Bankruptcy problems with interval uncertainty

In this paper, bankruptcy situations with interval data are studied. Two classical bankruptcy rules, namely the proportional rule and the rights-egalitarian rule, are extended to the interval setting. It turns out that these bankruptcy interval rules generate elements in the interval core of a related cooperative interval game.

[1]  Philip Wolfe,et al.  Contributions to the theory of games , 1953 .

[2]  Donald B. Gillies,et al.  3. Solutions to General Non-Zero-Sum Games , 1959 .

[3]  Ramon E. Moore Methods and applications of interval analysis , 1979, SIAM studies in applied mathematics.

[4]  Barry O'Neill,et al.  A problem of rights arbitration from the Talmud , 1982, Math. Soc. Sci..

[5]  R. Aumann,et al.  Game theoretic analysis of a bankruptcy problem from the Talmud , 1985 .

[6]  H. Peyton Young,et al.  On Dividing an Amount According to Individual Claims or Liabilities , 1987, Math. Oper. Res..

[7]  M. Maschler,et al.  Individual rights and collective responsibility: the rights–egalitarian solution , 1999 .

[8]  H. Moulin Priority Rules and Other Asymmetric Rationing Methods , 2000 .

[9]  Vito Fragnelli,et al.  Two Approaches to the Problem of Sharing Delay Costs in Joint Projects , 2002, Ann. Oper. Res..

[10]  Joaquín Sánchez-Soriano,et al.  Game Theory Techniques for University Management: An Extended Bankruptcy Model , 2002, Ann. Oper. Res..

[11]  R. Branzei,et al.  Shapley-like values for interval bankruptcy games , 2003 .

[12]  Rodica Brânzei,et al.  Cost sharing in a joint project , 2004 .

[13]  Joaquín Sánchez-Soriano,et al.  Compromise solutions for bankruptcy situations with references , 2008, Ann. Oper. Res..

[14]  R. Branzei,et al.  Cores and Stable Sets for Interval-Valued Games , 2008 .

[15]  Rodica Branzei,et al.  Convex Interval Games , 2009, Adv. Decis. Sci..

[16]  Silvia Miquel,et al.  Cooperation under interval uncertainty , 2008, Math. Methods Oper. Res..

[17]  R. Branzei,et al.  Allocation rules incorporating interval uncertainty , 2009 .

[18]  Rodica Branzei,et al.  How to Handle Interval solutions for Cooperative Interval Games , 2010, Int. J. Uncertain. Fuzziness Knowl. Based Syst..