Chapter 2: Important Terms, Notation and Classification of Games
2. Important terms, notation and classiﬁcation of games TERMS 2.1 The essential elements of a game are the players, actions, strategies, outcomes, payoﬀs, equilibria, the information and the order of the game (see, for example, Rasmusen 1989, pp. 23ﬀ.). The players are the actors in the game who take decisions. In the international environmental context the players are countries or the political representatives of countries, such as politicians or diplomats. Players can take actions, such as making catalytic converters for automobiles mandatory or not. In contrast, a strategy is a complete plan of action for each contingency which might arise during the game. In a game comprising several stages, a strategy speciﬁes how a player reacts at each point in time to all possible actions of fellow players. For instance, a participant to an IEA must specify an answer if a signatory to an IEA complies with its obligations but also if it violates the agreement. A particular combination of actions (resulting from the play of some strategy combination) leads to the outcome of the game. For instance, in the catalytic converter example outcomes could be measured as the nitrogen oxide concentration in the air, which depends on how many and which governments introduce stricter car regulations. Alternatively, the outcome could also be measured with respect to some other environmental index. The choice will depend on the focus of the analysis (Rasmusen 1989, p. 25). However, since game theory is mainly concerned with predicting which of the...
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