xxm problem requires a single decision maker to select a riable (over which this decision maker has complete ize r rewards and if r = 1 then the problem is a n problem, whereas if r 2 then the problem is a on problem.7 the strategic games that we are about to study re- cision makers, called players, to a select a single de- alled a strategy—to optimize a single reward. But ard depends on the other players' strategies i.e., it ion variables that are completely controlled by the hat players lack control over all decision variables wards is what makes a game a game, and what dis- an optimization problem. In this book, we do not ion problems in their own right, nor do we allow more than one reward—in other words, we do not games." Thus our agenda for games falls in the Figure O.l.8 gic interaction can be very complicated, and a game not exist unless the interaction can be described But this step is often exceedingly difficult, especially y and especially if we insist—and as modellers we yers' rewards be explicitly defined. Therefore, we a to strategic interactions that lend themselves read- mathematical description—and hence, for the most ith few players. Indeed six is many in this regard: aving served us so well, must now depart the scene. he book we introduce concepts by means of specific icating how to generalize them however, we avoid ts and proofs of theorems, referring instead to the ur approach to games is thus largely the opposite proach, but has the clear advantage in an introduc- fosters substantial progress. We can downplay the in due course, a decision variable can itself be a vector. Wha t from a vector optimization problem (or a game from a vector e number of rewards per decision maker. mples of optimization problems see, e.g., Chapters 3, 7 and 12 of es, see [244]. Figure 0.1 and all other figures in this book were al [239].
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