English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We study the core of normal form games with a continuum of players andwithout side payments. We consider the weak-core concept, which is anapproximation of the core, introduced by Weber, Shapley and Shubik. For payoffsdepending on the players' strategy profile, we prove that the weak-core isnonempty. The existence result establishes a weak-core element as a limit ofelements in weak-cores of appropriate finite games. We establish by examplesthat our regularity hypotheses are relevant in the continuum case and theweak-core can be strictly larger than the Aumann's $\alpha$-core. For gameswhere payoffs depend on the distribution of players' strategy profile, we provethat analogous regularity conditions ensuring the existence of pure strategyNash equilibria are irrelevant for the non-vacuity of the weak-core.

On the core of normal form games with a continuum of players : a correction