-
Previous Article
A substitute for the classical Neumann–Morgenstern characteristic function in cooperative differential games
- JDG Home
- This Issue
- Next Article
On the uniqueness of Nash equilibrium in strategic-form games
Faculty of Economics, Chuo University, 742-1 Higashinakano, Hachioji, Tokyo 192-0393, Japan |
We consider a sufficient condition for the uniqueness of a Nash equilibrium in strategic-form games: for any two distinct strategy profiles, there is a player who can obtain a higher payoff by unilaterally changing the strategy from one strategy profile to the other strategy profile. An example of a game that satisfies this condition is the prisoner's dilemma. Viewed as a solution concept, the Nash equilibrium satisfying the condition is stronger than strict Nash Equilibrium and weaker than strict dominant strategy equilibrium.
References:
[1] |
H. Carlsson and E. van Damme, Equilibrium selection in stag hunt games, Frontiers of Game Theory, MIT Press, Cambridge, MA, (1993), 237–253. |
[2] |
L. A. Chenault,
On the uniqueness of Nash equilibria, Economics Letters, 20 (1986), 203-205.
doi: 10.1016/0165-1765(86)90023-6. |
[3] |
A. A. Cournot, Researches into the Mathematical Principles of the Theory of Wealth, English edition of Recherches sur les Principes Mathématiques de la Théorie des Richesses, Kelley, New York, 1971. Google Scholar |
[4] |
D. Fudenberg and J. Tirole, Game Theory, The MIT Press, Cambridge, MA, 1991.
![]() |
[5] |
J. C. Harsanyi,
Oddness of the number of equilibrium points: A new proof, International Journal of Game Theory, 2 (1973), 235-250.
doi: 10.1007/BF01737572. |
[6] |
H. Hotelling,
Stability in competition, Economic Journal, 39 (1929), 41-57.
doi: 10.1007/978-1-4613-8905-7_4. |
[7] |
R. D. Luce and H. Raiffa, Games and Decisions: Introduction and Critical Survey, John Wiley & Sons, Inc., New York, N. Y., 1957. |
[8] | A. Mas-Colell, M. D. Whinston and J. R. Green, Microeconomic Theory, Oxford University Press, New York, 1995. Google Scholar |
[9] |
M. Maschler, E. Solan and S. Zamir, Game Theory, Cambridge University Press, Cambridge, 2013.
doi: 10.1017/CBO9780511794216.![]() ![]() |
[10] |
A. Matsumoto and F. Szidarovszky, Game Theory and Its Applications, Springer, Tokyo, 2016.
doi: 10.1007/978-4-431-54786-0. |
[11] |
J. F. Jr Nash,
Equilibrium points in n-person games, Proceedings of the National Academy of Sciences of the United States of America, 36 (1950), 48-49.
doi: 10.1073/pnas.36.1.48. |
[12] |
J. Nash, Non-cooperative games, Annals of Mathematics (2), 54 (1951), 286-295.
doi: 10.2307/1969529. |
[13] |
J. B. Rosen,
Existence and uniqueness of equilibrium points for concave $n$-person games, Econometrica, 33 (1965), 520-534.
doi: 10.2307/1911749. |
[14] | J. Sutton, Technology and Market Structure: Theory and History, The MIT Press, Cambridge, MA, 1998. Google Scholar |
[15] |
A. Takayama, Mathematical Economics, Second edition, Cambridge University Press, Cambridge, 1985.
![]() |
[16] |
H. Uzawa, Walras' existence theorem and Brouwer's fixed-point theorem, Economic Studies Quarterly, 13 (1962), 59-62. Google Scholar |
[17] |
E. van Damme, Stability and Perfection of Nash Equilibria, Second edition, Springer-Verlag, Berlin, 1991.
doi: 10.1007/978-3-642-58242-4. |
[18] |
A. van den Nouweland, Rock-paper-scissors: A new and elegant proof, Economics Bulletin, 3 (2007), 1-6. Google Scholar |
[19] |
A. Wald, Über einige Gleichungssysteme der mathematischen Ökonomie, Econometrica, 19 (1951), 368-403. Google Scholar |
show all references
References:
[1] |
H. Carlsson and E. van Damme, Equilibrium selection in stag hunt games, Frontiers of Game Theory, MIT Press, Cambridge, MA, (1993), 237–253. |
[2] |
L. A. Chenault,
On the uniqueness of Nash equilibria, Economics Letters, 20 (1986), 203-205.
doi: 10.1016/0165-1765(86)90023-6. |
[3] |
A. A. Cournot, Researches into the Mathematical Principles of the Theory of Wealth, English edition of Recherches sur les Principes Mathématiques de la Théorie des Richesses, Kelley, New York, 1971. Google Scholar |
[4] |
D. Fudenberg and J. Tirole, Game Theory, The MIT Press, Cambridge, MA, 1991.
![]() |
[5] |
J. C. Harsanyi,
Oddness of the number of equilibrium points: A new proof, International Journal of Game Theory, 2 (1973), 235-250.
doi: 10.1007/BF01737572. |
[6] |
H. Hotelling,
Stability in competition, Economic Journal, 39 (1929), 41-57.
doi: 10.1007/978-1-4613-8905-7_4. |
[7] |
R. D. Luce and H. Raiffa, Games and Decisions: Introduction and Critical Survey, John Wiley & Sons, Inc., New York, N. Y., 1957. |
[8] | A. Mas-Colell, M. D. Whinston and J. R. Green, Microeconomic Theory, Oxford University Press, New York, 1995. Google Scholar |
[9] |
M. Maschler, E. Solan and S. Zamir, Game Theory, Cambridge University Press, Cambridge, 2013.
doi: 10.1017/CBO9780511794216.![]() ![]() |
[10] |
A. Matsumoto and F. Szidarovszky, Game Theory and Its Applications, Springer, Tokyo, 2016.
doi: 10.1007/978-4-431-54786-0. |
[11] |
J. F. Jr Nash,
Equilibrium points in n-person games, Proceedings of the National Academy of Sciences of the United States of America, 36 (1950), 48-49.
doi: 10.1073/pnas.36.1.48. |
[12] |
J. Nash, Non-cooperative games, Annals of Mathematics (2), 54 (1951), 286-295.
doi: 10.2307/1969529. |
[13] |
J. B. Rosen,
Existence and uniqueness of equilibrium points for concave $n$-person games, Econometrica, 33 (1965), 520-534.
doi: 10.2307/1911749. |
[14] | J. Sutton, Technology and Market Structure: Theory and History, The MIT Press, Cambridge, MA, 1998. Google Scholar |
[15] |
A. Takayama, Mathematical Economics, Second edition, Cambridge University Press, Cambridge, 1985.
![]() |
[16] |
H. Uzawa, Walras' existence theorem and Brouwer's fixed-point theorem, Economic Studies Quarterly, 13 (1962), 59-62. Google Scholar |
[17] |
E. van Damme, Stability and Perfection of Nash Equilibria, Second edition, Springer-Verlag, Berlin, 1991.
doi: 10.1007/978-3-642-58242-4. |
[18] |
A. van den Nouweland, Rock-paper-scissors: A new and elegant proof, Economics Bulletin, 3 (2007), 1-6. Google Scholar |
[19] |
A. Wald, Über einige Gleichungssysteme der mathematischen Ökonomie, Econometrica, 19 (1951), 368-403. Google Scholar |
[1] |
Ru Li, Guolin Yu. Strict efficiency of a multi-product supply-demand network equilibrium model. Journal of Industrial & Management Optimization, 2021, 17 (4) : 2203-2215. doi: 10.3934/jimo.2020065 |
[2] |
Enkhbat Rentsen, Battur Gompil. Generalized Nash equilibrium problem based on malfatti's problem. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 209-220. doi: 10.3934/naco.2020022 |
[3] |
Xue-Ping Luo, Yi-Bin Xiao, Wei Li. Strict feasibility of variational inclusion problems in reflexive Banach spaces. Journal of Industrial & Management Optimization, 2020, 16 (5) : 2495-2502. doi: 10.3934/jimo.2019065 |
[4] |
Tôn Việt Tạ. Strict solutions to stochastic semilinear evolution equations in M-type 2 Banach spaces. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021050 |
[5] |
Liangliang Ma. Stability of hydrostatic equilibrium to the 2D fractional Boussinesq equations. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021068 |
[6] |
Suzete Maria Afonso, Vanessa Ramos, Jaqueline Siqueira. Equilibrium states for non-uniformly hyperbolic systems: Statistical properties and analyticity. Discrete & Continuous Dynamical Systems, 2021 doi: 10.3934/dcds.2021045 |
[7] |
Renhao Cui. Asymptotic profiles of the endemic equilibrium of a reaction-diffusion-advection SIS epidemic model with saturated incidence rate. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 2997-3022. doi: 10.3934/dcdsb.2020217 |
[8] |
Haodong Chen, Hongchun Sun, Yiju Wang. A complementarity model and algorithm for direct multi-commodity flow supply chain network equilibrium problem. Journal of Industrial & Management Optimization, 2021, 17 (4) : 2217-2242. doi: 10.3934/jimo.2020066 |
[9] |
Jian Yang, Bendong Lou. Traveling wave solutions of competitive models with free boundaries. Discrete & Continuous Dynamical Systems - B, 2014, 19 (3) : 817-826. doi: 10.3934/dcdsb.2014.19.817 |
[10] |
Feng Wei, Hong Chen. Independent sales or bundling? Decisions under different market-dominant powers. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1593-1612. doi: 10.3934/jimo.2020036 |
[11] |
Mats Gyllenberg, Jifa Jiang, Lei Niu, Ping Yan. On the classification of generalized competitive Atkinson-Allen models via the dynamics on the boundary of the carrying simplex. Discrete & Continuous Dynamical Systems, 2018, 38 (2) : 615-650. doi: 10.3934/dcds.2018027 |
[12] |
Xiaoyi Zhou, Tong Ye, Tony T. Lee. Designing and analysis of a Wi-Fi data offloading strategy catering for the preference of mobile users. Journal of Industrial & Management Optimization, 2021 doi: 10.3934/jimo.2021038 |
[13] |
Kai Kang, Taotao Lu, Jing Zhang. Financing strategy selection and coordination considering risk aversion in a capital-constrained supply chain. Journal of Industrial & Management Optimization, 2021 doi: 10.3934/jimo.2021042 |
[14] |
Wei Wang, Yang Shen, Linyi Qian, Zhixin Yang. Hedging strategy for unit-linked life insurance contracts with self-exciting jump clustering. Journal of Industrial & Management Optimization, 2021 doi: 10.3934/jimo.2021072 |
[15] |
Skyler Simmons. Stability of Broucke's isosceles orbit. Discrete & Continuous Dynamical Systems, 2021, 41 (8) : 3759-3779. doi: 10.3934/dcds.2021015 |
[16] |
Z. Reichstein and B. Youssin. Parusinski's "Key Lemma" via algebraic geometry. Electronic Research Announcements, 1999, 5: 136-145. |
[17] |
Ugo Bessi. Another point of view on Kusuoka's measure. Discrete & Continuous Dynamical Systems, 2021, 41 (7) : 3241-3271. doi: 10.3934/dcds.2020404 |
[18] |
Mikhail Dokuchaev, Guanglu Zhou, Song Wang. A modification of Galerkin's method for option pricing. Journal of Industrial & Management Optimization, 2021 doi: 10.3934/jimo.2021077 |
[19] |
Jun Tu, Zijiao Sun, Min Huang. Supply chain coordination considering e-tailer's promotion effort and logistics provider's service effort. Journal of Industrial & Management Optimization, 2021 doi: 10.3934/jimo.2021062 |
[20] |
Ronald E. Mickens. Positivity preserving discrete model for the coupled ODE's modeling glycolysis. Conference Publications, 2003, 2003 (Special) : 623-629. doi: 10.3934/proc.2003.2003.623 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]