Multi-variational principle, minimax theorem, and applications (Q1306849)

The main result of this paper shows that, given an \(n\)-person (noncooperative) game \(G\) (not necessarily having Nash equilibrium) with compact sets of individual strategies and given an \(\varepsilon\)-equilibrium \(a\) of \(G\) and a number \(\mu>0\), one can find a ``\(\varepsilon\)--modification'' \(\overline G\) of \(G\) such that \(\overline G\) has a Nash equilibrium whose distance to \(a\) is less than \(\mu\). This leads to interesting stability properties of equilibria for large classes of games.