Game Theory in International Economics

J. McMillan

• Publisher: Routledge
• Year: 2013
• Print ISBN: 9780415488402
• eBook ISBN: 9781136454448
• Edition: 1
• Topic: Business
• Subtopic: Business General
• Index: Business

This book gives an early demonstration of applications of game theory to international economics - applications that were to transform this area during the 1990s.

Game theory in international economics

JOHN McMILLAN¹
(Revised July, 1984)

1. STRATEGY AND TRADE

THE THEORY OF GAMES provides a set of mathematical techniques for analyzing situations in which each agent’s utility depends not only on his own actions but also on the actions of others; and all of the agents take these interdependencies into account when deciding their actions. Von Neumann and Morgenstern explained the difference between a game-theoretic problem and an optimization problem of the sort more traditionally solved in economic theory, such as a single consumer’s maximization problem:

Consider now a participant in a social exchange economy. His problem has, of course, many elements in common with a maximum problem. But it also contains some, very essential, elements of an entirely different nature. He too tries to obtain an optimum result. But in order to achieve this, he must enter into relations of exchange with others. If two or more persons exchange goods with each other, then the result for each one will depend in general not merely upon his own actions but on those of the others as well. Thus each participant attempts to maximize a function (his above-mentioned “result”) of which he does not control all variables. This is certainly no maximum problem, but a peculiar and disconcerting mixture of several conflicting maximum problems. Every participant is guided by another principle and neither determines all variables which affect his interest. This kind of problem is nowhere dealt with in classical mathematics [159, pp. 10–11].

Game theory has had little influence on the theory of international economics: little mention of game theory is to be found in the trade-theory textbooks. Despite game theory’s lack of impact on the body of trade theory, many of the important policy issues of international economics have some game-theoretic character: negotiations over mutual reductions of tariffs, either bilaterally or under the General Agreement on Tariffs and Trade; the international indebtedness and threatened default of some less-developed countries, such as Brazil and Mexico; the formation and preservation of customs unions, such as the European Economic Community; issues of international common property, addressed in the Law of the Sea Conference; the establishment of cartels to raise the price of internationally traded commodities, such as the Organization of Petroleum Exporting Countries; the extent to which competition from foreign firms removes the need to use antitrust provisions to restrain domestic monopolies; the international implications of domestic macroeconomic policies, such as high interest rates in the United States or persistent Japanese balance-of-payments surpluses; the international coordination of policies to stabilize the volatile prices of the exports of less-developed countries; the sharing of costs and responsibilities within international alliances, such as the North Atlantic Treaty Organization; the possible international redistributions of income considered in the North-South debate; the use of trade as a weapon in political warfare, such as the sanctions imposed on Rhodesia and the Soviet Union; international problems of pollution, for example the pollution of the Rhine affecting each of the countries it flows through, or acid rain falling on both the United States and Canada. In all of these examples, there is strategic interdependence: what one agent’s best action is depends upon what another agent does, and vice versa.

A common assumption in the theory of international trade is that countries are small: their exports and imports form such small fractions of total world trade that they cannot affect world prices. For many of the commodities imported or exported by most countries, this assumption is realistic. In some cases, however, a country’s trade in some particular commodity does comprise a significant proportion of world trade, so that the small-country assumption is inapplicable. As soon as the small-country assumption is dropped, questions which are inherently game-theoretic arise.

This monograph surveys several applications of game theory in international economics. It does not exhaust the list of questions which have been, or could be, analyzed using game theory. The topics covered were chosen both to illustrate the range of questions in international economics to which game theory can be fruitfully applied, and to exemplify various concepts of game theory. The monograph should be useful both to the specialist in international economics seeking to learn some game theory, and to the game theorist looking for a new and very fertile area in which to apply the techniques of game theory.

The analysis is presented as nontechnically as possible. This means that the results are not necessarily expressed in their full generality, or with all the necessary technical caveats. Nor are all of the results that can be extracted from these models presented: instead, an attempt has been made to convey the flavor of the analysis. Although no sophisticated mathematics are used in this monograph, some subsections, marked with asterisks (*), present material which is either somewhat more technical than the other subsections or not essential to understanding the concepts to be introduced. These subsections prove results stated in preceding subsections; on a quick reading, these subsections can be omitted without loss of continuity (though with some inevitable loss of precision).

Section 2 presents those basic concepts of game theory which seem to be the most useful to economists: the noncooperative equilibrium and some cooperative-game solution concepts. Section 3 looks at a more specialized question in game theory: in a dynamic game, cooperative behavior may occur in a non-cooperative context. The remaining sections describe some particular applications of game theory in international economics. Section 4 models as a game the interactions among different nations’ tariff policies. Section 5 considers possible government reactions to the oligopoly power of foreign and domestic firms. Section 6 reviews the evidence on international cartels as a case study of game-playing in practice. Section 7 considers the possibility of decentralized stabilization of world commodity prices. Section 8 models the exploitation of international common property. Section 9 examines the formation of customs unions. Section 10 summarizes some models of international transfers. Section 11 identifies an equivalence between a basic simplifying assumption used in trade theory (the community preference function) and a basic simplifying assumption used in game theory (transferable utility). Finally, Section 12 discusses some further questions of international economics to which game theory is applicable.

Game-theoretic concepts used include the static Nash equilibrium (in Section 4 and Section 10), the Stackelberg equilibrium (in Section 5), the repeated game (in Section 6), the stochastic game (in Section 7), the differential game and perfect equilibrium (in Section 8), the core (in Section 9), and transferable utility (in Section 11).

1.1 Bibliographic notes

For general surveys of the theory of international trade, see Chipman [26], Kemp [75], Dixit and Norman [37], and Woodland [164].

2. BASIC CONCEPTS OF GAME THEORY

This section introduces some of the more important ideas of game theory. No attempt is made at completeness; only those ideas which seem to be the most relevant to economics are discussed.

2.1 Definitions

The distinctive feature of a game is the presence of interdependencies among the agents: one agent’s utility depends not only on his own actions, but also on the actions of each of the other agents. It is the agents’ awareness of interactions among their decisions which give rise to t...

Table of contents

• Cover Page
• Half Title page
• Fundamentals of Pure and Applied Economics
• Title Page
• Copyright Page
• Original Title Page
• Original Copyright Page
• Contents
• Introduction to the Series
• Game Theory in International Economics
• 1. Strategy and Trade
• 2. Basic Concepts of Game Theory
• 3. Dynamic Games
• 4. Tariff Equilibrium
• 5. Tariffs and Foreign Competition
• 6. International Cartels
• 7. Price Stabilization
• 8. International Common Property
• 9. Customs Union and the Core
• 10. International Transfers
• 11. Countries as Coalitions
• 12. Further Topics
• References
• List of Symbols Used
• Index