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The bargaining set for almost-convex games

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Abstract

We generalize the well-known result of the coincidence of the bargaining set and the core for convex games (Maschler et al. 1972) to the class of games named almost-convex games, that is, coalitional games where all proper subgames are convex.

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References

  • Bondareva, O. N. (1963). Some applications of linear programming methods to the theory of cooperative games. Probl Kibern, 10, 119–139.

    Google Scholar 

  • Borm, P., Fiestras-Janeiro, G., Hamers, H., Sánchez, E., & Voorneveld, M. (2002). On the convexity of games corresponding to sequencing situations with due dates. Eur J Oper Res, 136, 616–634.

    Article  Google Scholar 

  • Branzei, R., Tijs, S., & Zarzuelo, J. (2009). Convex multi-choice games: characterizations and monotonic allocation schemes. Eur J Oper Res, 198, 571–575.

    Article  Google Scholar 

  • Csóka, P., Herings, J. J., Kóczy, L. Á., & Pintér, M. (2011). Convex and exact games with non-transferable utility. Eur J Oper Res, 209, 57–62.

    Article  Google Scholar 

  • Davis, M., & Maschler, M. (1963). Existence of stable payoff configurations for cooperative games. Bull Am Soc, 69, 106–108.

    Article  Google Scholar 

  • Davis, M., & Maschler, M. (1967). Existence of stable payoff configurations for cooperative games. In M. Shubik (Ed.), Essays in mathematical economics in honor of Oskar Morgestern (pp. 39–52). Princeton: Princeton University Press.

    Google Scholar 

  • Einy, E., & Wettstein, D. (1996). Equivalence between bargaining sets and the core of simple games. Int J Game Theory, 25, 65–71.

    Article  Google Scholar 

  • Einy, E., Holzman, R., Monderer, D., & Shitovitz, B. (1997). Core equivalence theorems for infinite convex games. J Econ Theory, 76, 1–12.

    Article  Google Scholar 

  • Granot, D. (2010). The reactive bargaining set for cooperative games. Int J Game Theory, 1, 73–93.

    Google Scholar 

  • Gellekom, J. R. G., Potters, J. A. M., & Reijnierse, J. H. (1999). Prosperity properties of TU-games. Int J Game Theory, 28, 211–227.

    Article  Google Scholar 

  • Hamers, H. (1997). On the concavity of delivery games. Eur J Oper Res, 99, 445–458.

    Article  Google Scholar 

  • Hamers, H., Klijn, F., & van Velzen, B. (2005). On the convexity of precedence sequencing games. Ann Oper Res, 137, 161–175.

    Article  Google Scholar 

  • Izquierdo, J. M., & Rafels, C. (2001). Average monotonic cooperative games. Games Econ Behav, 36, 174–192.

    Article  Google Scholar 

  • Izquierdo, J. M., & Rafels, C. (2012). A characterization of convex TU games by means of the Mas-Colell bargaining set (à la Shimomura). Int J Game Theory, 41, 381–395.

    Article  Google Scholar 

  • Maschler, M., Peleg, B., & Shapley, S. (1972). The kernel and bargaining set for convex games. Int J Game Theory, 39, 163–170.

    Google Scholar 

  • Mas-Colell, A. (1989). An equivalence theorem for a bargaining set. J Math Econ, 18, 129–139.

    Article  Google Scholar 

  • Meertens, M., Potters, J. A. M., & Reijnierse, J. H. (2007). On bargaining sets in symmetric games. Int Game Theory Rev, 9, 199–213.

    Article  Google Scholar 

  • Meggido, N. (1974). On the nonmonotonicity of the bargaining set, the kernel and the nucleolous of a game. SIAM J Appl Math, 27, 355–358.

    Article  Google Scholar 

  • Núñez, M., & Rafels, C. (1998). On extreme points of the core and reduced games. Ann Oper Res, 84, 121–133.

    Article  Google Scholar 

  • Potters, J. A. M., Poos, R., Tijs, S. H., & Muto, S. (1989). Clan games. Games Econ Behav, 1, 275–293.

    Article  Google Scholar 

  • Pulido, M., & Sánchez-Soriano, J. (2009). On the core, the Weber set and convexity in games with a priori unions. Eur J Oper Res, 193, 468–475.

    Article  Google Scholar 

  • Shapley, L. S. (1967). On balanced sets and cores. Nav Res Logist Q, 14, 453–460.

    Article  Google Scholar 

  • Shapley, L. S. (1971). Cores of convex games. Int J Game Theory, 1, 11–26.

    Article  Google Scholar 

  • Shimomura, K. (1997). Quasi-cores in bargaining sets. Int J Game Theory, 26, 283–302.

    Article  Google Scholar 

  • Solymosi, T. (1999). On the bargaining set, kernel and core of superadditive games. Int J Game Theory, 28, 229–240.

    Article  Google Scholar 

  • Solymosi, T. (2008). Bargaining sets and the core in partitioning games. Cent Eur J Oper Res, 16, 425–440.

    Article  Google Scholar 

  • Topkis, D. M. (1987). Activity optimization games with complementarity. Eur J Oper Res, 28, 358–368.

    Article  Google Scholar 

  • Vohra, R. (1991). An existence theorem for a bargaining set. J Math Econ, 20, 19–34.

    Article  Google Scholar 

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Acknowledgements

Institutional support from Ministerio de Ciencia e Innovación and FEDER under grant ECO2011-22765, and Generalitat de Catalunya under grant 2009SGR0960 is acknowledged.

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Correspondence to Josep M. Izquierdo.

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Getán, J., Izquierdo, J.M., Montes, J. et al. The bargaining set for almost-convex games. Ann Oper Res 225, 83–89 (2015). https://doi.org/10.1007/s10479-012-1226-y

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