Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  introduce a new measure of the discrepancy in strategic games beten the social lfare in a Nash equilibrium and in a social optimum, that  call selfishness level. It is the smallest fraction of the social lfare that needs to be offered to each player to achieve that a social optimum is realized in a pure Nash equilibrium. The selfishness level is unrelated to the price of stability and the price of anarchy and is invariant under positive linear transformations of the payoff functions. Also, it naturally applies to other solution concepts and other forms of games.#R##N##R##N# study the selfishness level of several ll-known strategic games. This allows us to quantify the implicit tension within a game beten players' individual interests and the impact of their decisions on the society as a whole. Our analyses reveal that the selfishness level often provides a deeper understanding of the characteristics of the underlying game that influence the players' willingness to cooperate.#R##N##R##N#In particular, the selfishness level of finite ordinal potential games is finite, while that of akly acyclic games can be infinite.  derive explicit bounds on the selfishness level of fair cost sharing games and linear congestion games, which depend on specific parameters of the underlying game but are independent of the number of players. Further,  show that the selfishness level of the n-players Prisoner's Dilemma is c/(b(n-1)-c), where b and c are the benefit and cost for cooperation, respectively, that of the n-players public goods game is (1 - c/n)/(c - 1), where c is the public good multiplier, and that of the Traveler's Dilemma game is 1/2 (b - 1), where b is the bonus. Finally, the selfishness level of Cournot competition (an example of an infinite ordinal potential game), Tragedy of the Commons, and Bertrand competition is infinite.
['Krzysztof R. Apt', 'Guido Schäfer']
I am writing a research paper on a idea Selfishness level of strategic games
[{"from": "human", "value": "I am writing a research paper on a idea Selfishness level of strategic games"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  introduce a new measure of the discrepancy in strategic games beten the social lfare in a Nash equilibrium and in a social optimum, that  call selfishness level. It is the smallest fraction of the social lfare that needs to be offered to each player to achieve that a social optimum is realized in a pure Nash equilibrium. The selfishness level is unrelated to the price of stability and the price of anarchy and is invariant under positive linear transformations of the payoff functions. Also, it naturally applies to other solution concepts and other forms of games.#R##N##R##N# study the selfishness level of several ll-known strategic games. This allows us to quantify the implicit tension within a game beten players' individual interests and the impact of their decisions on the society as a whole. Our analyses reveal that the selfishness level often provides a deeper understanding of the characteristics of the underlying game that influence the players' willingness to cooperate.#R##N##R##N#In particular, the selfishness level of finite ordinal potential games is finite, while that of akly acyclic games can be infinite.  derive explicit bounds on the selfishness level of fair cost sharing games and linear congestion games, which depend on specific parameters of the underlying game but are independent of the number of players. Further,  show that the selfishness level of the n-players Prisoner's Dilemma is c/(b(n-1)-c), where b and c are the benefit and cost for cooperation, respectively, that of the n-players public goods game is (1 - c/n)/(c - 1), where c is the public good multiplier, and that of the Traveler's Dilemma game is 1/2 (b - 1), where b is the bonus. Finally, the selfishness level of Cournot competition (an example of an infinite ordinal potential game), Tragedy of the Commons, and Bertrand competition is infinite."}]