Edited by Carlo Carraro and Vito Fragnelli
Chapter 11: A Conjectural Cooperative Equilibrium for Strategic Form Games
Sergio Currarini and Marco Marini* 1. INTRODUCTION Intuitively a cooperative equilibrium is a collective decision adopted by a group of individuals that can be viewed as stable (that is, an equilibrium) against all feasible deviations by single individuals or by proper subgroups. While modelling the possibilities of cooperation may not pose the social scientist particular problems, at least once an appropriate economic or social situation is clearly outlined, the deﬁnition of stability may be a more demanding task for the modeller. This is because the outcome, and the proﬁtability, of players’ deviations depend heavily on the conjectures they make over the reaction of other players. As an example, a neighbourhood rule to keep a common garden clean possesses diﬀerent stability properties depending on whether the conjectured reaction in the event of shirking is, in turn, that the garden would be kept clean anyway or, say, that the common garden would be abandoned as a result. Similarly, countries participating in an international environmental agreement will possess diﬀerent incentives to comply with the prescribed pollution abatements depending upon whether defecting countries expect the other partners to be inactive or to retaliate. The main focus of the present chapter are cooperative equilibria of games in strategic form. A cooperative equilibrium of a game in strategic form can be deﬁned as a strategy proﬁle such that no subgroup of players can ‘make eﬀective’ – by means of alternative strategy proﬁles – higher utility levels for its members than...
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