Chapter 3: Static Games with Discrete Strategy Space
INTRODUCTION 3.1 The aim of this chapter is threefold: 1. To analyze the eﬀect of the cost–beneﬁt structure on the outcome of a game. Here we shall deal with the prisoners’ dilemma (Section 3.2), the chicken game (Section 3.3), the assurance game and the no-conﬂict game (Section 3.4) in the two-country context. An extension to cover the general case of N countries is provided in Section 3.5. To introduce some basic game theoretical concepts such as an equilibrium in dominant strategies, a Nash equilibrium in pure and uncorrelated and correlated mixed strategies. To demonstrate that by playing uncorrelated or correlated mixed strategies the payoﬀ space in a game can be convexiﬁed (Section 3.6). This is some preparatory work needed for dynamic games in subsequent chapters. An application of correlated strategies is provided in Section 3.7. 2. 3. In this chapter we focus exclusively on simple static games with a discrete strategy space. The examples assume that governments can choose between two policy options; however, an extension to cover the case of larger action sets is straightforward. All games are non-cooperative and non-constant sum games. Trivially, by the deﬁnition of static games the sequence of moves is simultaneous and the time dimension and time structure are irrelevant. With respect to Table 2.1, the games in this chapter can be categorized as: 1b, 2b, 3a (b), 4a, 5a, 8a, 9a. Some aspects discussed in this and the two subsequent chapters can also be found in the...
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