Coalitional negotiation

We develop a two-stage negotiation model to study the impact of costly inspections on both the coalition formation outcome and the per-member payoffs. In the first stage, the players are forming coalitions and inside each coalition formed the members share the coalition benefits. We adopt the largest consistent set (LCS) to predict which coalition structures are possibly stable. We also introduce a refinement,the largest cautious consistent set (LCCS). In the second stage, the inspection game takes place inside each coalition. For games with positive spillovers, many coalition structures may belong to the LCS under costless inspection. The grand coalition, which is the efficient coalition structure, always belongs to the LCS and is the unique one to belong to the LCCS. Under costly inspection, the grand coalition does not always belong to the LCS. Nevertheless, there exists inspection cost parameters such that the LCS singles out the grand coalition.