Agreement theory and consensus

In order to formalize the act of agreement between two individuals, the concept of consensus functional equation, for a bi-variate map defined on an abstract choice set, is introduced. Then, and in a purely choice-theoretical framework, we relate the solutions of this equation to the notion of a rationalizable agreement rule. Finally, some results about the specific functional form of the solutions of the consensus functional equation in the setup of monetary payoffs and lotteries, over two outcomes, are also shown.