game theory

2. Two neighbouring countries have to decide whether they want to go to war or remain at peace. If countries remain at peace, their payoff is 1. If one country decides to go to war, its payoff is 4, while the other's is -2. If both countries go to war, their payoffs are -1. a) Assume the game lasts for five periods. Find all subgame-perfect Nash Equilibria. b) Now assume the game lasts infinitely. Formulate a profile of grim trig- ger strategies which rewards countries that stay at peace indefinitely and find the smallest discount factor that can support such strategies as a subgame- perfect NE