We show that the Shapley–Shubik power index on the domain of simple (voting) games can be uniquely characterized without the efficiency axiom. In our axiomatization, the efficiency is replaced by the following weaker requirement that we term the gain-loss axiom: any gain in power by a player...

We show that when firms have incomplete information about the market demand and their costs, a (Bayesian) Cournot equilibrium in pure strategies may not exist, or be unique. In fact, we are able to construct surprisingly simple and robust examples of duopolies with these features. However, we...