Academic journal article Journal of Risk and Insurance

Cooperative Decision Making under Risk

Academic journal article Journal of Risk and Insurance

Cooperative Decision Making under Risk

Article excerpt

Cooperative Decision Making Under Risk, by Jeroen Suijs, 1999, Norwell, Mass.: Kluwer Academic Publishers

Reviewer: Emilio Venezian, Rutgers University

This book is part of the series "Game Theory, Mathematical Programming, and Mathematical Economics" published by Kluwer Academic Publishers. The key words are important. A solid foundation in set theory and game theory is a prerequisite for reading this book; it is not for the unprepared or the faint-hearted. Mathematical programming is vital for at least one chapter, and mathematical economics is basic to the entire book.

The book deals with situations in which a number of decision makers facing an uncertain future must decide upon the basis for sharing the vicissitudes of chance. The decisions to be made involve "who is going to play with whom," "what ante is each player going to put up," and "how are we going to share the proceeds when the game is over." Unfortunately, in this book, each decision maker comes with a definite role. Either the decision maker is a consumer or a producer. In the insurance context, either you are a policyholder or you are an insurer. Cooperative games in which roles are not assigned a priori are not included. Thus, situations in which consumers might band together to form a cooperative, or even games in which new producers could be organized, are excluded from consideration.

A second restriction is that the preferences of all agents are describable in terms of utilities. It does, however, treat both transferable utility (TU) games and non-transferable utility (NTU) games. Simply speaking, in TU games it makes sense to add up the individual utilities, and in NTU games it does not. A simple case of an NTU game is that of two players in which each player's utility function depends on whether the player receives money or has to pay money.

The first two chapters introduce the book and the notion of cooperative game theory. The third chapter deals with stochastic cooperative games and introduces the general model used in their characterization. Chapter 4 deals primarily with the core of stochastic cooperative games. …

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