1. Noncooperative Games 1.1. Payoff Table 1.2. Payoff for Nan matrix for San Nan San G W G - 5 - | n - n W 0 - e - f r i San G W -6-±T2 0 - r 2 - e - ^ r 2 citly assuming that S and e are both independent of T\ ay be tempted to criticize this assumption—but tread u do so. In the real world, it is more than likely that d depend upon various aspects of the personalities of conflict. But our model ignores them. It differentiates and San solely by virtue of their transit times, T\ and ependence of S and e on these may well be weak. likes delays to be as short as possible, but in noncooper- eory it is traditional to like payoffs as large as possible. aking a delay small is the same thing as making its , we agree that the payoff to Nan is the negative of her he payoffs to Nan associated with pure strategy combi- GW, WG and WW are, respectively, —5 ^T2,0, T2 T2. It is customary to store these payoffs in a matrix, as where the rows correspond to strategies of Player 1 and orrespond to strategies of Player 2. ny particular confrontation, the actual payoff to Nan ategy combination GG or WW is a random variable. played repeatedly, however, then Nan's average payoff WW over an extended period should be well approxi- random variable's expected value and this is how we expected values as payoffs. Furthermore, for the game epeatedly, it is not necessary that the person Nan con- he finds herself at a 4-way junction in the circumstances ve, be the same individual every time. Rather, San is e for all individuals whose behavior is the same for the ur model (though for other purposes it might be very you like, San is any individual who exhibits San-like left-turning-at-a-4-way-junction behavior. Likewise, for
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