Chapter 9: Static Games with Continuous Strategy Space: Global Emission Game
INTRODUCTION 9.1 Up to now we have assumed that players have discrete action sets so that the normal form of the game could conveniently be displayed in a matrix. Though for many policy problems modeling decisions as a discrete choice seems adequate, other situations may be better modeled as a continuous choice problem such as the amount of emission reduction in a global policy game, for example, greenhouse gases (see also the discussion in Section 2.3). A continuous strategy set allows ﬁner tuning of actions and reactions and therefore leads to some interesting results which are absent in discrete policy games. This is true at least as long as mixed strategies are ruled out for discrete policy games. Though we dealt with mixed strategies in Chapter 3 and also mentioned some instances in which one can expect players to use mixed strategies, they were introduced mainly for technical reasons; that is, mixed strategies were required in the discrete strategy context to capture the entire feasible payoﬀ space when deriving folk theorem type results. In a continuous strategy setting it suﬃces to consider only pure strategies. This is true at least as long as games with a convex payoﬀ space are considered. Since all games in the remainder of this book satisfy this condition, we no longer have to bother about mixed strategies. The following analysis is based on a rather simple emission model. In particular, the payoﬀ or net beneﬁt functions contain emissions as the only argument. Thus,...
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