We introduce a notion of upper semicontinuity, weak upper semicontinuity, adn show that it, together with a weak form of payoff security, is enough to guarantee the existence of Nash equilibria in compact, quasiconcave normal form games.

We present a puri¯cation result for incomplete information games with a large ¯nite number of players that allows for compact metric spaces of actions and types. This result is then used to generalize the puri¯cation theorems of Schmeidler (1973), Rashid (1983) and Kalai (2004). Our proofs...

We present a purification result for incomplete information games with a large but finite number of players that allows compact metric spaces for both actions and types. We then compare our framework and findings to the early purification theorems of Rashid (1983. Equilibrium points of...

Balder's (2002) model of games with a measure space of players is integrated with the line of research on finite-player games with discontinuous payoff functions which follows Reny (1999). Specifically, we extend the notion of continuous security, introduced by McLennan, Monteiro and Tourky...

The book aims at describing the recent developments in the existence and stability of Nash equilibrium. The two topics are central to game theory and economics and have been extensively researched. Recent results on existence and stability of Nash equilibrium are scattered and the relationship...

Balder's [6] model of games with a measure space of players is integrated with the line of research on finite-player games with discontinuous payoff functions which follows Reny [47]. Specifically, we extend the notion of continuous security, introduced by McLennan, Monteiro & Tourky [38] and...

We present a result on approximate ex-post stability of Bayes–Nash equilibria in semi-anonymous Bayesian games with a large finite number of players. The result allows playersʼ action and type spaces to be general compact metric spaces, thus extending a result by Kalai (2004).