A Generalized Ky Fan Minimax Inequality on Finite-Dimensional Spaces

An existence result for a generalized inequality over a possible unbounded domain in a finite-dimensional space is established. The proof technique allows to avoid any monotonicity assumption. We adapt a weak coercivity condition introduced in Castellani and Giuli (J Glob Optim 75:163–176, 2019) for a generalized game which extends an older one proposed by Konnov and Dyabilkin (J Glob Optim 49:575–577, 2011) for equilibrium problems. Our main result encompasses and generalizes several existence results for equilibrium, quasiequilibrium and fixed-point problems.

Non-emptiness of the alpha-core: sufficient and necessary conditions

We give sufficient and necessary conditions for the non-emptiness of the alpha-core in the setting of strategic games with non-ordered and discontinuous preferences. In order to prove our results, we can avoid the use of Scarf’s Theorem for NTU-games, by suitably appealing to the Ky Fan minimax inequality. Examples clarify our conditions and allow the comparison of our results with the previous ones.