Static and Dynamic Games

Abstract

Any discussion of economic models is incomplete, if it does not contain an analysis of game theory and its various applications. This is because the models in game theory provide a substantial amount of generalization of most of the basic mathematical concepts we have so far used e.g., the concept of equilibrium, stability, saddle point and intertemporal optimum. A game may be veiwed as a team decision problem, when the different members of the team have cooperative or noncooperative (i.e. conflicting) objectives to optimize, with different or equal information structures and finite or infinite strategies to choose from. Four general ways to classify games are: (1) static or dynamic, where the latter involves intertemporal optimization by different players with strategies selected sequentially over time, (2) deterministic or stochastic, where for the latter it is assumed that there exist stochastic errors in the objective function or the constraints on the strategy choice, which may be due to incomplete information available to each player, (3) games of strategy (i.e. active game against rational opponents), or games against nature (i.e. passive game, where the opponent is viewed as nature, who is not assumed to have any motives of gain or retaliation), and (4) the three analytical forms of the game model: the extensive form, the normal form and the characteristic function form. The normal form is most frequently applied in two-person games, whereas the characteristic function form is most useful for nperson games with n greater than two.