zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Analysis of the dynamics of Cournot team-game with heterogeneous players. (English) Zbl 1187.91077
Summary: We study a dynamical system of a two-team Cournot game played by a team consisting of two firms with bounded rationality and a team consisting of one firm with naive expectation. The equilibrium solutions and the conditions of their locally asymptotic stability are studied. It is demonstrated that, as some parameters in the model are varied, the stability of the equilibrium will get lost and many such complex behaviors as the period bifurcation, chaotic phenomenon, periodic windows, strange attractor and unpredictable trajectories will occur. The great influence of the model parameters on the speed of convergence to the equilibrium is also shown with numerical analysis.
MSC:
91B26Market models (auctions, bargaining, bidding, selling, etc.)
37N40Dynamical systems in optimization and economics
91A12Cooperative games
91A10Noncooperative games
References:
[1]Y.Liu, Nash based strategies for the control of extended complex systems, Ph.D. Thesis, Pittsburg University, 2003.
[2]Ahmed, E.; Hegazi, A. S.: On dynamical multi-team and signaling games, Applied mathematics and computation 172, 524-530 (2006) · Zbl 1131.91013 · doi:10.1016/j.amc.2005.02.030
[3]Ahmeda, E.; Hegazi, A. S.; Elettreby, M. F.; Askar, S. S.: On multi-team games, Physica A 369, 809-816 (2006)
[4]Elettreby, M. F.; Hassan, S. Z.: Dynamical multi-team cournot game, Chaos solitons & fractals 27, 666-672 (2006)
[5]Asker, S. S.: On dynamical multi-team cournot game in exploitation of a renewable resource, Chaos solitons & fractals 32, 264-268 (2007) · Zbl 1133.91510 · doi:10.1016/j.chaos.2005.10.110
[6]Agiza, H. N.; Elsadany, A. A.: Chaotic dynamics in nonlinear duopoly game with heterogeneous players, Applied mathematics and computation 149, 843-860 (2004) · Zbl 1064.91027 · doi:10.1016/S0096-3003(03)00190-5
[7]Agiza, H. N.; Elsadany, A. A.: Nonlinear dynamics in the cournot duopoly game with heterogeneous players, Physica A 320, 512-524 (2003) · Zbl 1010.91006 · doi:10.1016/S0378-4371(02)01648-5
[8]Zhang, Jixiang; Da, Qingli; Wang, Yanhua: Analysis of nonlinear duopoly game with heterogeneous players, Economic modelling 24, 138-148 (2007)
[9]Du, Jianguo; Huang, Tingwen: New results on stable region of Nash equilibrium of output game model, Applied mathematics and computation 192, 12-19 (2007) · Zbl 1193.91036 · doi:10.1016/j.amc.2007.02.155
[10]A. Cournot, Researches into the Principles of the Theory of Wealth, Irwin Paper Back Classics in Economics, Hachette, Paris, 1963 (Engl. Trans. Chapter VII).
[11]Agiza, H. N.; Hegazi, A. S.; Elsadany, A. A.: Complex dynamics and synchronization of a duopoly game with bounded rationality, Mathematics and computers in simulation 58, 133-146 (2002) · Zbl 1002.91010 · doi:10.1016/S0378-4754(01)00347-0
[12]Agiza, H. N.; Hegazi, A. S.; Elsadany, A. A.: The dynamics of bowley’s model with bounded rationality, Chaos solitons & fractals 12, 1705-1717 (2001) · Zbl 1036.91004 · doi:10.1016/S0960-0779(00)00021-7