Microeconomics Practice Strategic Behavior
Master Strategic Behavior: Solved Problems
Step-by-step solutions based on Varian’s approach.
Problem 1: Nash Equilibrium (Pure Strategies)
Question: Consider the following payoff matrix for two firms deciding whether to Advertise or
Not Advertise.
Firm 2: Adv Firm 2: Not
Firm 1: Adv (10, 5) (15, 0)
Firm 1: Not (6, 8) (10, 2)
Find all Pure Strategy Nash Equilibria. Does either firm have a Dominant Strategy?
Solution
Step 1: Analyze Firm 1’s Best Responses
- If Firm 2 plays Adv, Firm 1 compares 10 vs 6. Best response: Adv.
- If Firm 2 plays Not, Firm 1 compares 15 vs 10. Best response: Adv.
Since Firm 1 plays Adv regardless of Firm 2, Adv is a Dominant Strategy for Firm 1.
Step 2: Analyze Firm 2’s Best Responses
- If Firm 1 plays Adv, Firm 2 compares 5 vs 0. Best response: Adv.
- If Firm 1 plays Not, Firm 2 compares 8 vs 2. Best response: Adv.
Adv is also a Dominant Strategy for Firm 2.
Step 3: Find Equilibrium
Since both play Adv, the intersection is the equilibrium.
Final Answer: The unique Nash Equilibrium is (Adv, Adv). Both firms have a Dominant
Strategy to Advertise.
Problem 2: Mixed Strategy Equilibrium
Question: In a penalty kick game, the Kicker can aim Left or Right. The Goalie can jump
Left or Right.
• If both go the same way (Goalie matches Kicker), Kicker gets 0, Goalie gets 100.
• If they go opposite ways (Goalie fails), Kicker gets 100, Goalie gets 0.
Find the Mixed Strategy Nash Equilibrium probabilities.
Solution
Step 1: Set up Payoff Matrix
Let p be probability Kicker aims Left. Let q be probability Goalie jumps Left.
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Master Strategic Behavior: Solved Problems
Step-by-step solutions based on Varian’s approach.
Problem 1: Nash Equilibrium (Pure Strategies)
Question: Consider the following payoff matrix for two firms deciding whether to Advertise or
Not Advertise.
Firm 2: Adv Firm 2: Not
Firm 1: Adv (10, 5) (15, 0)
Firm 1: Not (6, 8) (10, 2)
Find all Pure Strategy Nash Equilibria. Does either firm have a Dominant Strategy?
Solution
Step 1: Analyze Firm 1’s Best Responses
- If Firm 2 plays Adv, Firm 1 compares 10 vs 6. Best response: Adv.
- If Firm 2 plays Not, Firm 1 compares 15 vs 10. Best response: Adv.
Since Firm 1 plays Adv regardless of Firm 2, Adv is a Dominant Strategy for Firm 1.
Step 2: Analyze Firm 2’s Best Responses
- If Firm 1 plays Adv, Firm 2 compares 5 vs 0. Best response: Adv.
- If Firm 1 plays Not, Firm 2 compares 8 vs 2. Best response: Adv.
Adv is also a Dominant Strategy for Firm 2.
Step 3: Find Equilibrium
Since both play Adv, the intersection is the equilibrium.
Final Answer: The unique Nash Equilibrium is (Adv, Adv). Both firms have a Dominant
Strategy to Advertise.
Problem 2: Mixed Strategy Equilibrium
Question: In a penalty kick game, the Kicker can aim Left or Right. The Goalie can jump
Left or Right.
• If both go the same way (Goalie matches Kicker), Kicker gets 0, Goalie gets 100.
• If they go opposite ways (Goalie fails), Kicker gets 100, Goalie gets 0.
Find the Mixed Strategy Nash Equilibrium probabilities.
Solution
Step 1: Set up Payoff Matrix
Let p be probability Kicker aims Left. Let q be probability Goalie jumps Left.
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