In forming coalitions {coalition}, player power to affect outcome, including making coalitions, is the most-important factor. Player must gain equal or more value by being in coalition, or else player does not join group. Acceptable outcome requires Pareto optimum.
symmetry
All players can have same role {symmetric game}.
communication
Outcomes {discriminatory solution} can give less than fair share to outsider and keep rest for coalition, which typically happens when games allow communication.
set
Typically, each possible outcome dominates another outcome, and outcomes are intransitive, so no outcome dominates all others. Typically, many undominated outcomes result {imputation}.
An outcome {effective set} can dominate if players get more when in coalitions, and coalitions can form.
set: stability
Typically, at least one outcome in current set dominates all new outcomes, making pressure to stay in current set. If gains are large and number of people is large, stability is low.
Theories {Aumann-Masschler theory} can study game coalitions. Aumann-Masschler theory uses characteristic function form, determines outcomes for coalitions, does not try to predict coalitions or determine fairness or equity, assumes players are in only one coalition or act alone, and assumes coalitions have value equal to member-value sum. Aumann-Masschler theory uses no utility comparisons or Pareto optima.
objection
Games have bargaining sets. Players can want member to leave coalition, so remaining players can get more {objection}. Acceptable outcome has no objections or reciprocal objections.
Games that reach situations with two coalitions {characteristic function form} are like two-person games.
Strong imputations can cause dominating outcomes {self-policing set} outside current set to cause coalition members to take losses.
For all players, values {Shapley value} can measure difference between coalition utilities if player is in or out of coalition. All coalitions have Shapley values. Coalition closest to having half total power is most likely. Coalition must have at least half total power to determine outcome. In coalitions, strong players gain more than weak players, but strong-weak coalitions do not form often. Players do best in only one coalition.
Coalition value can equal or exceed {superadditivity} coalition-player-value sum, because utility can transfer.
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Date Modified: 2022.0225