Two-Stage Bargaining with Reversible Coalitions: The Case of Apex Games

This paper studies coalition formation and payoff division in apex games under the following assumptions: first, payoff division can only be agreed upon after the coalition has formed (two-stage bargaining); second, negotiations in the coalition can break down, in which case a new coalition may be formed (reversible coalitions).In contrast with the results of other two-stage models, all minimal winning coalitions may form and expected payoffs coincide with the per capita nucleolus.These results are robust to the details of the bargaining procedure.Surprisingly, having a two-stage process (rather than a one-stage process with simultaneous coalition formation and payoff division) benefits the apex player.bargaining;game theory;coalition

Noncooperative Bargaining in Apex Games and the Kernel

This paper studies non-cooperative bargaining with random proposers in apex games. Two di¤erent protocols are considered: the egalitarian propocol, which selects each player to be the proposer with the same probability, and the proportional protocol, which selects each player with a probability proportional to his number of votes. Expected equilibrium payo¤s coincide with the kernel for the grand coalition regardless of the protocol. Expected payo¤s conditional on a coalition may depend on the protocol: given a coalition of the apex player with a minor player, an egalitarian protocol yields a nearly equal split whereas a proportional protocol leads to a proportional split.noncooperative bargaining;apex games;kernel;random proposers

The Nucleolus as a Consistent Power Index in Noncooerative Majority Games

This paper studies noncooperative bargaining with random proposers in proper single games. A power index is called consistent if it can be obtained as an equilibrium of the game with random proposers using the index itself as probability vector. Unlike the Shapley-Shubik and Banzhaf indices, the nucleolus has this property. The proof uses the balancedness result in Kohlberg (1971) reinterpreting the balancing wieghts as mixed strategies.noncooperative bargaining;random proposers;nucleolus;consistency;balancedness

Two-Stage Bargaining with Reversible Coalitions:The Case of Apex Games

This paper studies coalition formation and payoff division in apex games under the following assumptions: first, payoff division can only be agreed upon after the coalition has formed (two-stage bargaining); second, negotiations in the coalition can break down, in which case a new coalition may be formed (reversible coalitions).In contrast with the results of other two-stage models, all minimal winning coalitions may form and expected payoffs coincide with the per capita nucleolus.These results are robust to the details of the bargaining procedure.Surprisingly, having a two-stage process (rather than a one-stage process with simultaneous coalition formation and payoff division) benefits the apex player.

A Bargaining Set Based on External and Internal Stability and Endogenous Coalition Formation

A new bargaining set based on notions of both internal and external stability is developed in the context of endogenous coalition formation.It allows to make an explicit distinction between within-group and outsidegroup deviation options.This type of distinction is not present in current bargaining sets.For the class of weighted majority games, the outcomes in the bargaining set containing a minimal winning coalition are characterized.Furthermore, it is shown that the bargaining set of any homogeneous weighted majority game contains an outcome for which the underlying coalition structure consists of a minimal winning coalition and its complement.The paper also introduces a new class of games called cooperation externalities games.For a symmetric cooperation externalities game conditions are provided such that every outcome in the bargaining set supports the same coalition structure.This coalition structure consists of one coalition of all players with an externality parameter higher than one and a collection of singleton coalitions, one for every player with a cooperation externality parameter lower than oneBargaining set;endogenous colation;formation;internal and external stability

The Nucleolus as a Consistent Power Index in Noncooerative Majority Games

This paper studies noncooperative bargaining with random proposers in proper single games. A power index is called consistent if it can be obtained as an equilibrium of the game with random proposers using the index itself as probability vector. Unlike the Shapley-Shubik and Banzhaf indices, the nucleolus has this property. The proof uses the balancedness result in Kohlberg (1971) reinterpreting the balancing wieghts as mixed strategies.

A Bargaining Set Based on External and Internal Stability and Endogenous Coalition Formation

A new bargaining set based on notions of both internal and external stability is developed in the context of endogenous coalition formation.It allows to make an explicit distinction between within-group and outsidegroup deviation options.This type of distinction is not present in current bargaining sets.For the class of weighted majority games, the outcomes in the bargaining set containing a minimal winning coalition are characterized.Furthermore, it is shown that the bargaining set of any homogeneous weighted majority game contains an outcome for which the underlying coalition structure consists of a minimal winning coalition and its complement.The paper also introduces a new class of games called cooperation externalities games.For a symmetric cooperation externalities game conditions are provided such that every outcome in the bargaining set supports the same coalition structure.This coalition structure consists of one coalition of all players with an externality parameter higher than one and a collection of singleton coalitions, one for every player with a cooperation externality parameter lower than one

A bilateral whitish lesion on the mucosa of the cheek

An 8-year-old girl with no medical history presented with a bilateral whitish lesion on the mucosa of the cheek, evident since early childhood. There was no relevant family history, and her parents had not presented similar lesions. They reported a progressive growth of the lesion in the last months, for which she had been evaluated by maxillofacial surgery, the lesion being oriented as a frictional keratosis. However, the use of occlusal splint was not associated with any improvement. She was otherwise asymptomatic. Physical examination revealed a bilateral, whitish, well-demarcated cheek mucosal plaque, which partially coincided with the dental occlusion line. The lesion did not detach with scratching (Figure 1). No other alterations were observed in the oral cavity or in the systematic physical examination