The computability of Nash equilibrium points of finite games is examined. When payoffs are computable there always exists an equilibrium in which all players use computable strategies. However, there is a computable sequence of games for which the equilibrium points do not constitute a computable sequence. For this reason, there can be no algorithm that, given arbitrary payoffs, computes a Nash...

In this paper, we study bifurcations of equilibrium points and periodic solutions observed in a resistively coupled oscillator with voltage ports. We classify equilibrium points and periodic solutions into four and eight di erent types, respectively, according to their symmetrical properties. By calculating D-type of branching sets (symmetry-breaking bifurcations) of equilibrium points and peri...

in the paper‎, ‎some new existence theorems of maximal elements for‎ ‎$mathscr{f}_{c,theta}$-mappings and $mathscr{f}_{c,theta}$-majorized mappings are established‎. ‎as applications, ‎some new existence theorems of equilibrium points for‎ ‎one-person games‎, ‎qualitative games and generalized games are obtained‎. ‎our results unify and generalize most known results‎ ‎in recent literature‎.

‎Financial market modeling and prediction is a difficult problem and drastic changes of the price causes nonlinear dynamic that makes the price prediction one of the most challenging tasks for economists‎. ‎Since markets always have been interesting for traders‎, ‎many traders with various beliefs are highly active in a market‎. ‎The competition among two agents of traders‎, ‎namely trend follo...

In this paper, we investigate the exact existence and dynamical behaviors of multiple equilibrium points for delayed competitive neural networks (DCNNs) with a class of nondecreasing piecewise linear activation functions with 2rðr≥1Þ corner points. It is shown that under some conditions, the N-neuron DCNNs can have and only have ð2r þ 1Þ equilibrium points, ðr þ 1Þ of which are locally exponent...

A mathematical model describing the dynamics  of a  delayed  stage structure prey - predator  system  with  prey  refuge  is  considered.  The  existence,  uniqueness  and bounded- ness  of  the  solution  are  discussed.    All  the  feasibl e  equilibrium  points  are determined.  The   stability  analysis  of  them  are  investigated.  By  employ ing  the time delay as the bifurcation parame...