Chapter 4: Finite Dynamic Games with Discrete Strategy Space: A First Approach
4. Finite dynamic games with discrete strategy space: a ﬁrst approach INTRODUCTION 4.1 In Chapter 3 it became apparent that in a static PD or a chicken game a full cooperative outcome cannot be achieved due to the free-rider incentive. Now, in a dynamic context, we have to investigate whether contingent cooperation can be established by using threats and punishments. The term ‘contingent’ emphasizes that it can never be an equilibrium strategy to cooperate unconditionally as long as there is a free-rider incentive. In order to establish contingent cooperation two requirements are necessary: ﬁrst, it must be possible to check compliance; second, in case of a deviation from an agreed strategy, an appropriate punishment must be available to players. Due to the assumption of complete information, the ﬁrst requirement is satisﬁed by deﬁnition, though in reality it may only partially be fulﬁlled. Whether the second requirement can be satisﬁed depends basically on two questions: 1. 2. How severe and credible is the punishment? Does it pay to forgo an immediate gain from free-riding in order to be rewarded by cooperation? For the ﬁrst question the punishment options in a game are important. Obviously, the harsher the punishment, the higher is the potential of deterrence from cheating. However, if the player conducting the punishment also suﬀers some loss because of the punishment, credibility becomes an important issue. In the game theoretical literature the problem of credibility has attracted great attention and we shall deal with this...
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