An aggressor country (A) and a defending country (D) are involved in a nuclear confronta-tion. There are 2 locations in country D that can be targets for the missiles of countryA. Country A has 2 miss

An aggressor country (A) and a defending country (D) are involved in a nuclear confronta-

tion. There are 2 locations in country D that can be targets for the missiles of country

A. Country A has 2 missiles available to send against any of country D’s locations, and

country D has 1 anti-missile battery available to defend either location. The anti-missile

battery can destroy all missiles that target the location that it defends. If a location is

undefended, then 2 million of country D’s citizens will die if a single missile strikes, and 3

million citizens will die if two missiles strike. Country A wants to maximise the number of

deaths in country D, and country D wants to minimise them.

(a) Describe this interaction between the two countries as a game in strategic form.

(b) Show that this game does not have a Nash equilibrium in pure strategies.

(c) Find all the Nash equilibria in mixed strategies for this game.