Elements of game theory

Political authorities are often collective bodies: cabinets, councils, houses of parliament, etc. The analytical tools for the study of interaction among members of collective bodies will be taken from the theory of games, especially from the theory of a specific type of n-person game that will be introduced and described in the present section and that will be called a ‘budgetary game’. In the next section some additional concepts with respect to budgetary games will be defined, namely those of the preference set, the dominant set and the Pareto superior set. With the help of these concepts it will be possible to review in the following sections some elementary game-theoretic results and to consider the consequences of these results for the problem of stability in budgetary games.

Up to this point the theory of public demand has been considered only at the level of the individual politician. In reality, we observe collective bodies. These bodies do not only decide for themselves but for all citizens of government. This state of affairs raises the question of how individual politicians interact with one another as members of a committee in the process of reaching decisions, and this question leads to the analysis of collective decision-making in the proper sense. As it turns out, game theory is an almost indispensable analytical tool when entering this domain.

The required elements of game theory will be introduced in a way that is understandable to the reader who has no prior knowledge.