We consider games with incomplete information a la Harsanyi, where the payoff of a player depends on an unknown state of nature as well as on the profile of chosen actions. As opposed to the standard model, the players in the game are not necessarily expected utility maximizers. Rather, their preferences over state-contingent utility vectors are represented by arbitrary functionals. Our first contribution is to provide simple and applicable definitions of both ex ante and interim equilibria in this generalized setting. Second, we characterize equilibrium existence in terms of the preferences of the participating players. It turns out that, given some standard properties of the functionals, equilibrium exists in every game if and only if all players are averse to uncertainty. Finally, for a subclass of preferences representing functionals, we show that there exists a symmetric equilibrium in every symmetric game if and only if all players share preferences.