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.

This paper addresses interactive one-machine sequencing situations in which the costs of processing a job are given by an exponential function of its completion time. The main difference with the standard linear case is that the gain of switching two neighbors in a queue is time-dependent and depends on their exact position. We illustrate that finding an optimal order is complicated in general and we identify specific subclasses, which are tractable from an optimization perspective. More specifically, we show that in these subclasses, all neighbor switches in any path from the initial order to an optimal order lead to a non-negative gain. Moreover, we derive conditions on the time-dependent neighbor switching gains in a general interactive sequencing situation to guarantee convexity of the corresponding cooperative game. These conditions are satisfied within our specific subclasses of exponential interactive sequencing situations.

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This paper studies sequencing situations with non-linear cost functions. We show that the neighbor switching gains are now time-dependent, in contrast to the standard sequencing situations with linear cost functions, which complicate finding an optimal order and stable allocations. We derive conditions on the time-dependent neighbor switching gains in a (general) sequencing situation to guarantee convexity of the associated sequencing game. Moreover, we provide two procedures that uniquely specify a path from the initial order to an optimal order and we define two corresponding allocation rules that divide the neighbor switching gains equally in every step of the path. We show that the same conditions on the gains also guarantee stability for the allocations prescribed by these rules.