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

We show that when firms have asymmetric information about the market demand and theirs 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...

We show that even in very simple oligopolies with di¤erential information a (Bayesian) Cournot equilibrium in pure strategies may not exist, or be unique. However, we ?nd su¢ cient conditions for existence, and for uniqueness, of Cournot equilibrium in a certain class of industries. More...