Awareness as an Equilibrium Notion: Normal-Form Games

We study normal-form games where parts of the games may not be common knowledge. Agents may be aware only of some facts describing the game. An awareness architecture is given by agents' awareness, and an infinite regress of conjectures about other agents and their conjectures. The problem is specified by the true underlying normal-form game, and by the set of possible awareness architectures. Awareness equilibrium is given by a feasible awareness architecture for each agent, strategies that are played and these strategies have to be consistent with the awareness architectures and agents' rationality. We first study games with complete information, where each player may be aware of a subset of the set of possible actions. We then study games with incomplete information, where each player may be aware of a subset of the set of types and probability over types. Our results illustrate how a departure from the assumption of common knowledge alters equilibium predictions.