论文标题
纳什平衡的连续时间近似
Continuous time approximation of Nash equilibria
论文作者
论文摘要
我们考虑近似于$ n $ functions $ f_1，\ dots，f_n $ of $ n $变量的nash平衡的问题。特别是，我们推断出$$ $ \ dot u_j（t）= - \ nabla_ {x_j} f_j（u（t））$$ $（j = 1，\ dots，n）$的条件。 $ f_1，\ dots，f_n $。为此，我们将调用最大单调操作员的理论。我们还将确定这些想法在游戏理论中的应用，并展示如何在功能空间中某些游戏理论问题中近似平衡。
We consider the problem of approximating Nash equilibria of $N$ functions $f_1,\dots, f_N$ of $N$ variables. In particular, we deduce conditions under which systems of the form $$ \dot u_j(t)=-\nabla_{x_j}f_j(u(t)) $$ $(j=1,\dots, N)$ are well posed and in which the large time limits of their solutions $u(t)=(u_1(t),\dots, u_N(t))$ are Nash equilibria for $f_1,\dots, f_N$. To this end, we will invoke the theory of maximal monotone operators. We will also identify an application of these ideas in game theory and show how to approximate equilibria in some game theoretic problems in function spaces.
