Catastrophe theory and dynamic games
Tài liệu tham khảo
CohenL. (1979). “Cyclic sets in multidimensional voting models,” J. Econ. Theory 20: 1–12.
DebreuG. (1976). “The application to economics of differential topology and global analysis: regular differentiable economies,” Am. Econ. Review 66: 280–287.
DownsA. (1957). Economic Theory of Democracy. New York: Harper and Row.
FreyB. and GarbersH. (1971). “Politico-econometrics: an estimation in political economy,” Political Studies 19: 316–320.
GilpinM.E. (1975). Group Selection in Predator Prey Communities. Princeton, New Jersey: Princeton University Press.
GolubitskyM. and GuilleminV. (1973). Stable Mappings and their Singularities. Berlin: Springer Verlag.
GreenbergJ. (1979). “Consistent majority rules over compact sets of alternatives,” Econometrica 47: 627–636.
GribbinJ. (1976). Forecasts, Famines and Freezes. New York: Walker and Co.
HirschM. and SmaleS. (1974). Differential Equations, Dynamical systems and Linear Algebra. New York: Academic Press.
IsnardC.A. and ZeemanE.C. (1976). “Some models from catastrophe theory in the social sciences,” in L.Collins (Ed.), The Use of Models in the Social Sciences. London: Tavistock Publications.
KramerG.H. (1973). “On a class of equilibrium conditions for majority rule,” Econometrica 41: 285–297.
KramerG.H. and KlevorickA.H. (1974). “Existence of a local co-operative equilibrium in a class of voting games,” Rev. Econ. Studies 41: 539–547.
LiT.Y. and YorkeJ.A. (1975). “Period Three implies chaos,” American Mathematical Monthly 82: 985–992.
Matthews, S.A. (1977). Undominated directions in simple games. Mimeo, California Institute of Technology.
Matthews, S.A. (1978). Pairwise symmetry conditions for voting equilibria. Mimeo, California Institute of Technology.
MayR.D. (1972). “Limit cycles in predator prey communities,” Science 177: 900–902.
MayR.D. (1974). “Biological populations with non-overlapping generations: stable points, cycles and chaos,” Science 186: 645–647.
MayR.D. (1975). “Biological populations obeying difference equations, stable points, stable cycles and chaos,” Journal of Theoretical Biology 51: 511–524.
MayR.D. and LeonardW. (1975). “Non-linear aspects of competition between three species,” SIAM Journal of Applied Mathematics 29: 243–252.
McKelveyR.D. (1976). “Intransitivities in multidimensional voting models and some implications for agenda control,” J. Econ. Theory 12: 472–482.
McKelveyR.D. (1979). “General conditions for global intransitivities in formal voting models: some implications for agenda control,” Econometrica 47: 1085–1111.
MeloW.de (1977). “Accessibility of an optimum,” in J.Palis and M.doCarmo, (Eds.), Geometry and Topology III. Berlin: Springer Verlag.
OsterG. and GuckenheimerJ. (1976). “Bifurcation phenomena in population models,” in J.E.Marsden and M.McCracken (Eds.), The Hopf Bifurcation and its Applications. Berlin: Springer Verlag.
PeixotoM. (1962). “Structural stbility on two-dimensional manifolds,” Topology 1: 101–120.
PlottC.R. (1967). “A notion of equilibrium and its possibility under majority rule,” Am. Econ. Rev. 57: 787–806.
RandD. (1976). “Thresholds in pareto sets,” J. Math. Econ. 3: 139–154.
RandD. (1978). “Exotic phenomena in games and duopoly models,” J. Math. Econ. 5: 173–184.
RubinsteinA. (1979). “A note about the “nowhere denseness” of societies having an equilibrium under majority rule,” Econometrica 47: 511–514.
SallesM. and WendellR.E. (1977). “A further result on the core of voting games,” Int. J. Game Theory 6: 35–40.
SenA.K. and PattanaikP.K. (1969). “Necessary and sufficient conditions for rational choice under majority decisions,” Journal of Economic Theory 1: 178–202.
SchofieldN. (1977a). “Transitivity of preferences on a smooth manifold of alternatives, Journal of Economic Theory 14: 149–171.
SchofieldN. (1977b). ‘Dynamic games of collective action,” Public Choise 30: 77–105.
SchofieldN. (1978a). “Instability of simple dynamic games,” Review Econ. Studies 65: 575–594.
Schofield, N. (1978b). Generic Instability of Voting Games. Presented at the Public Choice Meeting, March, New Orleans.
SchofieldN. (1978c). “The theory of dynamic games,” in P.C.Ordeshook (Ed.), Game Theory and Political Science. New York: New York University Press.
Schofield, N. (1980a). “Generic properties of simple Bergson Samuelson preference functions,” J. Math. Econ., in press.
SchofieldN. (1980b). “Individual and collective rationality,” in E.Vedung and L.Lewin (Eds.), Politics as Rational Action. Dordrecht, Holland: Reidel.
SimonC.P. and TitusC. (1975). “Characterization of optima in smooth pareto economic systems,” J. Math. Econ. 2: 297–330.
SmaleS. (1966). “Structurally stable systems are not dense,” Am. J. Math. 88: 491–496.
SmaleS. (1967). “Differential dynamic systems,” Bull. Am. Math. Soc. 73: 747–817.
SmaleS. (1973). “Global analysis and economics I: Pareto optimum and a generalization of Morse theory,” pp. 531–544 in M.Peixoto (Ed.), Dynamical Systems. New York: Academic Press.
SmaleS. (1974). “Global analysis and economics III: Pareto optima and price equilibria, J. Math. Econ. 1: 107–118.
SmaleS. (1976a). “On the differential equations of species in competition,” J. Math. Biol. 3: 5–7.
SmaleS. (1976b). “Exchange processes with price adjustment,” J. Math. Econ. 3: 211–226.
ThomR. (1972, 1975). Structural Stability and Morphogenesis: An Outline of a General Theory of Models. Reading. Mass: Benjamin. (Revised edition 1975, translated by D.H. Fowler.)
TullockG. (1967). “The general irrelevance of the general impossibility theorem,” Towards a Mathematics of Polities. Ann Arbor: University of Michigan Press, Chpt. III.
Zeeman, E.C. (1968). Lecture Notes on Dynamical Systems. Aarhus University.