Abstract:
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.