Nash-type equilibria on Riemannian manifolds: a variational approach (Q2445881)

In the present paper the author considers the Nash-type equilibrium problems, where the strategy sets \(K_i\), \(i=1,\dots,n\) are geodesic convex subsets of certain finite-dimensional Riemannian manifolds \((M_i,g_i)\), i.e., for any two points of \(K_i\) there exists a unique geodesic in \((M_i,g_i)\) connecting them which belongs entirely to \(K_i.\) The three Nash-type equilibria (Nash, Nash-Clarce, Nash-Stampacchia) are introduced and compared. The Nash-Stampacchia equilibrium on Hadamard manifolds is characterized. Existence and stability theorems of equilibrium points are proved. Some examples are discussed.