Topics to be Discussed Gaming and Strategic Decisions Dominant Strategies The Nash Equilibrium Revisited Repeated Games Lecture 13 2

Topics to be Discussed Sequential Games Threats, Commitments, and Credibility Entry Deterrence Lecture 13 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 Lecture 13 5

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? Lecture 13

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 Lecture 13 9

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 Lecture 13 14

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 Lecture 13 14

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 Lecture 13 14

Dominant Strategies Game Without Dominant Strategy The optimal decision of a player without a dominant strategy will depend on what the other player does. Lecture 13 16

Modified Advertising Game Firm B Don’t Advertise Advertise Advertise 10, 5 15, 0 20, 2 6, 8 Firm A Don’t Advertise Lecture 13 18

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 Lecture 13 18

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.” Lecture 13 21

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 Lecture 13 26

Beach Location Game Ocean B Beach A 200 yards C Where will the competitors locate (i.e. where is the Nash equilibrium)? Lecture 13 27

Beach Location Game Ocean B Beach A 200 yards C 2) Examples of this decision problem include: Locating a gas station Presidential elections Lecture 13 27

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 Lecture 13 37

Matching Pennies 1, -1 -1, 1 Player B Heads Tails Heads Player A Tails Lecture 13 36

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 Lecture 13 36

The Battle of the Sexes 2,1 0,0 1,2 Joan Jim Wrestling Opera Wrestling Lecture 13 33

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 Lecture 13 33

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. Lecture 13 39

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 Lecture 13 41

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 Lecture 13 41

Repeated Games Conclusion: With repeated game The Prisoners’ Dilemma can have a cooperative outcome with tit-for-tat strategy Lecture 13 44

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. Lecture 13 44

Sequential Games Players move in turn Players must think through the possible actions and rational reactions of each player Lecture 13 49

Sequential Games Examples Responding to a competitor’s ad campaign Entry decisions Responding to regulatory policy Lecture 13 50

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 Lecture 13 56

Sequential Games The Advantage of Moving First In this product-choice game, there is a clear advantage to moving first. Lecture 13 62

The Advantage of Moving First Sequential Games The Advantage of Moving First Assume: Duopoly Lecture 13 63

The Advantage of Moving First Sequential Games The Advantage of Moving First Duopoly Lecture 13 64

Choosing Output Firm 2 7.5 10 15 7.5 10 Firm 1 15 112.50, 112.50 56.25, 112.50 0, 0 112.50, 56.25 125, 93.75 50, 75 93.75, 125 75, 50 100, 100 10 Firm 1 15 Lecture 13 66

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, 112.50 56.25, 112.50 0, 0 112.50, 56.25 125, 93.75 50, 75 93.75, 125 75, 50 100, 100 10 15 Lecture 13 66

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 Lecture 13 68

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 Lecture 13 69

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 Lecture 13 70

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 Lecture 13 81

Entry Deterrence To deter entry, the incumbent firm must convince any potential competitor that entry will be unprofitable. Lecture 13 84

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) Lecture 13 86

Entry Deterrence Scenario Incumbent monopolist (I) and prospective entrant (X) X single cost = $80 million to build plant Lecture 13 87

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. Lecture 13 88

Entry Deterrence Question How could I keep X out? Is the threat credible? Lecture 13 89

Entry Deterrence How could I keep X out? 1) Make an investment before entry (irrevocable commitment) 2) Irrational behavior Lecture 13 92

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) Lecture 13 91

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 Lecture 13 91

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. Lecture 13 113

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. Lecture 13 114

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. Lecture 13 115