- The Lockhorns Cartoon Game Theory “Loretta’s Driving Because I’m Drinking and I’m Drinking Because She’s Driving” - The Lockhorns Cartoon Mike Shor Lecture 3

Review Understand the game you are in Note if the rules are flexible Anticipate your opponents’ reactions Understand the assumptions Recognize that not everyone else understands them Game Theory - Mike Shor

Game Theory - Mike Shor

Equilibrium Nash Equilibrium: Best Response: A set of strategies, one for each player, such that each player’s strategy is best for her given that all other players are playing their equilibrium strategies Best Response: The best strategy I can play given the strategy choices of all other players Everybody is playing a best response No incentive to unilaterally change my strategy Game Theory - Mike Shor

Identifying the Equilibrium Pure strategy equilibrium Consider mixed later Dominance Dominance solvable Only one dominant strategy Successive elimination of dominated strategies Cell-by-cell inspection Game Theory - Mike Shor

Cigarette Advertising on TV All US tobacco companies advertised heavily on TV Surgeon General issues official warning Cigarette smoking may be hazardous Cigarette companies’ reaction Fear of potential liability lawsuits Companies strike agreement Carry the warning label and cease TV advertising in exchange for immunity from federal lawsuits. 1964 1970 Game Theory - Mike Shor

Strategic Interactions Players: Reynolds and Philip Morris Strategies: { Advertise , Do Not Advertise } Payoffs: Companies’ Profits Each firm earns $50 million from its customers Advertising costs a firm $20 million Advertising captures $30 million from competitor How to represent this game? Game Theory - Mike Shor

Normal (Strategic) Form PLAYERS Philip Morris No Ad Ad Reynolds 50 , 50 20 , 60 60 , 20 30 , 30 STRATEGIES PAYOFFS Game Theory - Mike Shor

Normal Form Best reply for Reynolds: Advertise! If Philip Morris advertises: advertise If Philip Morris does not advertise: advertise Regardless of what you think Philip Morris will do Advertise! Philip Morris No Ad Ad Reynolds 50 , 50 20 , 60 60 , 20 30 , 30 Game Theory - Mike Shor

Dominant Strategy A strategy that outperforms all other choices no matter what opposing players do Firm 1’s strategies: { A, B, C } Firm 2’s strategies: { X, Y, Z } C is strictly dominant for Firm 1 if: P(C,X)>P(A,X) P(C,X)>P(B,X) P(C,Y)>P(A,Y) P(C,Y)>P(B,Y) P(C,Z)>P(A,Z) P(C,Z)>P(B,Z) C is weakly dominant for Firm 1 if: Some inequalities are weak (), at least one is strong(>) Game Theory - Mike Shor

Dominance Solvable If each player has a dominant strategy, the game is dominance solvable What is the equilibrium of the cigarette advertising game? COMMANDMENT If you have a dominant strategy, use it. Expect your opponent to use her dominant strategy if she has one. Game Theory - Mike Shor

Cigarette Advertising After the 1970 agreement, cigarette advertising decreased by $63 million Profits rose by $91 million Prisoner’s Dilemma An equilibrium is NOT necessarily efficient What if the game is not dominance solvable? Game Theory - Mike Shor

Two firms competing over sales A Strategic Situation Two firms competing over sales Time and The Economist must decide upon the cover story to run some week. The big stories of the week are: A presidential scandal (labeled S), and A proposal to deploy US forces to Grenada (G) Neither knows which story the other magazine will choose to run Game Theory - Mike Shor

One Dominant Strategy Who has a dominant strategy? The Economist G S Time 100 , 100 0 , 90 95 , 100 95 , 90 Who has a dominant strategy? Assume it will be played! Other player can plan accordingly. Game Theory - Mike Shor

Dominated Strategies The Economist G S Time 100 , 100 0 , 90 95 , 100 0 , 90 95 , 100 95 , 90 For The Economist: G dominant = S dominated Dominated Strategy: There exists another strategy which always does better regardless of opponents’ actions Game Theory - Mike Shor

Successive Elimination of Dominated Strategies If a strategy is dominated, eliminate it The size and complexity of the game is reduced Eliminate any dominant strategies from the reduced game Continue doing so successively Game Theory - Mike Shor

Example: Tourists & Natives Two bars (bar 1, bar 2) compete Can charge price of $2, $4, or $5 6000 tourists pick a bar randomly 4000 natives select the lowest price bar Bar 2 $2 $4 $5 Bar 1 10 , 10 14 , 12 14 , 15 12 , 14 20 , 20 28 , 15 15 , 14 15 , 28 25 , 25 Game Theory - Mike Shor

Successive Elimination of Dominated Strategies Does any player have a dominant strategy? Does any player have a dominated strategy? Eliminate the dominated strategies Reduce the normal-form game Iterate the above procedure What is the equilibrium? Game Theory - Mike Shor

Successive Elimination of Dominated Strategies Bar 2 $2 $4 $5 $2 10 , , 10 14 , , 12 14 , , 15 Bar 1 Bar 1 $4 12 , , 14 20 , , 20 28 , , 15 $5 15 , , 14 15 , , 28 25 , , 25 Bar 2 $4 $5 Bar 1 20 , 20 28 , 15 15 , 28 25 , 25 Game Theory - Mike Shor

No Dominated Strategies Often there are no dominated strategies Or: reducing the game is not sufficient There may be multiple equilibria Method: Cell-by-cell inspection Ask: Is each player playing the best response to the other player? Game Theory - Mike Shor

Types of Games Games of Assurance Games of Coordination Games of Chicken Game Theory - Mike Shor

Games of Assurance Two firms each earning $45,000 Both can invest the $45,000 into R&D R&D successful only if both invest If R&D successful, each earns $95,000 Firm 2 Invest Don’t Firm 1 50 , 50 0 , 45 45 , 0 45 , 45 Game Theory - Mike Shor

Cell-by-cell Inspection Consider { Invest , Don’t } Both players have an incentive to change their strategy: NOT an equilibrium Firm 2 Invest Don’t Firm 1 50 , 50 0 , 45 45 , 0 45 , 45 Game Theory - Mike Shor

Assurance Outcomes Two equilibria exist Both firms prefer (I ,I) to (D,D) Payoffs of 50 to each firm instead of 45 However, investing is risky Must have assurances How to achieve assurance? Strategic moves: commit to choosing I Sequential moves: leader chooses the equilibrium Game Theory - Mike Shor

Games of Coordination Joint ventures and the choice of supplier Two firms engaged in joint venture Must use the same supplier, but each firm has a preferred supplier Firm 2 A B Firm 1 100 , 50 0 , 0 50 , 100 Game Theory - Mike Shor

Coordination Outcomes Two equilibria exist Firms prefer different equilibria How to achieve the most desirable outcome for you? Strategic moves: commit to choosing A Sequential moves: leader chooses the equilibrium Game Theory - Mike Shor

Summary You must put yourself in your rival’s shoes Recognize dominant and dominated strategies Anticipate that your opponent will recognize them as well Game Theory - Mike Shor