Cones of Cooperation for Indefinitely Repeated

Michael A. Jones

No 1136, Discussion Papers from Northwestern University, Center for Mathematical Studies in Economics and Management Science

Abstract: A continuation probability is introduced to develop a theory of indefinitely repeated games where the extreme cases of finitely and infinitely repeated games are specific cases. The set of publicly correlated strategies (vectors) that satisfy a matrix inequality equilvalent to the one-stage-deviation principle forms a cone of cooperation. The geometry of these cones provides a means to verify intuition regarding the levels of cooperation attained when the discount parameter and continuation probability vary. A bifurcation point is identified which indicated whether or not a cooperative subgame perfect publicly correlated outcome exists for the indefinitely repeated game. When a cooperative equilibrium exists, a recursive relationship is used to construct an equilibrium strategy. New cooperative behavior is demonstrated in an indefinitely repeated game with infrequent shocks (a subsequence of the continuation probability goes to zero).

Date: 1995-06
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