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 consider individual support rather than group support. The main idea is to introduce individual 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. A unilaterally supportive strategy combination with respect to every possible derangement is called a unilateral support equilibrium.

Our main insight is that in a unilateral support equilibrium, every player is supported by every other player individually. This is reflected by the alternative formulation of a unilateral support equilibrium in terms of pay-off functions, instead of using derangements. 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.