Markov models of social dynamics: Theory and applications

This article shows how agent-based models of social dynamics can be treated rigorously and analytically as finite Markov processes, and their long-run properties are then given by an expanded version of the ergodic theorem for Markov processes. A Markov process model of a simplified market economy shows the fruitfulness of this approach.

[1]  D. Gale.  The law of supply and demand , 1955 .

[2]  H. Gintis,et al.  The Stability of Walrasian General Equilibrium , 2012 .

[3]  K. Arrow,et al.  EXISTENCE OF AN EQUILIBRIUM FOR A COMPETITIVE ECONOMY , 1954 .

[4]  Mauro Gallegati,et al.  Towards an Analytical Solution for Agent Based Models: An Application to a Credit Network Economy , 2011 .

[5]  R. Mantel.  Homothetic preferences and community excess demand functions , 1976 .

[6]  Sun Xiaomeng,et al.  Agent-based Microsimulation of Economy from A Complexity Perspective , 2000 .

[7]  H. Uzawa,et al.  Stability and Non-Negativity in a Walrasian Tatonnement Process , 1960 .

[8]  L. McKenzie,et al.  ON THE EXISTENCE OF GENERAL EQUILIBRIUM FOR A COMPETITIVE MARKET , 1959 .

[9]  A Stable Adjustment Process for a Competitive Economy , 1961 .

[10]  Venkatesh Bala,et al.  Chaotic tatonnement , 1993 .

[11]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[12]  D. Friedman.  Money-mediated disequilibrium processes in a pure exchange economy , 1979 .

[13]  L. Walras.  Elements of Pure Economics , 1954 .

[14]  Charles R. Plott,et al.  General equilibrium, markets, macroeconomics and money in a laboratory experimental environment , 1998 .

[15]  Frank Hahn,et al.  A THEOREM ON NON-TATONNEMENT STABILITY , 1962 .

[16]  A. Smithies.  The Stability of Competitive Equilibrium , 1942 .

[17]  A. Kirman.  Whom Or What Does the Representative Individual Represent , 1992 .

[18]  Donald G. Saari,et al.  Iterative Price Mechanisms , 1985 .

[19]  Harald Uhlig,et al.  Solving Nonlinear Stochastic Growth Models: a Comparison of Alternative Solution Methods , 1989 .

[20]  Benedikt Stefansson.  Swarm: An Object Oriented Simulation Platform Applied to Markets and Organizations , 1997, Evolutionary Programming.

[21]  R. Axtell.  The Complexity of Exchange , 1999 .

[22]  K. Arrow,et al.  General Competitive Analysis , 1971 .

[23]  T. Negishi,et al.  On the Formation of Prices , 1961 .

[24]  Donald W. Katzner.  The Walrasian Vision of the Microeconomy: An Elementary Exposition of the Structure of Modern General Equilibrium Theory , 1990 .

[25]  A. Rubinstein,et al.  Equilibrium in a market with sequential bargaining , 1985 .

[26]  Douglas Gale,et al.  Limit theorems for markets with sequential bargaining , 1987 .

[27]  COMPETITIVE STABILITY UNDER WEAK GROSS SUBSTITUTABILITY: NONLINEAR PRICE ADJUSTMENT AND ADAPTIVE EXPECTATIONS , 1962 .

[28]  P. Taylor,et al.  Evolutionarily Stable Strategies and Game Dynamics , 1978 .

[29]  A. Wald.  On Some Systems of Equations of Mathematical Economics , 1951 .

[30]  H. Uzawa,et al.  The Stability of Dynamic Processes , 1961 .

[31]  L. Hurwicz,et al.  SOME REMARKS ON THE EQUILIBRIA OF ECONOMIC SYSTEMS , 1960 .

[32]  T. Negishi.  WELFARE ECONOMICS AND EXISTENCE OF AN EQUILIBRIUM FOR A COMPETITIVE ECONOMY , 1960 .

[33]  H. Uzawa.  ON THE STABILITY OF EDGEWORTH'S BARTER PROCESS* , 1962 .

[34]  Hukukane Nikaido.  Stability of Equilibrium by the Brown-von Neumann Differential Equation , 1959 .

[35]  H. Sonnenschein.  Do Walras' identity and continuity characterize the class of community excess demand functions? , 1973 .

[36]  H. Scarf.  Some Examples of Global Instability of the Competitive Equilibrium , 1960 .

[37]  G. Debreu,et al.  Excess demand functions , 1974 .

[38]  Agent-Based Models of Organizations Handbook of Computational Economics II : Agent-Based Computational Economics , 2005 .

[39]  Herbert Gintis,et al.  The Dynamics of General Equilibrium , 2007 .

[40]  Donald G. Saari,et al.  Mathematical Complexity of Simple Economics , 1996 .

[41]  F. Bator.  American Economic Association The Simple Analytics of Welfare Maximization , 2007 .

[42]  Leigh Tesfatsion,et al.  Agent-Based Computational Economics: Growing Economies From the Bottom Up , 2002, Artificial Life.

[43]  L. McKenzie.  STABILITY OF EQUILIBRIUM AND THE VALUE OF POSITIVE EXCESS DEMAND , 1960 .

[44]  Duncan K. Foley,et al.  A Statistical Equilibrium Theory of Markets , 1994 .

[45]  Charles R. Plott,et al.  Global instability in experimental general equilibrium: the Scarf example , 2004, J. Econ. Theory.

[46]  F. Fisher.  Disequilibrium Foundations of Equilibrium Economics , 1984 .

[47]  D. Raphael,et al.  I: The Theory of Moral Sentiments , 1976 .

[48]  S. Smale,et al.  Exchange processes with price adjustment , 1976 .

[49]  L. Samuelson,et al.  Evolutionary Stability in Asymmetric Games , 1992 .

[50]  Hai Yang,et al.  ACM Transactions on Intelligent Systems and Technology - Special Section on Urban Computing , 2014 .

[51]  Gerard Debreu,et al.  A Social Equilibrium Existence Theorem* , 1952, Proceedings of the National Academy of Sciences.

[52]  R. Mantel.  On the characterization of aggregate excess demand , 1974 .

[53]  Bryan Ellickson,et al.  Competitive Equilibrium: Theory and Applications , 1994 .

[54]  Josef Hofbauer,et al.  Evolutionary Games and Population Dynamics , 1998 .

[55]  L. Hurwicz,et al.  ON THE STABILITY OF THE COMPETITIVE EQUILIBRIUM, I1 , 1958 .

[56]  H. Nikaidô.  ON THE CLASSICAL MULTILATERAL EXCHANGE PROBLEM , 1956 .

[57]  Ken Binmore,et al.  Matching and Bargaining in Dynamic Markets , 1988 .

[58]  Claus Weddepohl.  Simulating tatonnement in a production economy , 1997 .