Who’s Who in Networks. Wanted: The Key Player

Coralio Ballester (), Antoni Calvó-Armengol and Yves Zenou ()

No 5329, CEPR Discussion Papers from C.E.P.R. Discussion Papers

Abstract: Finite population non-cooperative games with linear-quadratic utilities, where each player decides how much action she exerts, can be interpreted as a network game with local payoff complementarities, together with a globally uniform payoff substitutability component and an own concavity effect. For these games, the Nash equilibrium action of each player is proportional to her Bonacich centrality in the network of local complementarities, thus establishing a bridge with the sociology literature on social networks. This Bonacich-Nash linkage implies that aggregate equilibrium increases with network size and density. We then analyze a policy that consists in targeting the key player, that is, the player who, once removed, leads to the optimal change in aggregate activity. We provide a geometric characterization of the key player identified with an inter-centrality measure, which takes into account both a player’s centrality and her contribution to the centrality of the others.

Keywords: centrality measures; peer effects; policies; social networks (search for similar items in EconPapers)
JEL-codes: A14 C72 L14 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-gth, nep-net and nep-soc
Date: 2005-10
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Working Paper: Who's Who in Networks. Wanted: the Key Player (2005)
Journal Article: Who's Who in Networks. Wanted: The Key Player (2006)
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