We introduce the concept of disjoint payoff matching which can be used to show that the mixed extension of a compact game is payoff secure. By putting minor structure on the discontinuities, we need only check payoffs at each strategy rather than in neighborhoods of each strategy profile,...

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...