This is the first volume in a three-volume exposition of Martin Shubik’s vision of “mathematical institutional mathematics” — a term he coined in 1959 to describe the theoretical underpinnings needed for the construction of an economic dynamics. The goal is to develop a process-oriented theory of money and financial institutions that reconciles micro- and macroeconomics, using as a prime tool the theory of games in strategic and extensive form. The approach involves a search for minimal financial institutions that appear as a logical, technological, and institutional necessity, as part of the “rules of the game.” Money and financial institutions are assumed to be the basic elements of the network that transmits the sociopolitical imperatives to the economy.
Volume 1 deals with a one-period approach to economic exchange with money, debt, and bankruptcy. Volume 2 explores the new economic features that arise when we consider multiperiod finite and infinite horizon economies. Volume 3 will consider the specific role of financial institutions and government, and formulae the economic financial control problem linking micro- and macroeconomics.
This book presents Martin Shubik’s important contribution to the development of game theory, and shows how game theory methods can be used in the study of prices, money and financial institutions.
After introducing the reader to his career and the influences which developed his research, Professor Martin Shubik addresses the price system considering issues such as competitive equilibrium, economic exchange and production. He explores the competitive price system and the emergence of money and financial systems to develop a theory of monetary and financial institutions. Specifically, he examines the role of money in the economy using both cooperative and non-cooperative solutions in game theory. Throughout the book Martin Shubik stresses that the value of games, which can be both played and analysed, provides an important link between theory and process and institutional studies.
There is a natural tradeoff between the benefits of increasing the number of competitors in an insurance market and the drawback to the weakening of the law of large numbers due to the diminishing of average reserves. In this investigation we consider the possibility for optimal layers of reinsurance and retrocession in the design of the insurance industry. A general question which may be asked of all financial institutions is what factors limit the number of layers of paper which can be constructed?
This book presents the most important published articles of Martin Shubik who has made a path-breaking contribution to game theory and political economy. The volume shows how game theory can be used to explore fundamental problems in economics, political science and operations research.
The book opens with an introduction to the career of Martin Shubik and the influences which have shaped his research. In this, and the chapters which follow, Martin Shubik stresses the importance of formulative models as playable games and the treatment of information to describe decision making among individuals, using examples from industrial organization. He demonstrates that games are a fruitful way to extend our knowledge of competition among the few. In addition, he considers the importance of gaming in economics and business suggesting that experimental games can be used to illustrate problems and principles in multi-person decision making.
The basic distinction in the optimization conditions between the general equilibrium model of a T period exchange economy and a strategic market game process model is between a set of equations homogeneous of order zero and a set of nonhomogeneous equations. The latter have an amount M of outside or fiat money added to the system. If there is an outside bank willing to lend or accept deposits at an interest rate rho > 0 at the end of time T the initial amount of money M will have been consumed in interest payments to the outside bank. The price level is fully determined and in an economy where all assets are traded, the float is financed efficiently, otherwise there is a price wedge between buying and selling prices.
We construct stationary Markov equilibria for an economy with fiat money, one non-durable commodity, countably-many time periods, and a continuum of agents. The total production of commodity remains constant, but individual agents’ endowments fluctuate in a random fashion, from period to period. In order to hedge against these random fluctuations, agents find it useful to hold fiat money which they can borrow or deposit at appropriate rates of interest; such activity may take place either at a central bank (which fixes interest rates judiciously) or through a money-market (in which interest rates are determined endogenously).
We carry out an equilibrium analysis, based on a careful study of Dynamic Programming equations and on properties of the Invariant Measures for associated optimally-controlled Markov chains. This analysis yields the stationary distribution of wealth across agents, as well as the stationary price (for the commodity) and interest rates (for the borrowing and lending of fiat money).
A distinctive feature of our analysis is the incorporation of bankruptcy, both as a real possibility in an individual agent’s optimization problem, as well as a determinant of interest rates through appropriate balance equations. These allow a central bank (respectively, a money-market) to announce (respectively, to determine endogenously) interest rates in a way that conserves the total money-supply and controls inflation.
General results are provided for the existence of such stationary equilibria, and several explicitly solvable examples are treated in detail.
A discussion of some of the problems in the utilization of game theoretic solution concepts is given. It is suggested that a considerable broadening of solution concepts is called for to take into account sufficient context. Mass agent simulations appear to offer promise for some economic and societal problems.
A discussion of some of the problems in the utilization of game theoretic solution concepts is given. It is suggested that a considerable broadening of solution concepts is called for to take into account sufficient context. Mass agent simulations appear to offer promise for some economic and societal problems.
Over many years some simple cooperative games have been considered in lectures on game theory. The games were selected in order to provide insight into various normative theories of solution to n-person games. It is suggested that the results indicate that when solutions have outcomes in common, predictability is higher than when they are apart. The core is attractive but less so when it is heavily nonsymmetric.
Over many years some simple cooperative games have been considered in lectures on game theory. The games were selected in order to provide insight into various normative theories of solution to n-person games. It is suggested that the results indicate that when solutions have outcomes in common, predictability is higher than when they are apart. The core is attractive but less so when it is heavily nonsymmetric.
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 Lévy 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 large, the market price is generally locked within the price range they define