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Solutions to Chapter 2 Exercises
SOLVED EXERCISES
S1. (a) Assuming a sufficient supply of yogurt is available for all shoppers, each shopper is
(b) Again, probably not an interaction between mutually aware players. (There may be a
(c) For a college senior, the choice here is a decision, unless you argue that a game is being
S2. (a) (i) Simultaneous play; (ii) zero-sum; (iii) can be repeated, although description is of a
(b) (i) Sequential play; (ii) non-zero-sum game for voters; (iii) usually not repeated (though
(c) (i) Simultaneous play; (ii) non-zero-sum; (iii) not repeated; (iv) imperfect information;
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
S4. To solve each problem, the probability of each event must be multiplied by its respective payoff,
and then all the results must be added together for the expected payoff.
(a) Expected payoff = 0.5(20) + 0.1(50) + 0.4(0) = 15.
S5. Prediction is about looking into the future to foresee which actions and outcomes will arise,
UNSOLVED EXERCISES
U1. (a) This is a game, because the choice of funding may hinder or help the candidate run
(b) Fred is trying to optimize his purchase of songs by determining whether he would get
(c) One might be tempted to consider this to be merely a decision on Belle’s part, unless you
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
(d) This is a game between NBC and the potential distributors, in which the distributors may
(e) This is a game, because China’s outcome is directly affected by how the United States
U2. (a) (i) Simultaneous, because each day the two sales representatives privately decide how
(ii) The game is not zero-sum.
(v) The rules are fixed.
(b) (i) Sequential, because the contestants are asked one at a time.
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
(iv) This is a game of imperfect information for the first three contestants, because they
(c) (i) Each hand of poker is a distinct simultaneous game, but the tournament requires
(ii) The game is zero-sum.
(v) The rules are fixed.
(vi) Cooperative agreements are possible: there are multiple prizes, and a subset of
(d) (i) Passengers do not know when others check in, so it is simultaneous.
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
U3. This is only true for constant-sum games. There are numerous games in which both can win, for
example, two investors purchasing stock in the same company can both win as the stock price increases.
U4. Before answering the subquestions, it helps to calculate the probability of each player winning or
losing. The probability of winning and losing for Confucius is identical to the probability for Bob.
(a) For Alice, the probability of having all heads is 0.5 • 0.5 • 0.5 = 0.125, and the probability
(c) For Confucius, there are three ways to have two heads and one tail land: the first quarter
could be the tail, the second quarter could be the tail, or the third quarter could be the tail. The probability
(d) The payoff of Confucius is 0.375 • 2 + 0.625 • –1 = 0.125.
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
U5. One possible example is that in many card games, when a player has only one remaining card,
But players may know all the rules and still surprise another, because their actions are not
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
