1. Topics to be Discussed Gaming and Strategic Decisions
Dominant Strategies
The Nash Equilibrium Revisited
Repeated Games
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2. Topics to be Discussed Sequential Games
Threats, Commitments, and Credibility
Entry Deterrence
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3. Gaming and Strategic Decisions
Noncooperative versus Cooperative Games
Noncooperative Game
Negotiation and enforcement of a binding contract are not possible
Example: Two competing firms assuming the others behavior determine, independently, pricing and advertising strategy to gain market share
Binding contracts are not possible
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4. A Game “Ingredients” needed: identity of players;
action space for each player (strategies available);
payoffs for each combination of possible actions;
(order of moves).
How do we solve it?
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5. Dominant Strategies Dominant Strategy
One that is optimal no matter what an opponent does.
An Example
A & B sell competing products
They are deciding whether to undertake advertising campaigns
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6. Payoff Matrix for Advertising Game
Firm B
Don’t
Advertise
Advertise
Advertise
10, 5
15, 0
10, 2
6, 8
Firm A
Don’t
Advertise
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7. Payoff Matrix for Advertising Game
Observations
A: regardless of B, advertising is the best
B: regardless of A, advertising is best
Firm A
Advertise
Don’t
Firm B
10, 5
15, 0
10, 2
6, 8
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8. Payoff Matrix for Advertising Game
Observations
Dominant strategy for A & B is to advertise
Do not worry about the other player
Equilibrium in dominant strategy
Firm A
Advertise
Don’t
Firm B
10, 5
15, 0
10, 2
6, 8
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9. Dominant Strategies Game Without Dominant Strategy
The optimal decision of a player without a dominant strategy will depend on what the other player does.
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10. Modified Advertising Game
Firm B
Don’t
Advertise
Advertise
Advertise
10, 5
15, 0
20, 2
6, 8
Firm A
Don’t
Advertise
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11. Modified Advertising Game
Observations
A: No dominant strategy; depends on B’s actions
B: Advertise
Question
What should A do? (Hint: consider B’s decision
10, 5
15, 0
20, 2
6, 8
Firm A
Advertise
Don’t
Firm B
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12. The Nash Equilibrium Revisited
“I’m doing the best I can given what you are doing”
“You’re doing the best you can given what I am doing.”
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13. Beach Location Game Scenario
Two competitors, Y and C, selling soft drinks
Beach 200 yards long
Sunbathers are spread evenly along the beach
Price Y = Price C
Customer will buy from the closest vendor
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14. Beach Location Game
Ocean B
Beach A
200 yards C
Where will the competitors locate (i.e. where is the Nash equilibrium)?
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15. Beach Location Game OceanB
Beach A
200 yards C
2) Examples of this decision problem include:
Locating a gas station
Presidential elections
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16. The Nash Equilibrium Revisited
Mixed Strategy
Pure Strategy
Player makes a specific choice
Mixed Strategy
Player makes a random choice among two or more possible actions based on a set of chosen probabilities
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17. Matching Pennies 1, -1 -1, 1 Player B Heads Tails Heads Player A Tails
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18. Matching Pennies Observations Pure strategy: No Nash equilibrium
Mixed strategy: Random choice is a Nash equilibrium
Would a firm set price based on random choice assumption?
Player A
Heads
Tails
Player B
1, -1
-1, 1
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19. The Battle of the Sexes 2,1 0,0 1,2 Joan Jim Wrestling Opera Wrestling
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20. The Battle of the Sexes Pure Strategy Mixed Strategy
Both watch wrestling
Both watch opera
Mixed Strategy
Jim chooses wrestling
Joan chooses wrestling
Jim
Wrestling
Opera
Joan
2,1
0,0
1,2
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21. Repeated Games Oligopolistic firms play a repeated game.
With each repetition of the Prisoners’ Dilemma, firms can develop reputations about their behavior and study the behavior of their competitors.
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22. Pricing Problem 10, 10 100, -50 50, 50 -50, 100 Firm 2 Firm 1
Low Price
High Price
Low Price
10, 10
100, -50
50, 50
-50, 100
Firm 1
High Price
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23. Pricing Problem Non-repeated game Repeated game Strategy is Low1, Low2
Tit-for-tat strategy is the most profitable
Firm 1
Low Price
High Price
Firm 2
10, 10
100, -50
50, 50
-50, 100
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24. Repeated Games Conclusion: With repeated game
The Prisoners’ Dilemma can have a cooperative outcome with tit-for-tat strategy
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25. Repeated Games Conclusion:
This is most likely to occur in a market with:
Few firms
Stable demand
Stable cost
Cooperation is difficult at best since these factors may change in the long-run.
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26. Sequential Games Players move in turn
Players must think through the possible actions and rational reactions of each player
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27. Sequential Games Examples Responding to a competitor’s ad campaign
Entry decisions
Responding to regulatory policy
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28. The Extensive Form of a Game
Backward Induction
The Extensive Form of a Game
The Extensive Form of a Game
Using a decision tree
Work backward from the best outcome for Firm 1
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29. Sequential Games The Advantage of Moving First
In this product-choice game, there is a clear advantage to moving first.
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30. The Advantage of Moving First
Sequential Games
The Advantage of Moving First
Assume: Duopoly
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31. The Advantage of Moving First
Sequential Games
The Advantage of Moving First
Duopoly
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32. Choosing Output Firm 2 7.5 10 15 7.5 10 Firm 1 15 112.50, 112.50
56.25,
0, 0
112.50, 56.25
125, 93.75
50, 75
93.75, 125
75, 50
100, 100 10
Firm 1 15
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33. Choosing Output This payoff matrix illustrates various outcomes
Move together, both produce 10
Question
What if Firm 1 moves first?
Firm 1
7.5
Firm 2
112.50,
56.25,
0, 0
112.50, 56.25
125, 93.75
50, 75
93.75, 125
75, 50
100, 100 10 15
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34. Threats, Commitments, and Credibility
Strategic Moves
What actions can a firm take to gain advantage in the marketplace?
Deter entry
Induce competitors to reduce output, leave, raise price
Implicit agreements that benefit one firm
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35. Threats, Commitments, and Credibility
How To Make the First Move
Demonstrate Commitment
Firm 1 must constrain his behavior to the extent Firm 2 is convinced that he is committed
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36. Threats, Commitments, and Credibility
Empty Threats
If a firm will be worse off if it charges a low price, the threat of a low price is not credible in the eyes of the competitors.
Empty threat may be a Nash Equilibrium but not Subgame Perfect
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37. Wal-Mart Stores’ Preemptive Investment Strategy
Question
How did Wal-Mart become the largest retailer in the U.S. when many established retail chains were closing their doors?
Hint
How did Wal-Mart gain monopoly power?
Preemptive game with Nash equilibrium
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38. Entry Deterrence
To deter entry, the incumbent firm must convince any potential competitor that entry will be unprofitable.
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39. Entry Possibilities 100, 20 200, 0 130, 0 70, -10 Potential Entrant
Enter
Stay out
High price
(accommodation)
100, 20
200, 0
130, 0
70, -10
Incumbent
Low Price
(warfare)
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40. Entry Deterrence Scenario
Incumbent monopolist (I) and prospective entrant (X)
X single cost = $80 million to build plant
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41. Entry Deterrence Scenario
If X does not enter I makes a profit of $200 million.
If X enters and charges a high price I earns a profit of $100 million and X earns $20 million.
If X enters and charges a low price I earns a profit of $70 million and X earns $-10 million.
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42. Entry Deterrence Question How could I keep X out?
Is the threat credible?
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43. Entry Deterrence How could I keep X out?
1) Make an investment before entry (irrevocable commitment)
2) Irrational behavior
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44. After $50 million Early Investment
Entry Deterrence
After $50 million Early Investment
Potential Entrant
Enter
Stay out
High price
(accommodation)
50, 20
150, 0
130, 0
70, -10
Incumbent
Low Price
(warfare)
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45. After $50 million Early Investment
Entry Deterrence
After $50 million Early Investment
Warfare likely
X will stay out
Incumbent
Enter
Stay out
High price
(accommodation)
Low Price
(warfare)
Potential Entrant
50, 20
150, 0
130, 0
70, -10
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46. Summary
A game is cooperative if the players can communicate and arrange binding contracts; otherwise it is noncooperative.
A Nash equilibrium is a set of strategies such that all players are doing their best, given the strategies of the other players.
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47. Summary
Some games have no Nash equilibrium in pure strategies, but have one or more equilibria in mixed strategies.
Strategies that are not optimal for a one-shot game may be optimal for a repeated game.
In a sequential game, the players move in turn.
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48. Summary
An empty threat is a threat that one would have no incentive to carry out.
To deter entry, an incumbent firm must convince any potential competitor that entry will be unprofitable.
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