The North Korea Summit Suppose that North Korea's lead Kim Jong-un is considering proposing a summit meeting with the President of the United States to negotiate North Korea's denuclearization and an end to economic sanctions against North Korea. If Kim Jong-un proposes a summit meeting, the President can either choose to negotiate or reject negotiations and continue the current policy of containment. The United States does not know in advance whether the Kim Jong-un is being earnest or duplicitous

We will model this as a game between Kim Jong-un and the President, with Kim Jong-un as player 1 and the President as player 2. (thus the payoffs to Kim Jong-un are listed first)

a. There is a probability p that Kim Jong-un's proposal is in earnest,
b. and a probability 1 -p that Kim Jong-un is being duplicitous and will attempt to use an end to sanctions to accelerate North Korea's program to become a full-fledged nuclear power
c. If Kim Jong-un makes no proposal, then the payoffs are (0, 0) (nothing changes)
d. If Kim Jong-un makes a proposal and it is rejected, then the payoffs are (1,0) (nothing changes for the U. S., but Kim Jong-un loses face with his advisors).
e. If Kim Jong-un is being earnest and the United States negotiates the payoffs are (2,2): (the President receives recognition for securincg a lasting peace and conditions improve in North Korea.
f. If Kim Jong-un is being duplicitous and the U. S. negotiates the payoffs are (4, -4) (Kim Jong-un and North Korea gain but at the expense of the United States)

1. Make a sketch of this game in extensive form.
2. Convert the extensive form game to normal form 1/2 and find any (Bayesian) Nash equilibria
3. Assume that p =