Nontransferable utility bankruptcy games

Top - Tập 28 - Trang 154-177 - 2019
Arantza Estévez-Fernández1, Peter Borm2, M. Gloria Fiestras-Janeiro3
1Department of Econometrics and Operations Research, Tinbergen Institute, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
2Department of Econometrics and Operations Research & CentER, Tilburg University, Tilburg, The Netherlands
3Departamento de Estatística e Investigación Operativa, Universidade de Vigo, Vigo, Spain

Tóm tắt

In this paper, we analyze bankruptcy problems with nontransferable utility (NTU) from a game theoretical perspective by redefining corresponding NTU-bankruptcy games in a tailor-made way. It is shown that NTU-bankruptcy games are both coalition-merge convex and ordinally convex. Generalizing the notions of core cover and compromise stability for transferable utility (TU) games to NTU-games, we also show that each NTU-bankruptcy game is compromise stable. Thus, NTU-bankruptcy games are shown to retain the two characterizing properties of TU-bankruptcy games: convexity and compromise stability. As a first example of a game theoretical NTU-bankruptcy rule, we analyze the adjusted proportional rule and show that this rule corresponds to the compromise value of NTU-bankruptcy games.

Tài liệu tham khảo

Aumann RJ (1985) An axiomatization of the non-transferable utility value. Econometrica 53:599–612 Aumann R, Maschler M (1985) Game theoretic analysis of a bankruptcy problem from the talmud. J Econ Theory 36:195–213 Borm P, Keiding H, McLean RP, Oortwijn S, Tijs S (1992) The compromise value for NTU-games. Int J Game Theory 21:175–189 Chun Y, Thomson W (1992) Bargaining problems with claims. Math Soc Sci 24:19–33 Csóka P, Herings P, Kóczy L, Pintér M (2011) Convex and exact games with non-transferable utility. Eur J Oper Res 209:57–62 Curiel IJ, Maschler M, Tijs S (1987) Bankruptcy games. Z Oper Res 31:A 143–A 159 Dietzenbacher BJ (2018) Bankruptcy games with nontransferable utility. Math Soc Sci 92:16–21 Estévez-Fernández A, Fiestras-Janeiro MG, Mosquera MA, Sánchez E (2012) A bankruptcy approach to the core cover. Math Methods Oper Res 76:343–359 Fragnelli V, Gastaldi F (2017) Remarks on the integer Talmud solution for integer bankruptcy problems. TOP 25:127–163 Fragnelli V, Gagliardo S, Gastaldi F (2014) Integer solutions to bankruptcy problems with non-integer claims. TOP 22:892–933 Fragnelli V, Gagliardo S, Gastaldi F (2016) Bankruptcy problems with non-integer claims: definition and characterizations of the ICEA solution. TOP 24:88–130 Greenberg J (1985) Cores of convex games without side payments. Math Oper Res 10:523–525 Hendrickx R, Borm P, Timmer J (2002) A note on NTU convexity. Int J Game Theory 31:29–37 Herrero C, Martínez R (2008) Ballanced allocation methods for claims problems with indivisibilities. Soc Choice Welf 30:603–617 O’Neill B (1982) A problem of rights arbitration from the talmud. Math Soc Sci 2:345–371 Orshan G, Valenciano F, Zarzuelo JM (2003) The bilateral consistent prekernel, the core, and NTU bankruptcy problems. Math Oper Res 28:268–282 Peleg B, Sudhölter P (2007) Introduction to the theory of cooperative games, vol 34. Springer, Berlin Predtetchinski A, Herings P (2004) A necessary and sufficient condition for the non-emptiness of the core of a non-transferable utility game. J Econ Theory 116:84–92 Quant M, Borm P, Reijnierse H, van Velzen B (2005) The core cover in relation to the nucleolus and the Weber set. Int J Game Theory 33:491–503 Shapley LS (1971) Cores of convex games. Int J Game Theory 1:11–26 Sharkey WW (1981) Convex games without side payments. Int J Game Theory 10:101–106 Thomson W (2003) Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey. Math Soc Sci 45:249–297 Thomson W (2015) Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: an update. Math Soc Sci 74:867–880 Tijs SH (1981) Bounds for the core and the \(\tau \)-value. In: Moeschlin O, Pallaschke D (eds) Game Theory and Mathematical Economics. North-Holland, Amsterdam, pp 123–132 Tijs SH, Lipperts F (1982) The hypercube and the core cover of \(n\)-person cooperative games. Cahiers du Centre d’Études de Researche Opérationelle 24:27–37 Vidal-Puga J (2008) Forming coalitions and the Shapley NTU value. Eur J Oper Res 190:659–671 Vilkov V (1977) Convex games without side payments. Vestnik Leningradskiva Universitata 7:21–24 (In Russian) Weber RJ (1988) Probabilistic values for games. In: Roth AE (ed) The Shapley value: essays in honor of Lloyd S Shapley. Cambridge University Press, Cambridge, pp 101–119