Martin Shubik Publications

The interaction of capital stock with overlapping generations is investigated where the time structures of human capital and other physical capital does not match. We consider the economies with either gold or fiat as the outside money and consider the financing problems that appear in the financing of capital stock. The complexity of the underlying physical structure combined with concern for efficiency and equity help to determine the financial structure.

This essay considers the potential for utilizing web games for research and teaching. It discusses a specific gaming facility that has been constructed and utilized. The gaming facility can be made available for use for those interested in utilizing it for teaching and/or research purposes. The goal is to have this facility be of use for both single play and repeated matrix games. Much of the discussion here is aimed at single play games as a desirable benchmark preliminary to the study of repeated games. Properties of the one stage games are discussed and instructions for the use of the system are supplied. Extensions to multistage games and incomplete information are noted.

This essay considers the potential for utilizing web games for research and teaching. It discusses a specific gaming facility that has been constructed and utilized. The gaming facility can be made available for use for those interested in utilizing it for teaching and/or research purposes. The goal is to have this facility be of use for both single play and repeated matrix games. Much of the discussion here is aimed at single play games as a desirable benchmark preliminary to the study of repeated games. Properties of the one stage games are discussed and instructions for the use of the system are supplied. Extensions to multistage games and incomplete information are noted.

We use a laboratory experiment to compare general equilibrium economies in which agents individually allocate their private goods among consumption, investment in production and maintenance of a depreciating public facility. The public facility is financed either by voluntary anonymous contributions (VAC) or taxes. We find that rates of taxation chosen by majority vote remain at an intermediate level, converging neither to zero nor to 100%, and the experimental economies sustain public goods at levels between the finite- and infinite-horizon optima. This contrasts with a rapid decline of public goods under voluntary anonymous contributions (VAC). Both the payoff efficiency and production of private goods are higher when taxes are set endogenously instead of being fixed at the optimum level. When subjects choose between VAC and taxation, 23 out of 24 majority votes favor taxation.

We use a laboratory experiment to compare general equilibrium economies in which agents individually allocate their private goods among consumption, investment in production, and replenishing/ refurbishing a depreciating public facility in a dynamic game with long-term investment opportunities. The public facility is financed either by voluntary anonymous contributions (VAC) or taxes. We find that rates of taxation chosen by majority vote remain at an intermediate level (far from zero or 100%), and the experimental economies sustain public goods at levels between the finite- and infinite-horizon optima. This contrasts with a rapid decline of public goods under VAC. Both the payoff efficiency and production of private goods are higher when taxes are set endogenously instead of being fixed at the optimum level externally. When subjects choose between VAC and taxation, 23 out of 24 majority votes favor taxation.

We compare general equilibrium economies in which building and maintenance of a depreciating public facility is financed either by anonymous voluntary contributions or by taxing agents on their income from private production. Agents start with an endowment of private goods and money, while the government starts with an endowment of public good and money. All private goods produced are tendered for sale in exchange for money in a sell-all market mechanism. Agents’ proceeds from sale are taxed, and they individually allocate their private goods between current consumption and investment in production for the following period. The optimal levels of supply of the public good, and tax rate to sustain it over time, are defined and calculated for infinite and finite horizons. These equilibrium theoretical predications are compared to the outcomes of laboratory economies when (1) the starting public facility is either at or below the optimal level; and (2) the tax rate is either exogenously set at the optimal level, or at the median of rates proposed by individual agents. We find that the experimental economies sustain public goods at about 70-90 percent of the infinite horizon but considerably more than the finite horizon optimum. Payoffs (efficiency) is at 90 percent of the infinite horizon equilibrium level even when the rate of taxation is determined by voting. Starting conditions play only a minor role for outcomes of the economies, as efficiency and the stock of public good adjusts to about the same level irrespective of the starting level. These results contrast with rapid decline in provision of public goods under anonymous voluntary contributions, and point to the possibility that the social institution of government enforced taxation may have evolved to address the problem of under-production of public goods through anonymous voluntary contributions.

Three models of a monetary economy are considered, in order to show the effects of a gold demonetization: the first with a gold money, the second with demonetized gold but no central bank, and the third with demonetized gold, but with a central bank. The distinctions between ownership and control are discussed.

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.

Modifying a parallel dynamic programming approach to a simple deterministic economy, we consider the effect of an innovation in the means of production. The success of the innovation is assumed to depend on the availability of financing, locus of financial control, the amount of resources invested, and on a random event. The relationship between money and physical assets is critical. In this first part stress is laid on the innovation behavior of Robinson Crusoe in a premonetary economy, then on his actions in a monetary economy in partial equilibrium. Part 2 considers the closed monetary economy with several differentiated agents.

The possibility of the presence of multiple equilibria in closed exchange and production-and-exchange economies is usually ignored in macroeconomic models even though they are important in real economies. We argue that default and bankruptcy laws serve to provide the conditions for uniqueness of an equilibrium. In this paper, we report experimental evidence on the effectiveness of this approach to resolving multiplicity: a society can assign default penalties on fiat money so that the economy selects one of the equilibria. The laboratory data show that the choice of default penalty takes the economy near the chosen equilibrium. The theory and evidence together reinforce the idea that accounting, bankruptcy and possibly other aspects of social mechanisms play an important role in resolving the otherwise mathematically intractable challenges associated with multiplicity of equilibria in closed economies.

Closed exchange and production-and-exchange economies may have multiple equilibria, a fact that is usually ignored in macroeconomic models. Our basic argument is that default and bankruptcy laws are required to prevent strategic default, and these laws can also serve to provide the conditions for uniqueness. In this paper we report experimental evidence on the effectiveness of this approach to resolving multiplicity: society can assign default penalties on fiat money so the economy selects one of the equilibria. Our data show that the choice of default penalty takes the economy to the neighborhood of the chosen equilibrium. The theory and evidence together reinforce the idea that accounting, bankruptcy and possibly other aspects of social mechanisms play an important role in resolving the otherwise mathematically intractable challenges associated with multiplicity of equilibria in closed economies. Additionally we discuss the meaning and experimental implications of default penalties that support an active bankruptcy-modified competitive equilibrium.