Assume there are two countries involved in a war. Country A is considering invading Country B through a bridge which is the only access point to country B. If country A invades through the bridge country B has the option to either fight or run away. Once country B chooses either to fight or run away, country A can decide either to retreat through bridge or continue with the assault.
A) when the two countries fight, the confrontation ends in a stalemate and both armies are vanished. If one country decides to fight while the other country runs away, the country fighting keeps its numbers while the country retreating loses half of its army. If both countries run away they both lose half of their army.
Draw a game tree and find the Nash equilibrium for this game. Explain.
B) Can country A change the outcome of the game by burning the bridge they are crossing to invade and committing its troops to fight? expand the game tree to show this option for county A and find the new Nash equilibrium. Explain