Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  studies the Nash stability in hedonic coalition formation games.  address the following issue: for a general problem formulation, is there any utility allocation method ensuring a Nash-stable partition?  propose the definition of the Nash-stable core and  analyze the conditions for having a non-empty Nash-stable core. More precisely,  prove that using relaxed efficiency in utility sharing allows to ensure a non empty Nash-stable core. Then, a decentralized algorithm called Nash stability establisher is proposed for finding the Nash stability in a game whenever at least one exists. The problem of finding the Nash stability is formulated as a non-cooperative game. In the proposed approach, during each round, each player determines its strategy in its turn according to a random round-robin scheduler.  prove that the algorithm converges to an equilibrium if it exists, which is the indicator of the Nash stability.
['Cengis Hasan', 'Eitan Altman', 'Jean-Marie Gorce']
I am writing a research paper on a idea On the Nash Stability in the Hedonic Coalition Formation Games
[{"from": "human", "value": "I am writing a research paper on a idea On the Nash Stability in the Hedonic Coalition Formation Games"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  studies the Nash stability in hedonic coalition formation games.  address the following issue: for a general problem formulation, is there any utility allocation method ensuring a Nash-stable partition?  propose the definition of the Nash-stable core and  analyze the conditions for having a non-empty Nash-stable core. More precisely,  prove that using relaxed efficiency in utility sharing allows to ensure a non empty Nash-stable core. Then, a decentralized algorithm called Nash stability establisher is proposed for finding the Nash stability in a game whenever at least one exists. The problem of finding the Nash stability is formulated as a non-cooperative game. In the proposed approach, during each round, each player determines its strategy in its turn according to a random round-robin scheduler.  prove that the algorithm converges to an equilibrium if it exists, which is the indicator of the Nash stability."}]