Temple University

Department of Economics

Economics 92, Principles of Microeconomics (Honors)

Homework: Subgame Perfect Equilibrium

In this game the firm Raider has entered the market for computer chip sets.   Target has had the market to itself.  Simultaneously Raider and Target must choose a price strategy: Hi or Lo.  Subsequently Raider then chooses an advertising plan.  If Raider observes that both firms have chosen the same price strategy then she chooses between running advertisements or running no ads.  If the firms have chosen different price plans then there is no advertising.  The payoffs are shown at the terminal ends of the game tree.

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1. Check the boxes corresponding to the nodes at which there are subgames:

A     B      C      D      E      F       G
There are subgames at A,D and G.

2. A strategy profile tells the players what to do at each node within a subgame at which s/he has a decision to make and in this example consists of a plan for each player.  Enumerate the strategy profiles that support the node paths shown in the following table.  For example, Raider's plan of (HiA, NoAdvD, AdvG) and Target's plan of (HiA) support the path ABD. Given the payoffs, Raider may never choose "No Adv" at D, but (HiA, NoAdvD, AdvG) is still a plan.  There are, in fact, four plans for Raider that support the path ABD when combined with Target's HiA plan.  For a given player and path enclose each strategy plan in parentheses.
Enter Raider's strategies in each subgame in the order ADG.

 

Player
Path Raider Target
ABD Hi, A, A
Hi, not A, A
Hi, A, not A
Hi, not A, not A		 Hi
ABE Hi, A, A
Hi, not A, A
Hi, A, not A
Hi, not A, not A		 Lo
ACF Lo, A, A
Lo, not A, A
Lo, A, not A
Lo, not A, not A		 Hi
ACG Lo, A, A
Lo, not A, A
Lo, A, not A
Lo, not A, not A		 Lo

3. If you inspect the table you will see that Raider has eight unique plans and Target has just two.  Use the eight plans for Raider and the two for Target to write the normal form of the entire game.  How many Nash equilibria are there? Eight

4.  Not all of Raider's plans are credible.  In this game not all of the Nash equilibria are subgame perfect. Write the strategy profile(s) for Raider and Target that is(are) a subgame perfect equilibrium.

{( Hi, A, A), ( Lo)} and {( Lo, A, A), ( Hi)}