Cooperative n-person Stackelberg games

Stackelberg games and their resulting nonconvex programming problems can be used to model the behavior of independent decision-makers acting within a hierarchy. An examination is made of the formation of coalitions within such organizations of optimizers for a large class of hierarchical problems. The mathematical characteristics of these games and the implications of their solutions are considered.<<ETX>>

[1]  Jonathan F. Bard.  An Algorithm for Solving the General Bilevel Programming Problem , 1983, Math. Oper. Res..

[2]  Wayne F. Bialas,et al.  Two-Level Linear Programming , 1984 .

[3]  William F. Lucas,et al.  An Overview of the Mathematical Theory of Games , 1972 .

[4]  H. Raiffa,et al.  Games and Decisions: Introduction and Critical Survey. , 1958 .

[5]  Alan S. Manne,et al.  Multi-level Planning: Case Studies in Mexico , 1973 .

[6]  J. Friedman.  Game theory with applications to economics , 1986 .

[7]  Y. Dirickx,et al.  Systems Analysis by Multilevel Methods: With Applications to Economics and Management , 1981 .

[8]  Michael Maschler,et al.  The Power of a Coalition , 1963 .

[9]  R. L. Keeney,et al.  Decisions with Multiple Objectives: Preferences and Value Trade-Offs , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[10]  T. Caplow.  Further Development of a Theory of Coalitions in the Triad , 1959, American Journal of Sociology.

[11]  George B. Dantzig,et al.  Decomposition Principle for Linear Programs , 1960 .

[12]  W. E. Vinacke,et al.  An Experimental Study of Coalitions in the Triad , 1957 .

[13]  Jonathan F. Bard,et al.  An explicit solution to the multi-level programming problem , 1982, Comput. Oper. Res..

[14]  Ue-Pyng Wen,et al.  Mathematical methods for multilevel linear programming , 1981 .

[15]  Wilfred Candler,et al.  A linear two-level programming problem, , 1982, Comput. Oper. Res..

[16]  Stelios Kafandaris,et al.  Systems Analysis by Multilevel Methods; With Applications to Economics and Management , 1980 .

[17]  G. Owen,et al.  Game Theory (2nd Ed.). , 1983 .

[18]  Tjalling C. Koopmans.  Note on a social system composed of hierarchies with overlapping personnel , 1969 .

[19]  J. Bard.  Optimality conditions for the bilevel programming problem , 1984 .

[20]  Richard E. Wendell,et al.  Multiple Objective Mathematical Programming with Respect to Multiple Decision-Makers , 1980, Oper. Res..

[21]  Mark Karwan,et al.  Multilevel optimization: A mathematical programming perspective , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[22]  Louis J. Billera,et al.  Global Stability in n-Person Games , 1972 .

[23]  Bezalel Peleg,et al.  An inductive method for constructing mimmal balanced collections of finite sets , 1965 .

[24]  Wayne Bialas,et al.  Coalition formation in n-person stackelberg games , 1982, 1982 21st IEEE Conference on Decision and Control.

[25]  R. Brandis.  The Limits of Organization , 1975 .

[26]  Yacov Y. Haimes,et al.  Computational Results for Water Pollution Taxation Using Multilevel Approach , 1972 .

[27]  R. Radner,et al.  Economic theory of teams , 1972 .

[28]  Harold P. Benson,et al.  On the structure and properties of a linear multilevel programming problem , 1989 .

[29]  P. P. Shenoy,et al.  On coalition formation in simple games: A mathematical analysis of Caplow's and Gamson's theories☆ , 1978 .

[30]  T. Caplow.  A Theory of Coalitions in the Triad , 1956 .

[31]  B. Tolwinski.  Closed-loop Stackelberg solution to a multistage linear-quadratic game , 1981 .

[32]  Arnoldo C. Hax,et al.  Feature Article - Organizational Design: A Survey and an Approach , 1981, Oper. Res..

[33]  Heinrich von Stackelberg,et al.  Stackelberg (Heinrich von) - The Theory of the Market Economy, translated from the German and with an introduction by Alan T. PEACOCK. , 1953 .

[34]  Peter B. Luh,et al.  A control-theoretic view on incentives , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[35]  George B. Dantzig,et al.  Linear programming and extensions , 1965 .

[36]  Lloyd S. Shapley,et al.  On balanced sets and cores , 1967 .

[37]  Wayne F. Bialas,et al.  On two-level optimization , 1982 .

[38]  James W. Friedman,et al.  Oligopoly and the theory of games , 1977 .

[39]  P. P. Shenoy,et al.  On coalition formation: a game-theoretical approach , 1979 .

[40]  R. Cassidy,et al.  Efficient Distribution of Resources Through Three Levels of Government , 1971 .

[41]  Martin J. Beckmann.  Tinbergen lectures on organization theory , 1983 .

[42]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

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

[44]  A. Stechow,et al.  Decomposition , 1902, The Indian medical gazette.

[45]  Martin J. Beckmann,et al.  Rank in organizations , 1978 .

[46]  J. Cruz,et al.  On the Stackelberg strategy in nonzero-sum games , 1973 .

[47]  Arnoldo C. Hax,et al.  Hierarchical integration of production planning and scheduling , 1973 .

[48]  J. Nash,et al.  NON-COOPERATIVE GAMES , 1951, Classics in Game Theory.

[49]  Ue-Pyng Wen,et al.  The hybrid algorithm for solving the three-level linear programming problem , 1986, Comput. Oper. Res..

[50]  Yu-Chi Ho,et al.  A control-theoretic view on incentives , 1980 .

[51]  L. Shapley,et al.  ON MARKET GAMES , 1969, Classics in Game Theory.

[52]  José Fortuny-Amat,et al.  A Representation and Economic Interpretation of a Two-Level Programming Problem , 1981 .

[53]  T. Fabian,et al.  Decomposition, Pricing for Decentralization and External Economies , 1964 .

[54]  William A. Gamson,et al.  A theory of coalition formation , 1961 .

[55]  G. Papavassilopoulos.  Stochastic quadratic Nash and leader-follower games , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[56]  W. Lucas,et al.  N‐person games in partition function form , 1963 .