Who’s Who in Networks. Wanted: The Key Player
AbstractFinite 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.
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Bibliographic InfoPaper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 5329.
Date of creation: Oct 2005
Date of revision:
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Other versions of this item:
- Coralio Ballester & Antoni Calvó-Armengol & Yves Zenou, 2004. "Who's Who in Networks. Wanted: The Key Player," Working Papers 178, Barcelona Graduate School of Economics.
- Coralio Ballester & Antoni Calvo-Armengol & Yves Zenou, 2005. "Who's Who in Networks. Wanted: the Key Player," NajEcon Working Paper Reviews 666156000000000586, www.najecon.org.
- A14 - General Economics and Teaching - - General Economics - - - Sociology of Economics
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- L14 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Transactional Relationships; Contracts and Reputation
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-12-09 (All new papers)
- NEP-GTH-2005-12-09 (Game Theory)
- NEP-NET-2005-12-09 (Network Economics)
- NEP-SOC-2005-12-09 (Social Norms & Social Capital)
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