Equilibria with discontinuous preferences: New fixed point theorems

We prove new equilibrium existence results for games and economies with discontinuous and non-ordered preferences. To do so, we introduce the notion of “continuous inclusion property”, and prove new fixed point theorems which extend and generalize the results of Fan [17], Glicksberg [20], Browder [7], and Gale and Mas-Colell [19]. Our results also extend the previous work of Yannelis [47] and Wu and Shen [46].