Scholarlink

<p>In the presented paper, we discuss the relation between KKM, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\text {L}^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mtext>L</mtext> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>, and Sperner principles in abstract convex spaces. Next, we introduce a new class of spaces, called <i>S</i>-convex, whose elements satisfy the listed properties. This allows us to extend the Nash equilibrium theorem. Moreover, we give an example illustrating that the generalization of Nash’s theorem given by Park (Int. J. Math. Stat. 6(S10), 77–88, 2010, Nonlinear Anal. 73, 1028–1042, 2010) is incorrect. Finally, we provide detailed proof of the existence of equilibrium in the improved model.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

KKM, \(\text {L}^*\), Sperner principles and Nash equilibrium

  • 期刊论文

  • 发表日期：

    2026年2月20日

查看全文
  • Przemysław Tkacz

摘要

In the presented paper, we discuss the relation between KKM, \(\text {L}^*\) L ∗ , and Sperner principles in abstract convex spaces. Next, we introduce a new class of spaces, called S-convex, whose elements satisfy the listed properties. This allows us to extend the Nash equilibrium theorem. Moreover, we give an example illustrating that the generalization of Nash’s theorem given by Park (Int. J. Math. Stat. 6(S10), 77–88, 2010, Nonlinear Anal. 73, 1028–1042, 2010) is incorrect. Finally, we provide detailed proof of the existence of equilibrium in the improved model.