A sufficient and necessary condition is presented for the existence of a Nash equilibrium in n-person noncooperative games in normal form where strategy sets are not necessarily convex. Under the convexity condition, we show that this new sufficient and necessary condition is a particular case...

We consider a single machine scheduling problem to minimize the weighted completion time variance. This problem is known to be NP-hard in the strong sense. We propose a lower bound based on splitting of jobs and the Viswanathkumar and Srinivasan procedure and a heuristic. The test on more than...

This paper investigates the existence of pure strategy, dominant-strategy, and mixed strategy Nash equilibria in discontinuous and nonconvex games. We introduce a new notion of very weak continuity, called weak transfer continuity, which holds in a large class of discontinuous economic games and...

This paper investigates the existence of strong Nashequilibria (SNE) in continuous and convex games. We show that the concavity and an additional condition on payoff functions, together with the compactness of strategy space, permit the existence of strong Nash equilibria. These conditions are...

This paper characterizes the existence of equilibria in minimax inequalities without assuming any form of quasi-concavity of functions and convexity or compactness of choice sets. A new condition, called “local dominatedness property”, is shown to be necessary and further, under some mild...