scholarly journals REEXAMINATION OF THE PERFECTNESS CONCEPT FOR EQUILIBRIUM POINTS IN EXTENSIVE GAMES

2020 ◽  
pp. 317-354
Author(s):  
R. Selten
Keyword(s):  
Equilibrium Points ◽  
Extensive Games

THE CENTIPEDE OF ROSENTHAL

2007 ◽  
Vol 09 (02) ◽  
pp. 341-345
Author(s):  
EZIO MARCHI
Keyword(s):  
Equilibrium Points ◽  
Short Note ◽  
Subgame Perfect Equilibrium ◽  
Perfect Information ◽  
Private Communication ◽  
Perfect Equilibrium ◽  
Payoff Functions ◽  
The Relationship ◽  
Extensive Games

In this short note we extend the very well known Centipede game of Rosenthal to the same extensive games with perfect information. The only difference that here the Centipede games have instead of numbers as payoff functions, they have variables. We introduce and study the relationship between the structure of subgame perfect equilibrium points (see Osborne (1994), Binmore (1994)) and the friendly equilibrium points due to Marchi (2004a) and (2004b). We solve an Asheim's conjecture (private communication).

Mathematical views of the fractional Chua's electrical circuit described by the Caputo-Liouville derivative

2021 ◽  
Vol 67 (1 Jan-Feb) ◽  
pp. 91
Author(s):  
N. Sene
Keyword(s):  
Caputo Derivative ◽  
Local Stability ◽  
Numerical Scheme ◽  
Equilibrium Points ◽  
Electrical Circuit ◽  
Maximal Lyapunov Exponent ◽  
Electrical Circuits ◽  
Adaptive Controls ◽  
Liouville Derivative

This paper revisits Chua's electrical circuit in the context of the Caputo derivative. We introduce the Caputo derivative into the modeling of the electrical circuit. The solutions of the new model are proposed using numerical discretizations. The discretizations use the numerical scheme of the Riemann-Liouville integral. We have determined the equilibrium points and study their local stability. The existence of the chaotic behaviors with the used fractional-order has been characterized by the determination of the maximal Lyapunov exponent value. The variations of the parameters of the model into the Chua's electrical circuit have been quantified using the bifurcation concept. We also propose adaptive controls under which the master and the slave fractional Chua's electrical circuits go in the same way. The graphical representations have supported all the main results of the paper.

Dynamics of a delayed competitive system affected by toxic substances with imprecise biological parameters

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5271-5293
Author(s):  
A.K. Pal ◽  
P. Dolai ◽  
G.P. Samanta
Keyword(s):  
Equilibrium Points ◽  
Stable Limit Cycle ◽  
Limit Cycle Oscillation ◽  
Toxic Substances ◽  
Stable Limit ◽  
Biological Parameters ◽  
Delay Model ◽  
Competitive System ◽  
Interval Numbers ◽  
Cycle Oscillation

In this paper we have studied the dynamical behaviours of a delayed two-species competitive system affected by toxicant with imprecise biological parameters. We have proposed a method to handle these imprecise parameters by using parametric form of interval numbers. We have discussed the existence of various equilibrium points and stability of the system at these equilibrium points. In case of toxic stimulatory system, the delay model exhibits a stable limit cycle oscillation. Computer simulations are carried out to illustrate our analytical findings.

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