BNN动力学下一类连续博弈均衡解的存在性及稳定性

THE EXISTENCE AND STABILITY OF THE EQUILIBRIUM POINT FOR A CLASS OF CONTINUOUS GAMES IN BNN DYNAMICS

本文研究了一类连续博弈解的存在性及稳定性.利用BNN动力学理论和方法,将演化博弈论中的几个经典例子:鹰–鸽博弈、协调博弈和猜硬币博弈转化为连续型支付函数的连续博弈后,获得了鹰–鸽连续博弈的Nash平衡点是演化稳定和连续稳定的,推广了文献[8]中关于演化博弈Nash平衡点及稳定性结果.

In this paper, we apply BNN dynamics theory of existence and stability of the equilibrium point to a class of continuous games. We turn some classic example of Hawk-Dove game, matching pennies game and coordination game mentioned in evolutionary game theory to a type of continuous games which have continuous payoff function, and study the existence and stability of the equilibrium point. This research demonstrates that under the BNN dynamics the Nash equilibrium point of Hawk-Dove continuous games is an evolutionarily stable and continuously stable strategy, which extends the results in [8].