로고    scopus 로고
    • Complementarity problems in restructured natural gas markets
    • Lectures notes in economics and mathematical systems, Berlin: Springer
    • Gabriel, S., & Smeers, Y. (2006). Complementarity problems in restructured natural gas markets. In Lectures notes in economics and mathematical systems: Vol. 563. Recent advances in optimization (pp. 343-373). Berlin: Springer.
    • (2006) Recent Advances in Optimization , vol.563 , pp. 343-373
    • Gabriel, S.1    Smeers, Y.2
  • 48
    • 27344437220 scopus 로고    scopus 로고
    • A mixed complementarity-based equilibrium model of natural gas markets
    • Gabriel, S. A., Kiet, S., & Zhuang, J. (2005). A mixed complementarity-based equilibrium model of natural gas markets. Operations Research, 53, 799-818.
    • (2005) Operations Research , vol.53 , pp. 799-818
    • Gabriel, S.A.1    Kiet, S.2    Zhuang, J.3
  • 50
    • 46749133536 scopus 로고    scopus 로고
    • Approximations of Nash equilibria
    • Gürkan, G., & Pang, J.-S. (2009). Approximations of Nash equilibria. Mathematical Programming, 117, 223-253.
    • (2009) Mathematical Programming , vol.117 , pp. 223-253
    • Gürkan, G.1    Pang, J.-S.2
  • 51
    • 0026417165 scopus 로고
    • Generalized Nash games and quasi-variational inequalities
    • Harker, P. T. (1991). Generalized Nash games and quasi-variational inequalities. European Journal of Operational Research, 54, 81-94.
    • (1991) European Journal of Operational Research , vol.54 , pp. 81-94
    • Harker, P.T.1
  • 52
    • 0028444427 scopus 로고
    • Pricing of track time in railroad operations: An internal market approach
    • Harker, P. T., & Hong, S. (1994). Pricing of track time in railroad operations: an internal market approach. Transportation Research, Part B Methodological, 28, 197-212.
    • (1994) Transportation Research, Part B Methodological , vol.28 , pp. 197-212
    • Harker, P.T.1    Hong, S.2
  • 53
    • 21944444492 scopus 로고    scopus 로고
    • Optimal charges on river effluent from lumped and distributed sources
    • Haurie, A., & Krawczyk, J.-B. (1997). Optimal charges on river effluent from lumped and distributed sources. Environmental Modeling and Assessment, 2, 93-106.
    • (1997) Environmental Modeling and Assessment , vol.2 , pp. 93-106
    • Haurie, A.1    Krawczyk, J.-B.2
  • 55
    • 34247497843 scopus 로고    scopus 로고
    • Nash-Cournot equilibria in electric power markets with piecewise linear demand functions and joint constraints
    • Hobbs, B., & Pang, J.-S. (2007). Nash-Cournot equilibria in electric power markets with piecewise linear demand functions and joint constraints. Operations Research, 55, 113-127.
    • (2007) Operations Research , vol.55 , pp. 113-127
    • Hobbs, B.1    Pang, J.-S.2
  • 56
    • 0002860654 scopus 로고
    • Game theory for economic analysis
    • Hotelling, H. (1929). Game theory for economic analysis. Economic Journal, 39, 41-47.
    • (1929) Economic Journal , vol.39 , pp. 41-47
    • Hotelling, H.1
  • 59
    • 76749124148 scopus 로고    scopus 로고
    • (Technical Report). Judge Business School at University of Cambridge, UK
    • Jiang, H. (2007). Network capacity management competition (Technical Report). Judge Business School at University of Cambridge, UK.
    • (2007) Network Capacity Management Competition
    • Jiang, H.1
  • 60
    • 0036431266 scopus 로고    scopus 로고
    • Continuity properties of Walras equilibrium points
    • Jofré, A., & Wets, R. J.-B. (2002). Continuity properties of Walras equilibrium points. Annals of Operation Research, 114, 229-243.
    • (2002) Annals of Operation Research , vol.114 , pp. 229-243
    • Jofré, A.1    Wets, R.J.-B.2
  • 64
    • 18144368863 scopus 로고    scopus 로고
    • Coupled constraint Nash equilibria in environmental games
    • Krawczyk, J.-B. (2005). Coupled constraint Nash equilibria in environmental games. Resource and Energy Economics, 27, 157-181.
    • (2005) Resource and Energy Economics , vol.27 , pp. 157-181
    • Krawczyk, J.-B.1
  • 65
    • 33847397017 scopus 로고    scopus 로고
    • Numerical solutions to coupled-constraint (or generalised Nash) equilibrium problems
    • Krawczyk, J.-B. (2007). Numerical solutions to coupled-constraint (or generalised Nash) equilibrium problems. Computational Management Science, 4, 183-204.
    • (2007) Computational Management Science , vol.4 , pp. 183-204
    • Krawczyk, J.-B.1
  • 66
    • 0034406492 scopus 로고    scopus 로고
    • Relaxation algorithms to find Nash equilibria with economic applications
    • Krawczyk, J.-B., & Uryasev, S. (2000). Relaxation algorithms to find Nash equilibria with economic applications. Environmental Modeling and Assessment, 5, 63-73.
    • (2000) Environmental Modeling and Assessment , vol.5 , pp. 63-73
    • Krawczyk, J.-B.1    Uryasev, S.2
  • 67
    • 0000528550 scopus 로고
    • Existence d'un équilibre général de concurrence imperfait: Une introduction
    • Laffont, J., & Laroque, G. (1976). Existence d'un équilibre général de concurrence imperfait: Une introduction. Econometrica, 44, 283-294.
    • (1976) Econometrica , vol.44 , pp. 283-294
    • Laffont, J.1    Laroque, G.2
  • 68
    • 34848892933 scopus 로고    scopus 로고
    • Illinois, USA, Argonne National Laboratory Preprint ANL/MCS-P1243-0405
    • Leyffer, S., & Munson, T. (2005). Solving multi-leader-follower games. Argonne National Laboratory Preprint ANL/MCS-P1243-0405, Illinois, USA.
    • (2005) Solving Multi-leader-follower Games
    • Leyffer, S.1    Munson, T.2
  • 69
    • 0031474433 scopus 로고    scopus 로고
    • A new approach to Tikhonov well-posedness for Nash equilibria
    • Margiocco, M., Patrone, F., & Pusilli Chicco, L. (1997). A new approach to Tikhonov well-posedness for Nash equilibria. Optimization, 40, 385-400.
    • (1997) Optimization , vol.40 , pp. 385-400
    • Margiocco, M.1    Patrone, F.2    Pusilli Chicco, L.3
  • 73
    • 44349188128 scopus 로고    scopus 로고
    • Variational stability of social Nash equilibria
    • Morgan, J., & Scalzo, V. (2008). Variational stability of social Nash equilibria. International Game Theory Review, 10, 17-24.
    • (2008) International Game Theory Review , vol.10 , pp. 17-24
    • Morgan, J.1    Scalzo, V.2
  • 78
    • 0001730497 scopus 로고
    • Non-cooperative games
    • Nash, J. F. (1951). Non-cooperative games. Annals of Mathematics, 54, 286-295.
    • (1951) Annals of Mathematics , vol.54 , pp. 286-295
    • Nash, J.F.1
  • 81
    • 0000099472 scopus 로고
    • Existence of Nash equilibrium in n person games without quasi-concavity
    • Nishimura, K., & Friedman, J. (1981). Existence of Nash equilibrium in n person games without quasi-concavity. International Economic Review, 22, 637-648.
    • (1981) International Economic Review , vol.22 , pp. 637-648
    • Nishimura, K.1    Friedman, J.2
  • 83
    • 20444468651 scopus 로고    scopus 로고
    • Manuscript, Department of Mathematical Sciences, The Johns Hopkins University
    • Pang, J.-S. (2002). Computing generalized Nash equilibria. Manuscript, Department of Mathematical Sciences, The Johns Hopkins University.
    • (2002) Computing Generalized Nash Equilibria
    • Pang, J.-S.1
  • 84
    • 0003317924 scopus 로고
    • Nonsmooth equations: Motivation and algorithms
    • Pang, J.-S., & Qi, L. (1993). Nonsmooth equations: motivation and algorithms. SIAM Journal on Optimization, 3, 443-465.
    • (1993) SIAM Journal on Optimization , vol.3 , pp. 443-465
    • Pang, J.-S.1    Qi, L.2
  • 86
    • 48849088211 scopus 로고    scopus 로고
    • Distributed power allocation with rate constraints in Gaussian parallel interference channels
    • Pang, J.-S., Scutari, G., Facchinei, F., & Wang, C. (2008). Distributed power allocation with rate constraints in Gaussian parallel interference channels. IEEE Transactions on Information Theory, 54, 3471-3489.
    • (2008) IEEE Transactions on Information Theory , vol.54 , pp. 3471-3489
    • Pang, J.-S.1    Scutari, G.2    Facchinei, F.3    Wang, C.4
  • 87
    • 76749122539 scopus 로고    scopus 로고
    • Design of cognitive radio systems under temperature-interference constraints: A variational inequality approach
    • (submitted)
    • Pang, J.-S., Scutari, G., Palomar, D. P., & Facchinei, F. (2009). Design of cognitive radio systems under temperature-interference constraints: a variational inequality approach. IEEE Transactions on Signal Processing (submitted).
    • (2009) Ieee Transactions On Signal Processing
    • Pang, J.-S.1    Scutari, G.2    Palomar, D.P.3    Facchinei, F.4
  • 89
    • 0000607524 scopus 로고
    • Convergence analysis of some algorithms for solving nonsmooth equations
    • Qi, L. (1993). Convergence analysis of some algorithms for solving nonsmooth equations. Mathematics of Operations Research, 18, 227-244.
    • (1993) Mathematics of Operations Research , vol.18 , pp. 227-244
    • Qi, L.1
  • 90
    • 0027543961 scopus 로고
    • A nonsmooth version of Newton's method
    • Qi, L., & Sun, J. (1993). A nonsmooth version of Newton's method. Mathematical Programming, 58, 353-367.
    • (1993) Mathematical Programming , vol.58 , pp. 353-367
    • Qi, L.1    Sun, J.2
  • 91
    • 0023995073 scopus 로고
    • Game theory approach for the integrated design of structures and controls
    • Rao, S. S., Venkayya, V. B., & Khot, N. S. (1988). Game theory approach for the integrated design of structures and controls. AIAA Journal, 26, 463-469.
    • (1988) AIAA Journal , vol.26 , pp. 463-469
    • Rao, S.S.1    Venkayya, V.B.2    Khot, N.S.3
  • 92
    • 0000246317 scopus 로고    scopus 로고
    • On the existence of pure and mixed strategy Nash equilibria in discontinuous games
    • Reny, P. J. (1999). On the existence of pure and mixed strategy Nash equilibria in discontinuous games. Econometrica, 67, 1026-1056.
    • (1999) Econometrica , vol.67 , pp. 1026-1056
    • Reny, P.J.1
  • 93
    • 20444505395 scopus 로고
    • Shadow prices for measures of effectiveness. I. Linear model
    • Robinson, S. M. (1993a). Shadow prices for measures of effectiveness. I. Linear model. Operations Research, 41, 518-535.
    • (1993) Operations Research , vol.41 , pp. 518-535
    • Robinson, S.M.1
  • 94
    • 18144396969 scopus 로고
    • Shadow prices for measures of effectiveness. II. General model
    • Robinson, S. M. (1993b). Shadow prices for measures of effectiveness. II. General model. Operations Research, 41, 536-548.
    • (1993) Operations Research , vol.41 , pp. 536-548
    • Robinson, S.M.1
  • 96
    • 0018922522 scopus 로고
    • Existence and uniqueness of equilibrium points for concave n-person games
    • Rosen, J. B. (1965). Existence and uniqueness of equilibrium points for concave n-person games. Econometrica, 33, 520-534.
    • (1965) Econometrica , vol.33 , pp. 520-534
    • Rosen, J.B.1
  • 97
    • 85003406325 scopus 로고
    • Structural synthesis-its genesis and development
    • Schmit, L. A. (1981). Structural synthesis-its genesis and development. AIAA Journal, 19, 1249-1263.
    • (1981) AIAA Journal , vol.19 , pp. 1249-1263
    • Schmit, L.A.1
  • 98
    • 0342716764 scopus 로고
    • Structural design using equilibrium programming formulations
    • 110175
    • Scotti, S. J. (1995). Structural design using equilibrium programming formulations. NASA Technical Memorandum 110175.
    • (1995) Nasa Technical Memorandum
    • Scotti, S.J.1
  • 99
    • 85032752025 scopus 로고    scopus 로고
    • Flexible design of cognitive radio wireless systems: From game theory to variational inequality theory
    • Scutari, G., Palomar, D. P., Pang, J.-S., & Facchinei, F. (2009). Flexible design of cognitive radio wireless systems: from game theory to variational inequality theory. IEEE Signal Processing Magazine, 26, 107-123.
    • (2009) IEEE Signal Processing Magazine , vol.26 , pp. 107-123
    • Scutari, G.1    Palomar, D.P.2    Pang, J.-S.3    Facchinei, F.4
  • 101
    • 33847275138 scopus 로고    scopus 로고
    • An equilibrium model for urban transit assignment based on game theory
    • Sun, L.-J., & Gao, Z.-Y. (2007). An equilibrium model for urban transit assignment based on game theory. European Journal of Operational Research, 181, 305-314.
    • (2007) European Journal of Operational Research , vol.181 , pp. 305-314
    • Sun, L.-J.1    Gao, Z.-Y.2
  • 102
    • 0001547275 scopus 로고
    • Transfer continuities, generalizations of the Weierstrass and maximum theorems: A full characterization
    • Tian, G., & Zhou, J. (1995). Transfer continuities, generalizations of the Weierstrass and maximum theorems: a full characterization. Journal of Mathematical Economics, 24, 281-303.
    • (1995) Journal of Mathematical Economics , vol.24 , pp. 281-303
    • Tian, G.1    Zhou, J.2
  • 104
    • 0028447256 scopus 로고
    • On relaxation algorithms in computation of noncooperative equilibria
    • Uryasev, S., & Rubinstein, R. Y. (1994). On relaxation algorithms in computation of noncooperative equilibria. IEEE Transactions on Automatic Control, 39, 1263-1267.
    • (1994) IEEE Transactions on Automatic Control , vol.39 , pp. 1263-1267
    • Uryasev, S.1    Rubinstein, R.Y.2
  • 107
    • 44949269402 scopus 로고
    • Nash equilibrium with strategic complementarities
    • Vives, X. (1994). Nash equilibrium with strategic complementarities. Journal of Mathematical Economics, 19, 305-321.
    • (1994) Journal of Mathematical Economics , vol.19 , pp. 305-321
    • Vives, X.1
  • 108
    • 54249155092 scopus 로고    scopus 로고
    • 1 optimization reformulations of the generalized Nash equilibrium problem
    • 1 optimization reformulations of the generalized Nash equilibrium problem. Optimization Methods & Software, 23, 953-973.
    • (2008) Optimization Methods & Software , vol.23 , pp. 953-973
    • von Heusinger, A.1    Kanzow, C.2
  • 109
    • 67651018689 scopus 로고    scopus 로고
    • Optimization reformulations of the generalized Nash equilibrium problem using Nikaido-Isoda-type functions
    • von Heusinger, A., & Kanzow, C. (2009a). Optimization reformulations of the generalized Nash equilibrium problem using Nikaido-Isoda-type functions. Computational Optimization and Applications, 43, 353-377.
    • (2009) Computational Optimization and Applications , vol.43 , pp. 353-377
    • von Heusinger, A.1    Kanzow, C.2
  • 110
    • 70350287828 scopus 로고    scopus 로고
    • Relaxation methods for generalized Nash equilibrium problems with inexact line search
    • von Heusinger, A., & Kanzow, C. (2009b). Relaxation methods for generalized Nash equilibrium problems with inexact line search. Journal of Optimization Theory and Applications, 143, 159-183.
    • (2009) Journal of Optimization Theory and Applications , vol.143 , pp. 159-183
    • von Heusinger, A.1    Kanzow, C.2
  • 112
    • 21244466146 scopus 로고
    • Zur Theorie der Gesellschaftsspiele
    • von Neumann, J. (1928). Zur Theorie der Gesellschaftsspiele. Mathematische Annalen, 100, 295-320.
    • (1928) Mathematische Annalen , vol.100 , pp. 295-320
    • von Neumann, J.1
  • 115
    • 20044372188 scopus 로고    scopus 로고
    • Spatial oligopolistic electricity models with Cournot generators and regulated transmission prices
    • Wei, J.-Y., & Smeers, Y. (1999). Spatial oligopolistic electricity models with Cournot generators and regulated transmission prices. Operations Research, 47, 102-112.
    • (1999) Operations Research , vol.47 , pp. 102-112
    • Wei, J.-Y.1    Smeers, Y.2
  • 116
    • 11244349968 scopus 로고    scopus 로고
    • The generalized Nash equilibrium model for oligopolistic transit market with elastic demand
    • Zhou, J., Lam, W. H. K., & Heydecker, B. G. (2005). The generalized Nash equilibrium model for oligopolistic transit market with elastic demand. Transportation Research, Part B Methodological, 39, 519-544.
    • (2005) Transportation Research, Part B Methodological , vol.39 , pp. 519-544
    • Zhou, J.1    Lam, W.H.K.2    Heydecker, B.G.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.