Unilateral Support Equilibria

The concept of Berge equilibria is based on supportive behavior among the players: each player is supported by the group of all other players. In this paper, we extend this concept by maintaining the idea of supportive behavior among the players, but eliminating the underlying coordination issues. We suggest to consider individual support rather than group support. The main idea is to introduce support relations, modeled by derangements. In a derangement, every player supports exactly one other player and every player is supported by exactly one other player. Subsequently, we define a new equilibrium concept, called a unilateral support equilibrium, which is unilaterally supportive with respect to every possible derangement. We show that a unilateral support equilibrium can be characterized in terms of pay-off functions so that every player is supported by every other player individually. Moreover, it is shown that every Berge equilibrium is also a unilateral support equilibrium and we provide an example in which there is no Berge equilibrium, while the set of unilateral support equilibria is non-empty. Finally, the relation between the set of unilateral support equilibria and the set of Nash equilibria is explored.