Abstract
Suppose that individual payoffs depend on the network connecting them. Consider the following simultaneous move game of network formation: players announce independently the links they wish to form, and links are formed only under mutual consent. We provide necessary and sufficient conditions on the network link marginal payoffs such that the set of pairwise stable, pairwise-Nash and proper equilibrium networks coincide, where pairwise stable networks are robust to one-link deviations, while pairwise-Nash networks are robust to one-link creation but multi-link severance. Under these conditions, proper equilibria in pure strategies are fully characterized by one-link deviation checks.
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Antoni Calvó-Armengol heart breakingly passed away on 3 November 2007. His memory will forever remain radiant and warm, like he always was.
We thank William Thomson, an associate editor and two anonymous referees for their suggestions that led to substantial improvements. We also thank Sjaak Hurkens, Bettina Klaus, Jordi Massó and Giovanni Neglia for helpful conversations. The first author gratefully acknowledges the financial support from the Spanish Ministry of Education and FEDER through grant SEJ2005-01481/ECON, the Fundación BBVA and the Barcelona Economics Program of XREA. The second author is grateful to the Netherlands Organization for Scientific Research (NWO) for its support under grant VIDI-452-06-013.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Calvó-Armengol, A., İlkılıç, R. Pairwise-stability and Nash equilibria in network formation. Int J Game Theory 38, 51–79 (2009). https://doi.org/10.1007/s00182-008-0140-7
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DOI: https://doi.org/10.1007/s00182-008-0140-7