Maybe the European Union's future is more "à la carte" — a set of coalitions of the willing, as it were.
Coalition formation is a fundamental approach to multi-agent coordination, and a key challenge in this context is the coalition structure generation problem, where a set of agents must be partitioned into the best set of coalitions.
The conditions under which the set of coalition-proof Nash equilibria coincides with the set of strong Nash equilibria are formulated by Konishi et al. [50].
Bernheim et al. [44] note that for two-person games, the set of coalition-proof equilibria coincides with the set of Nash equilibria that are not Pareto-dominated by any other Nash equilibrium.
The set of relevant coalitions for a game V, ε V, is the set of coalitions S, |S| ≥ 2, s.t.: ∃ y ∈ V(S) | y > x S. where x S = (x i )i∈S and x i = sup {t ∈ R | te i ∈ V(i)}.
The domination relation between two different payoff configurations (P1, x1), (P2, x2) is: (P1,x1)dom(P2,x2) ⇔ ∃ R ∈ P1|x i 1 > x i 2, i ∈ R The set of relevant coalitions for a game V, ε V, is the set of coalitions S, |S| ≥ 2, s.t.: ∃ y ∈ V(S) | y > x S where x S = (x i )i∈S and x i = sup {t ∈ R | te i ∈ V(i)}.
We present different variants of the algorithm, which we call Coalition Linkage (C-Link) and demonstrate how such algorithm can be adapted to graph restricted coalition formation problems (where an interaction graph defined among the agents restricts the set of feasible coalitions).
To this end, we model the formation problem as a Graph-Constrained Coalition Formation (GCCF) one, where the set of feasible coalitions is restricted by a graph (i.e., the social network).
