A non-cooperative bargaining procedure generalising the Kalai-Smorodinsky bargaining solution to NTU games (Q2743763)

The authors propose a new value for NTU games (games without transferable utility), that they call the \(\omega\)-value and applies without any domain restriction. Of course, they check that it differs from other NTU values found in the literature like the Shapley value, the Harsanyi value, the compromise value, the consistent value or the MC-value. NEWLINENEWLINENEWLINEThe \(\Omega\)-value arises as a natural generalization to NTU games of both the Kalai-Smorodinsky (K-S) solution for pure bargaining games and the \(\chi\)-value (that equals the \(\tau\)-value in the convex case) for essential TU games. NEWLINENEWLINENEWLINEThree approaches are used to introduce the \(\Omega\)-value. The first one follows the K-S definitory procedure and obtains the \(\Omega\)-value of a game as the only efficient point in the segment that links suitable upper and lower bounds. This enables the authors to show that \(\Omega\) applies to any game and also that it extends the K-S solution and the \(\chi\)-value. NEWLINENEWLINENEWLINEThe second approach fairly generalizes Moulin's implementation of the K-S solution. A bargaining procedure is defined by means of a non-cooperative game in extensive form associated to a given NTU game. This non-cooperative game possesses subgame perfect Nash equilibria and all of them assign as a payoff vector to the players the \(\Omega\)-value of the NTU game. NEWLINENEWLINENEWLINEFinally, the third approach is the axiomatic one. Efficiency, symmetry, covariance and restricted monotonicity are shown to characterize the \(\Omega\)-value. Alternatively, efficiency, covariance and restricted proportionality form a second axiomatic system for \(\Omega\). This shows again that the new value generalizes the K-S solution.