2. Army 1 of country 1 must decide whether to attack army 2 of country 2 which is occupying an island between the two countries (i.e. army 1 moves first). In the event of an attack, army 2 may fight or retreat over a bridge to its mainland. Each army prefers to occupy the island than not to occupy it; a fight is the worst outcome for both armies. (a) Model the situation as an extensive form game with perfect information. Find a Nash Equilibrium of this game which is not subgame perfect. (b) Find the only Subgame Perfect Nash Equilibrium and compare with the equilibrium in the previous question. (c) Assume now that army 2 has the possibility of burning the bridge to its mainland. If it does, army 2 would then not be able to retreat if army 1 attacked. i. Write down the extensive form of this game. Show that army 2 can increase its payoff in a Subgame Perfect Nash equilibrium in the new game. Interpret what this fact illustrates ii.

2. Army 1 of country 1 must decide whether to attack army 2 of country 2 which is occupying an island between the two countries (i.e. army 1 moves first). In the event of an attack, army 2 may fight or retreat over a bridge to its mainland. Each army prefers to occupy the island than not to occupy it; a fight is the worst outcome for both armies. (a) Model the situation as an extensive form game with perfect information. Find a Nash Equilibrium of this game which is not subgame perfect. (b) Find the only Subgame Perfect Nash Equilibrium and compare with the equilibrium in the previous question. (c) Assume now that army 2 has the possibility of burning the bridge to its mainland. If it does, army 2 would then not be able to retreat if army 1 attacked. i. Write down the extensive form of this game. Show that army 2 can increase its payoff in a Subgame Perfect Nash equilibrium in the new game. Interpret what this fact illustrates ii.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Based on the following game, what are the secure strategies for player 1 and player 2? Player 1 S1 and 12 S1 and t1 S2 and 12 S2 and 11 s1 S2 Player 2 tl 10,15 -10,7 t2 15,8 10,20
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