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Martin Shubik Publications

Publish Date
Abstract

The exchange economy E can be reformulated as a strategic market game. In particular the point of concern here involves the introduction of a specified amount of credit or fiat money to monetize exchange. Dubey and Shubik (1979) and Shubik and Wilson (1977) have studied the possibility of introducing a fixed amount M of money to finance trade. When one formulates exchange as a game of strategy using any form of credit or fiat money where there is any possibility whatsoever that an individual will be unable to pay back that which he has borrowed, the rules of the game require that the procedure to be followed in case of default must be specified. This is not a mere institutional detail but a logical necessity. It is however reasonable to expect that one might try to design a default penalty sufficiently harsh to discourage strategic default.

Abstract

Suppose that we reformulate the exchange economy as a strategic market game. As all purchases are paid for in cash it is possible to attach precise meaning to what is meant by enough money. As the game is a single simultaneous bid and offered at m trading posts and m prices are all simultaneously determined, in essence the trading technology is completely specified.

Economics Letters
Abstract

The exchange economy E can be reformulated as a strategic market game. In particular the point of concern here involves the introduction of a specified amount of credit or fiat money to monetize exchange. Dubey and Shubik (1979) and Shubik and Wilson (1977) have studied the possibility of introducing a fixed amount M of money to finance trade. When one formulates exchange as a game of strategy using any form of credit or fiat money where there is any possibility whatsoever that an individual will be unable to pay back that which he has borrowed, the rules of the game require that the procedure to be followed in case of default must be specified. This is not a mere institutional detail but a logical necessity. It is however reasonable to expect that one might try to design a default penalty sufficiently harsh to discourage strategic default.

JEL Classification: 021, 026

Keywords: Cash flow competitive equilibrium, Strategic market games

Abstract

Suppose that we reformulate the exchange economy as a strategic market game. As all purchases are paid for in cash it is possible to attach precise meaning to what is meant by enough money. As the game is a single simultaneous bid and offered at m trading posts and m prices are all simultaneously determined, in essence the trading technology is completely specified.

JEL Classification: 021, 026

Keywords: Exchange economy, strategic market game; commodity money

Abstract

In this paper we paint with a broad brush. Our purpose is to present an overview, a status report, and by implication, an indication of what needs to be done at this time. We first provide a survey of topics in the economics of defense and in economic warfare, then we comment on some naval aspects of these topics.

Abstract

This paper takes the context of political and military command as given and considers the fundamental question of how a modern navy fits in with the usual conception of nuclear deterrence between the United States and the Soviet Union. We here summarize the major issues, questions, and conclusions from this research as they serve to provide the context for our observations on the relevance of and potential for operations research and decision sciences contributions to providing understanding and analysis for these critical and highly qualitative problems.

Abstract

The central contribution of game theory to defense analysis has been a language for the understanding of how to formulate and study strategic or cross-purposes optimization in situations involving two or more actors. It is suggested here in this discussion that two fundamentally different classes of application of game theory to problems in defense have emerged. The first is the application of two-person zero sum game theory to military, primarily tactical situations which for the purposes at hand can be reasonably well modeled in this manner. The second is the application of two or more person nonconstant sum game theory to strategic problems involving threat analysis, crises control and the interface between international diplomatic relations and war.

Abstract

The central contribution of game theory to defense analysis has been a language for the understanding of how to formulate and study strategic or cross-purposes optimization in situations involving two or more actors. It is suggested here in this discussion that two fundamentally different classes of application of game theory to problems in defense have emerged. The first is the application of two-person zero sum game theory to military, primarily tactical situations which for the purposes at hand can be reasonably well modeled in this manner. The second is the application of two or more person nonconstant sum game theory to strategic problems involving threat analysis, crises control and the interface between international diplomatic relations and war.

JEL Classification: 114, 026

Keywords: Game theory, war, national defense

Abstract

Among the major properties of a money are that it can serve as (1) a numeraire, (2) a means of exchange, (3) a store of value, and (4) a source of liquidity. Among the lesser properties are that it should be easy to transport and identify, it should be durable, easily divisible, hard to counterfeit and easy to store. A possibly desirable property is that it is an anonymous “bearer instrument,” but the price of anonymity is that it is hard to recover if it is stolen. A personal check which is bank money can be stopped and is more personal than a $100 bill. The properties of a money are systemic and strategic and are most naturally formalized by means of strategic market games. Here we concentrate on the four major properties noted above and include comments on the cost of liquidity and the role of various assets as near monies.

Abstract

Among the major properties of a money are that it can serve as (1) a numeraire, (2) a means of exchange, (3) a store of value, and (4) a source of liquidity. Among the lesser properties are that it should be easy to transport and identify, it should be durable, easily divisible, hard to counterfeit and easy to store. A possibly desirable property is that it is an anonymous “bearer instrument,” but the price of anonymity is that it is hard to recover if it is stolen. A personal check which is bank money can be stopped and is more personal than a $100 bill. The properties of a money are systemic and strategic and are most naturally formalized by means of strategic market games. Here we concentrate on the four major properties noted above and include comments on the cost of liquidity and the role of various assets as near monies.

JEL Classification: 023, 310

Keywords: Strategic market games, Properties of money

Abstract

If an exchange economy is modeled as a strategic market game with one commodity serving as a money, then if there is no credit available and if all traders are insignificant in size, so that an individual does not influence prices, the noncooperative equilibria (NEs) of the game will coincide with the competitive equilibria of the exchange economy provided that there is enough money to facilitate trade. The meaning of ‘enough money’ is that the NEs are interior. In other words the constraint that an individual cannot spend more of the means of payment than he holds is not binding on any individual’s plans. The condition on enough money is characterized both by the total amount of money in the system and its distribution. It is possible that an economy may not have enough money no matter how it is distributed; it is also possible that a redistribution will give rise to interior solutions. These statements are made precise and illustrated by means of specific examples. If there is enough money but it is maldistributed it is shown that a loan market ‘100 per cent backed by gold’ will bring efficiency.

Abstract

If an exchange economy is modeled as a strategic market game with one commodity serving as a money, then if there is no credit available and if all traders are insignificant in size, so that an individual does not influence prices, the noncooperative equilibria (NEs) of the game will coincide with the competitive equilibria of the exchange economy provided that there is enough money to facilitate trade. The meaning of ‘enough money’ is that the NEs are interior. In other words the constraint that an individual cannot spend more of the means of payment than he holds is not binding on any individual’s plans. The condition on enough money is characterized both by the total amount of money in the system and its distribution. It is possible that an economy may not have enough money no matter how it is distributed; it is also possible that a redistribution will give rise to interior solutions. These statements are made precise and illustrated by means of specific examples. If there is enough money but it is maldistributed it is shown that a loan market ‘100 per cent backed by gold’ will bring efficiency.

JEL Classification: 021

Keywords: Strategic market game, Noncooperative equilibria, Enough money, Money