Game Theory and Public Policy
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Game Theory and Public Policy

Roger A. McCain

Game theory is useful in understanding collective human activity as the outcome of interactive decisions. In recent years it has become a more prominent aspect of research and applications in public policy disciplines such as economics, philosophy, management and political science, and in work within public policy itself. Here Roger McCain makes use of the analytical tools of game theory with the pragmatic purpose of identifying problems and exploring potential solutions in public policy.
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Chapter 11: Coalition Formation and Stability

Roger A. McCain


you let the farmers alone . . . all they got to do is gang up efficiently among themselves . . . but they never can stay ganged up they run out on each other. (Archy the cockroach in Marquis,1950) We have seen enough to suspect, and perhaps become persuaded, that neither cooperative nor non-cooperative game theory can alone supply a satisfactory foundation for public policy studies. This part of the book will outline a model of coalition formation that draws on elements of both cooperative and non-cooperative game theory. The theory will proceed from the following foundational assumptions: (1) Since externalities may occur, the cooperative game analysis will represent the game in partition function form. (2) The cooperative game analysis will also allow for nonaggregative games including games of “imperfect recall,” so that the game in partition function form may not be superadditive. (3) In general, coalition structures other than the grand coalition may be stable. (4) Cooperative relations take place only within coalitions, so that there are no side payments between coalitions and the interdependent strategy decisions of different coalitions are non-cooperative. (5) Accordingly, the partition functions are determined as the payoffs to non-cooperative equilibria in the play between coalitions. (6) Individual agents decide non-cooperatively to affiliate themselves into coalitions to choose joint strategies and receive or make side payments for the coalitional play. This might be described as a model of encapsulated cooperation.1 This chapter will outline a cooperative analysis of games in partition function form, focusing on assumptions (1)–(3). The...

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