No abstract

No abstract

Nash equilibrium, Normal form games, Recursion, C72,

We show that to each linear solution that has the inessential game property, there is an inner product on the space of games such that the solution to each game is the best additive approximation of the game (w.r.t. the norm derived from this inner product). If the space of games has an inner product, then the function that to each game assigns the best additive approximation of this game (w.r.t. to the norm derived from this inner product) is a linear solution that has the inessential game property. Both claims remain valid also if solutions are required to be efficient. JEL Classification: C78

We study non-cooperative link formation games in which players have to decide how much to invest in relationships with other players. The relationship between equilibrium strategies and network centrality measures are investigated in games where there is a common valuation of players as friends. If the utility from relationships with other players is bilinear, then indegree, eigenvector centrality, and the Katz-Bonacich centrality measure put the players in opposite order than the common valuation. If the utility from relationships is strictly concave, then these measures order the players in the same way as the common valuation.