Farsightedness and Cautiousness in Coalition Formation Games with Positive Spillovers

Abstract

We adopt the largest consistent set defined by Chwe (1994; J. Econ. Theory 63: 299-325) to predict which coalition structures are possibly stable when players are farsighted. We also introduce a refinement, the largest cautious consistent set, based on the assumption that players are cautious. For games with positive spillovers, many coalition structures may belong to the largest consistent set. The grand coalition, which is the efficient coalition structure, always belongs to the largest consistent set and is the unique one to belong to the largest cautious consistent set.

Game-Theoretic Analysis of Cooperation Among Supply Chain Agents: Review and Extensions

“…Mauleon and Vannetelbosch (2004) refine the LCS by assuming that defecting coalition S 0 should contemplate the possibility to end with positive probability at any coalition structure B ∈ Y , where V = B or V B. They call the set obtained under this criteria the largest cautious consistent set (LCCS).…”

Farsighted coalitional stability in TU-games

“…When coalition {1, 2, 3} is called upon to move, one of its best responses is to propose a farsighted stable imputation y, which directly dominates x and where y({1, 2, 3}) = 3 and not to propose a farsighted stable imputation x, where x({1, 2, 3}) ≤ 3. Mauleon and Vannetelbosch (2004) introduce another refinement of the largest consistent set based on the assumption that players are cautious. This refinement, the largest cautious consistent set, is successfully applied to coalition formation games.…”

“…In the general context of social environments as defined by Chwe (1994), it has been noted that a farsighted stable set can be too exclusive while the largest consistent set can be too inclusive (see Chwe, 1994, Xue, 1998, Xue, Diamantoudi, 2003, Mauleon, Vannetelbosch, 2004). Proposition 2 below picks out a minimal set of properties on (N, v) for which the largest consistent is too inclusive in the sense that no imputation is excluded from this set.…”

Limited farsightedness in network formation

“…But as such it entangles patience and farsightedness. Moreover, their dynamic equilibrium model 1 See the work of Chwe [1994], Xue [1998], Herings et al [2004Herings et al [ , 2009, Mauleon and Vannetelbosch [2004], Page et al [2005], and Page and Wooders [2009].…”