Enjoying cooperative games: The R package GameTheory

This paper focuses on cooperative games with transferable utility. We propose the computation of three solutions, the Shapley value for n agents, the nucleolus with a maximum of four agents and the per capita nucleolus. The current approach is also focused on conflicting claims problems, a particular case of coalitional games. We provide the computation of the most well-known and used claims solutions: the proportional, the constrained equal awards, the constrained equal losses, the Talmud, the random arrival and the adjusted proportional rules.

[1]  Cori Vilella,et al.  The global carbon budget: a conflicting claims problem , 2016, Climatic Change.

[2]  Hervé Moulin,et al.  Axiomatic cost and surplus sharing , 2002 .

[3]  Elena Inarra,et al.  Restoring a Fish Stock: A Dynamic Bankruptcy Problem , 2008, Land Economics.

[4]  Robert J. Aumann,et al.  Linearity of unrestrictedly transferable utilities , 1960 .

[5]  Jaemin Shin,et al.  A semantic e-Kanban system for network-centric manufacturing: technology, scale-free convergence, value and cost-sharing considerations , 2012 .

[6]  M. Maschler The bargaining set, kernel, and nucleolus , 1992 .

[7]  William Thomson,et al.  Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update , 2015, Math. Soc. Sci..

[8]  D. Schmeidler The Nucleolus of a Characteristic Function Game , 1969 .

[9]  M. Plummer,et al.  CODA: convergence diagnosis and output analysis for MCMC , 2006 .

[10]  William Thomson,et al.  Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey , 2003, Math. Soc. Sci..

[11]  Martin Shubik,et al.  A Method for Evaluating the Distribution of Power in a Committee System , 1954, American Political Science Review.

[12]  E. Iñarra,et al.  Bankruptcy of Fishing Resources: The Northern European Anglerfish Fishery , 2002, Marine Resource Economics.

[13]  Jean Lemaire,et al.  Cooperative Game Theory and its Insurance Applications , 1991, ASTIN Bulletin.

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

[15]  Lech Krus,et al.  Cooperative game solution concepts to a cost allocation problem , 2000, Eur. J. Oper. Res..

[16]  Kurt Jörnsten,et al.  Common mistakes in computing the nucleolus , 2015, Eur. J. Oper. Res..

[17]  Attila Szolnoki,et al.  Coevolutionary Games - A Mini Review , 2009, Biosyst..

[18]  Ichiro Nishizaki,et al.  Fuzzy programming and profit and cost allocation for a production and transportation problem , 2001, Eur. J. Oper. Res..

[19]  Juan D. Moreno-Ternero,et al.  A common ground for resource and welfare egalitarianism , 2012, Games Econ. Behav..

[20]  Juan D. Moreno-Ternero,et al.  A Unifying Framework for the Problem of Adjudicating Conflicting Claims , 2011 .

[21]  C. Radhakrishna,et al.  Use of Cooperative Game Theory Concepts for Loss Allocation in Multiple Transaction Electricity Markets , 2009 .

[22]  L. Shapley A Value for n-person Games , 1988 .

[23]  A. Roth,et al.  Two-sided matching , 1990 .

[24]  J. Neumann,et al.  Theory of games and economic behavior , 1945, 100 Years of Math Milestones.

[25]  L. S. Shapley,et al.  17. A Value for n-Person Games , 1953 .

[26]  S. C. Littlechild,et al.  Aircraft Landing Fees: A Game Theory Approach , 1977 .

[27]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[28]  Marek Kaminski,et al.  Parametric rationing methods , 2006, Games Econ. Behav..

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

[30]  R. Gomory,et al.  A Primal Method for the Assignment and Transportation Problems , 1964 .

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

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

[33]  Brenton Kenkel,et al.  Estimating Extensive Form Games in R , 2014 .