Which acceptable agreements are equilibria?

This paper proposes a one shot normal form game of agreement formation. It introduces a new notion of strategy, which is, for each player, to say which of the possible agreements are acceptable. Therefore, the strategy is a vector of choices. For a given strategy profile, different sizes are then acceptable and it is assumed that the largest agreement is achieved. I propose a concept of strong Nash equilibrium, which satisfies what is called a property of perfection in restricted games. The idea is that, even if the set of agreements to be proposed is restricted, the corresponding players' choices have to be self-enforcing. For a large class of payment functions exhibiting positive externalities, I characterise the set of equilibria and show that a unique agreement is generated. Two examples are given: firstly a cartel, which is a collusive agreement and secondly an agreement to contribute to a public good.