GAME THEORY

In the previous section we have considered a case in which two stakeholders, a producer and a distributor, make their decisions in a specific order. The producer (leader) determines product quality, as well as the probability distribution of demand as a consequence; the distributor (follower) chooses the order quantity. In other cases, however, decisions are taken simultaneously, at least in principle. In fact, the term “simultaneously” need not be taken literally; the point is that no player has any information about what others have previously chosen and cannot use this as an input for her decision. Predicting the outcome of the joint decisions is no easy task in general, and it is the aim of game theory. There is no hope to treat this challenging subject adequately in a few pages, but for our purposes it is quite enough to grasp a few fundamental concepts; these will be illustrated by very stylized examples in this section; in the next one, we consider a paradoxical result in traffic networks, which is a result of noncooperation between decision makers, namely, drivers in that case.

For the sake of simplicity, we consider a very stylized setting:

• There are only two decision makers (players); each player has an objective (payoff) that she wants to maximize and there is no form of cooperation.
• Only one decision has to be made; hence, we do not consider sequential games in which multiple decisions are made over time.
• We assume complete information and common knowledge.¹¹ Formalizing these concepts precisely is not that trivial, but (very) loosely speaking they mean that there is no uncertainty about the data of the problem nor about the mechanisms that map decisions into payoffs. The two players agree on their view of the world, the rules of the game, and know the incentives of the other party; furthermore, each player knows that the other one has all of the relevant information.

There are different ways to represent a game. The best way to understand the basic concepts is by considering the situation in which players must choose within a very small and discrete set of available actions, and the game is represented in normal form.