13 research outputs found
Construction of Stationary Markov Equilibria in a Strategic Market Game
This paper studies stationary noncooperative equilibria in an economy with fiat money , one nondurable commodity , countably many time periods, no credit or futures market, and a measure space of agents — who may differ in their preferences and in the distributions of their (random) endowments. These agents are immortal, and hold fiat money as a means of hedging against the random fluctuations in their endowments of the commodity. In the aggregate, these fluctuations offset each other, and equilibrium prices are constant. We carry out an equilibrium analysis that focuses on distribution of wealth, on consumption, and on price formation. A careful analysis of the one-agent, infinite-horizon optimization problem, and of the invariant measure for the associated optimally controlled Markov chain, leads by aggregation to a stationary noncooperative or competitive equilibrium . This consists of a price for the commodity and of a distribution of wealth across agents which, under appropriate simple strategies for the agents, stay fixed from period to period and preserve the basic quantities of the model. We hope that, in future work, we shall be able to address additional features of the model treated here, such as borrowing and lending at appropriate (endogenously determined) interest rates, the endogenous production of the commodity, overlapping generations of agents, and bankruptcy and treatment of creditors
Selecting a Unique Competitive Equilibrium with Default Penalties
The enlargement of the general-equilibrium structure to allow default subject to penalties results in a construction of a simple mechanism for selecting a unique competitive equilibrium. We consider economies for which a common credit money can be applied to uniquely select any competitive equilibrium with suitable default penalties. We identify two classes of such economies. One consists of economies with utility functions being homogeneous of degree 1; the other consists of economies with the number of consumers equal to the number of commodities and traders having quasi-linear utility functions with respect to different commodities.Competitive equilibrium, Credit mechanism, Marginal utility of income, Welfare economics
The Present and Future of Game Theory
A broad nontechnical coverage of many of the developments in game theory since the 1950s is given together with some comments on important open problems and where some of the developments may take place. The nearly 90 references given serve only as a minimal guide to the many thousands of books and articles that have been written. The purpose here is to present a broad brush picture of the many areas of study and application that have come into being. The use of deep techniques flourishes best when it stays in touch with application. There is a vital symbiotic relationship between good theory and practice. The breakneck speed of development of game theory calls for an appreciation of both the many realities of conflict, coordination and cooperation and the abstract investigation of all of them.Game theory, Application and theory, Social sciences, Law, Experimental gaming, conflict, Coordination and cooperation
Innovation and Equilibrium?
A discussion is given of the problems involved in the formal modeling of the innovation process. The link between innovation and finance is stressed. The nature of how the circular flow of funds is broken and the role of finance in evaluation and control is discussed.Innovation, Invention, Circular flow, Finance
Innovation and Equilibrium?
A discussion is given of the problems involved in the formal modeling of the innovation process. The link between innovation and finance is stressed. The nature of how the circular flow of funds is broken and the role of finance in evaluation and control is discussed
Price Variations in a Stock Market With Many Agents
Large variations in stock prices happen with sufficient frequency to raise
doubts about existing models, which all fail to account for non-Gaussian
statistics. We construct simple models of a stock market, and argue that the
large variations may be due to a crowd effect, where agents imitate each
other's behavior. The variations over different time scales can be related to
each other in a systematic way, similar to the Levy stable distribution
proposed by Mandelbrot to describe real market indices. In the simplest, least
realistic case, exact results for the statistics of the variations are derived
by mapping onto a model of diffusing and annihilating particles, which has been
solved by quantum field theory methods. When the agents imitate each other and
respond to recent market volatility, different scaling behavior is obtained. In
this case the statistics of price variations is consistent with empirical
observations. The interplay between ``rational'' traders whose behavior is
derived from fundamental analysis of the stock, including dividends, and
``noise traders'', whose behavior is governed solely by studying the market
dynamics, is investigated. When the relative number of rational traders is
small, ``bubbles'' often occur, where the market price moves outside the range
justified by fundamental market analysis. When the number of rational traders
is larger, the market price is generally locked within the price range they
define.Comment: 39 pages (Latex) + 20 Figures and missing Figure 1 (sorry), submitted
to J. Math. Eco
The Theory of Money and Financial Institutions
A sketch of a game theoretic approach to the Theory of Money and Financial Institutions is presented in a nontechnical, nonmathematical manner. The detailed argument and specifics are presented in previous articles and in a forthcoming book.
Competitive Equilibria of Economies with a Continuum of Consumers and Aggregate Shocks
This paper studies competitive equilibria of a production economy with aggregate productivity shocks and with a continuum of consumers subject to borrowing constraints and individual labor endowment shocks. The dynamic economy is described in terms of sequences of aggregate distributions. The existence of competitive equilibrium is proven and a recursive characterization is established. In particular, it is shown that for any competitive equilibrium, there is a first period payoff equivalent competitive equilibrium that is generated by a recursive equilibrium with the state space including expected discounted utilities.