Following the June 2018 Singapore summit between President Trump and North Korean leader Kim Jong-un, the US asked North Korea to turn over an inventory of its nuclear assets. The North

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Koreans refused. One reason for wanting an inventory is that it could be compared to what the US knows about North Koreas nuclear program. As the New York Times reports, American officials, mindful of North Koreas past failures to honor promises, are insisting that North Korea move quickly toward denuclearization by submitting an inventory of its nuclear weapons and fissile materials. (Sept 19, 2018). Not declaring sites that the US knows about could indicate that North Korea is not very serious about reaching a meaningful agreement. From the North Korean perspective, providing an inventory would be very costly in the event that negotiations break down and there is a future conflict. The inventory could become a target list. The signaling game below captures some aspects of this situation. North Korea has to decide whether to provide an inventory of its nuclear assets or not. The US then has to choose whether to go for a deal full of mutual compromises or to maintain a hard negotiating stance and discount the chances of reaching an agreement. The US wants to go for a deal if NK is willing to accept significant limitations on its nuclear program but wants to take a hard stance and likely forgo trying to make a deal if NK is unwilling to accept significant limitations. The cost of providing a declaration of assets is higher if the North is unwilling, namely 2d, and less, d, if it is willing to limit its program. Finally, the US is unsure if North Korea is willing to accept significant limitations, but believes that NK will accept limitations (NKW) with probability 2/5, and that the North is unwilling (NKU) with probability 3/5.(a) Assuming d = 15, find all of the separating Perfect Bayesian equilibrium or show that there are none. Be sure to justify your answer. (b) For what values of d are there separating equilibria? Explain why separation breaks down if d is too small and why it breaks down if d is too large. (c) Find all (pure-strategy) pooling Perfect Bayesian equilibria when d = 15. (d) Do any of the equilibria you found in (c) pass the Intuitive Criterion? If so, which ones pass, and why? If not, why do they fail?