A pandemic is gaining strength in the United Republic. Health experts advise the citizens to behave in a way that reduces the risk of conta- gion. For simplicity, suppose that each citizen chooses between heeding the advice (playing the p strategy) or ignoring the advice (playing the s strategy). The restrictions involved in heeding the advice and playing p come at a private cost to the citizen; all citizens benefit from curtailing the pandemic, that is, from having many people playing p). To be specific, the payoffs are given by p(x) s(x) = 1 + 2x 2 + 2x where x is the fraction of citizens that heed the advice and play p (0 ≤ x ≤ 1). (a) Draw a diagram illustrating the payoffs from playing p (heeding the health advice) and s (ignoring the advice) as functions of x. (b) Describe all of the possible equilibria in this 'pandemic game' and calculate the payoffs at the equilibrium (equilibria). Which of these equilibria is (are) most likely to obtain in this game? Explain your answer. (c) Analyze how a government mandate backed by police enforcement and punishment for violations can affect the payoffs and change the equilibrium outcome. (d) Suppose the government mandate faces opposition: it is seen by some as an infringement on personal freedom. How would you respond to this objection?
A pandemic is gaining strength in the United Republic. Health experts advise the citizens to behave in a way that reduces the risk of conta- gion. For simplicity, suppose that each citizen chooses between heeding the advice (playing the p strategy) or ignoring the advice (playing the s strategy). The restrictions involved in heeding the advice and playing p come at a private cost to the citizen; all citizens benefit from curtailing the pandemic, that is, from having many people playing p). To be specific, the payoffs are given by p(x) s(x) = 1 + 2x 2 + 2x where x is the fraction of citizens that heed the advice and play p (0 ≤ x ≤ 1). (a) Draw a diagram illustrating the payoffs from playing p (heeding the health advice) and s (ignoring the advice) as functions of x. (b) Describe all of the possible equilibria in this 'pandemic game' and calculate the payoffs at the equilibrium (equilibria). Which of these equilibria is (are) most likely to obtain in this game? Explain your answer. (c) Analyze how a government mandate backed by police enforcement and punishment for violations can affect the payoffs and change the equilibrium outcome. (d) Suppose the government mandate faces opposition: it is seen by some as an infringement on personal freedom. How would you respond to this objection?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:A pandemic is gaining strength in the United Republic. Health experts
advise the citizens to behave in a way that reduces the risk of conta-
gion. For simplicity, suppose that each citizen chooses between heeding
the advice (playing the p strategy) or ignoring the advice (playing the s
strategy). The restrictions involved in heeding the advice and playing p
come at a private cost to the citizen; all citizens benefit from curtailing
the pandemic, that is, from having many people playing p). To be specific,
the payoffs are given by
p(x)
1+ 2x
s(x)
2+ 2x
where a is the fraction of citizens that heed the advice and play p (0 <
x< 1).
(a) Draw a diagram illustrating the payoffs from playing p (heeding the
health advice) and s (ignoring the advice) as functions of x.
(b) Describe all of the possible equilibria in this 'pandemic game' and
calculate the payoffs at the equilibrium (equilibria). Which of these
equilibria is (are) most likely to obtain in this game? Explain your
answer.
(c) Analyze how a government mandate backed by police enforcement
and punishment for violations can affect the payoffs and change the
equilibrium outcome.
(d) Suppose the government mandate faces opposition: it is seen by some
as an infringement on personal freedom. How would you respond to
this objection?
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