Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In finite games, the graph of the Nash equilibrium correspondence is a semialgebraic set (i.e. it is defined by finitely many polynomial inequal- ities). This fact implies many game theoretical results about the structure of equilibria.  show that many of these results can be readily exported to Poisson games even if the expected utility functions are not polynomials.  do this proving that, in Poisson games, the graph of the Nash equilibrium correspondence is a globaly subanalytic set. Many of the properties of semialgebraic sets follow from a set of axioms that the collection of globaly subanalytic sets also satisfy. Hence,  easily show that every Poisson game has finitely many connected components and that at least one of them contains a stable set of equilibria. By the same reasoning,  also show how generic determinacy results in finite games can be extended to Poisson games.
['Claudia Meroni', 'Carlos Pimienta']
I am writing a research paper on a idea The structure of Nash equilibria in Poisson games
[{"from": "human", "value": "I am writing a research paper on a idea The structure of Nash equilibria in Poisson games"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In finite games, the graph of the Nash equilibrium correspondence is a semialgebraic set (i.e. it is defined by finitely many polynomial inequal- ities). This fact implies many game theoretical results about the structure of equilibria.  show that many of these results can be readily exported to Poisson games even if the expected utility functions are not polynomials.  do this proving that, in Poisson games, the graph of the Nash equilibrium correspondence is a globaly subanalytic set. Many of the properties of semialgebraic sets follow from a set of axioms that the collection of globaly subanalytic sets also satisfy. Hence,  easily show that every Poisson game has finitely many connected components and that at least one of them contains a stable set of equilibria. By the same reasoning,  also show how generic determinacy results in finite games can be extended to Poisson games."}]