Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  introduce a network design game where the objective of the players is to design the interconnections beten the nodes of two different networks    $G_{1}$    and    $G_{2}$    in order to maximize certain local utility functions. In this setting, each player is associated with a node in    $G_{1}$    and has functional dependencies on certain nodes in    $G_{2}$   .  use a distance-based utility for the players in which the goal of each player is to purchase a set of edges (incident to its associated node) such that the sum of the distances beten its associated node and the nodes it depends on    $G_{2}$    is minimized.  consider a heterogeneous set of players (i.e., players have their own costs and benefits for constructing edges).  show that finding a best response of a player in this game is NP-hard. Despite this,  characterize some properties of the best response actions, which are helpful in determining a Nash equilibrium for certain instances of this game. In particular,  prove the existence of pure Nash equilibria in this game when    $G_{2}$    contains a star subgraph, and provide an algorithm that outputs such an equilibrium for any set of players. Finally,  show that the price of anarchy in this game can be arbitrarily large.
['Ebrahim Moradi Shahrivar', 'Shreyas Sundaram']
I am writing a research paper on a idea The Game-Theoretic Formation of Interconnections Between Networks
[{"from": "human", "value": "I am writing a research paper on a idea The Game-Theoretic Formation of Interconnections Between Networks"}, {"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 network design game where the objective of the players is to design the interconnections beten the nodes of two different networks    $G_{1}$    and    $G_{2}$    in order to maximize certain local utility functions. In this setting, each player is associated with a node in    $G_{1}$    and has functional dependencies on certain nodes in    $G_{2}$   .  use a distance-based utility for the players in which the goal of each player is to purchase a set of edges (incident to its associated node) such that the sum of the distances beten its associated node and the nodes it depends on    $G_{2}$    is minimized.  consider a heterogeneous set of players (i.e., players have their own costs and benefits for constructing edges).  show that finding a best response of a player in this game is NP-hard. Despite this,  characterize some properties of the best response actions, which are helpful in determining a Nash equilibrium for certain instances of this game. In particular,  prove the existence of pure Nash equilibria in this game when    $G_{2}$    contains a star subgraph, and provide an algorithm that outputs such an equilibrium for any set of players. Finally,  show that the price of anarchy in this game can be arbitrarily large."}]