Chapter 2

Strategic Games

2.1. Introduction to Strategic Games

A strategic game is a static model that describes interactive situations among

several

players.1

According to this model, all the players make their deci-

sions simultaneously and independently. From the mathematical perspec-

tive, strategic games are very simple objects. They are characterized by the

strategies available to the players along with their payoff functions. Even

though one may think of the payoffs of the players as money, we have al-

ready seen in Chapter 1 that payoff functions may be representations of

more general preferences of the players over the set of possible outcomes.

These general preferences may account for other sources of utility such as

unselfishness, solidarity, or personal affinities.

Throughout this book it is implicitly assumed that each player is ratio-

nal in the sense that he tries to maximize his own payoff. Moreover, for a

rational player, there is no bound in the complexity of the computations he

can make or in the sophistication of his

strategies.2

We start this chapter by formally introducing the concept of strategic

game and then we move to the most widely studied solution concept in

game theory: Nash equilibrium. We discuss some important classes of

games, with special emphasis on zero-sum games. Later we study other so-

lution concepts different from Nash equilibrium (Section 2.9) and, towards

1

Strategic games are also known as games in normal form.

2This

assumption is standard in classic game theory and in most of the fields in which it is applied,

especially in economics. Rubinstein (1998) offers a deep treatment of different directions in which the

rationality of the agents can be bounded along with the corresponding implications.

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http://dx.doi.org/10.1090/gsm/115/02