978-0393919684 Chapter 11 Solution Manual

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Solutions to Chapter 11 Exercises

SOLVED EXERCISES

(b) Because the line for action X is above the line for action Y when 100 people choose X,

S2. (a) This game is a prisoners’ dilemma since s(n) is greater than p(n + 1) for all n. Any single

player can always raise his payoff by switching from participating to shirking.

Using calculus, you can find the same answer by differentiating T(n) from part (b). T (ʹn) = 2n +

Or you can find the same answer using a graph of T(n):

(d) When n = 74, each participant receives a benefit p(74) = 74. If one participant were to

(e) If the game is repeated, the players can take turns playing the role of shirker (and

S3. (a) Let x be the proportion of the population in Alphaville. Then the payoffs to living in the

(b) The graph below shows that there are five equilibria. Three exist where A(x) and B(x)

Betaville:

Betaville, and x will fall. If x is just above 0.2, people will move to Alphaville, and x will rise. Thus, the x

S4. (a) A person will voluntarily contribute if his benefit from so doing exceeds the $100 cost.

Assuming that n other people are already contributing, a person’s benefit from beginning to contribute is

(b) There are two stable Nash equilibria in this game. When n = 0, no one is contributing,

and no one wants to. When n = 100, everybody is contributing, and each person receives a private gain

S5. Here is one possible account. The diagram below shows a possible configuration of industry-level

supply and demand. Demand has the normal downward-sloping shape. For supply, over the range from

On the macroeconomic level, we see a function relating national product to national income

(demand) with the shape shown below:

S6. Answers should include careful descriptions of the (usually two) strategies available to the group

of players and of the benefits derived from the two different choices. Good descriptions of benefits should

UNSOLVED EXERCISES

U1. (a) The game is Chicken if p(2) < s(1) and if s(0) < p(1). Under these conditions, one player

shirks while the other works and works while the other shirks. To get Version I of Chicken, it must also be

(b) The two-person game is an assurance-type game if s(1) < p(2), p(1) < s(0), and s(0) <

p(2) all hold. These three inequalities indicate that Build is the best response to Build, that Not is the best

U2. (a) See diagram below:

(b) (i) With no communication, a high level of risk aversion leads very few students to

answer the question.

(ii) With pregame discussion, some students try to commit to answering the question; this

can be done by pledging to answer on the Web site or by indicating that you have answered and

U3. (a) See diagram below:

(b) There are three possible equilibria. At x = 0 (nobody on the local roads), the benefit on

the highway exceeds the benefit on local roads; nobody will switch to a local road. At x = 0.1, the benefits

U4. (a) See diagram below:

(b) There are two possible equilibria:

engineer’s pay. This equilibrium is unstable.

stable.

increase in their number creates a marginal spillover effect that outweighs the marginal private gain.

B(3, n) = 2.2 + n – 3 > 3 – n = S(3, n) whenever n ≥ 2

B(4, n) = 2.2 + n – 4 > 4 – n = S(4, n) whenever n ≥ 3

That is, IN is dominant for country 3 when countries 1 and 2 choose IN. Now IN is dominant for country

(d) For country i, the benefit of choosing IN when all other countries choose IN is B(i, 11),

and the benefit of choosing OUT when all countries choose OUT is S(i, 0). The benefits of these two

scenarios for each country (by rank) are given in the following table:

i B(i, 11) S(i, 0)

1 12.2 1

2 11.2 2