Chapter 10: Finite Dynamic Games with Continuous Strategy Space and Static Representations of Dynamic Games
INTRODUCTION 10.1 From the previous chapter it became evident that in a static setting there is underprovision of the public good ‘environmental quality’. In the Nash equilibrium global emissions are too high from a global point of view. Thus one may wonder whether more positive results could be obtained in a dynamic, though ﬁnite time horizon. This question will be analyzed within two approaches. The ﬁrst approach remains in the tradition of repeated games, as encountered in previous chapters. More precisely, we proceed as in Chapter 4: ﬁrst the equilibrium (or the equilibria) of the constituent game is determined; and second, one investigates whether the ﬁnitely repeated play of the stage game leads to more optimistic results. Again, a simultaneous and a sequential move version of the constituent game can be distinguished. In the former case the analysis is simple. If the constituent game is the global emission game described in Chapter 9, where there is a unique Nash equilibrium (NE) due to assumption A1, the repeated play of this stage game NE is the only equilibrium in a ﬁnite time horizon. This is an immediate implication of Theorem 4.2. In the case of sequential moves, it is shown in Section 10.2 that there is a unique subgame-perfect equilibrium (SPE) of the emission stage game and hence, again, by Theorem 4.2, the ﬁnitely repeated play of this stage game equilibrium is the only equilibrium of the overall game. Thus, the outcome in the ﬁnitely repeated emission game does not di...
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