SimultaneousGames (ppt)
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    SimultaneousGames (ppt) SimultaneousGames (ppt) Presentation Transcript

    • “ Loretta’s driving because I’m drinking and I’m drinking because she’s driving.” Game Theory and Business Strategy - The Lockhorns Original content © Mike Shor , 2001-2004.
    • Review
      • Understanding the game
      • Noting if the rules are flexible
      • Anticipating our opponents’ reactions
      • Thinking one step ahead
      • Where does this lead us?
        • We’ve defined the “game” but not the outcome
    • Equilibrium
      • The likely outcome of a game when rational, strategic agents interact
        • Each player is playing his or her best strategy given the strategy choices of all other players
        • No player has incentive to change his or her action unilaterally
      • Outline:
        • Model interactions as games
        • Identify the equilibria
        • Decide if they are likely to occur
    • Equilibrium Illustration
      • The Lockhorns
    • Cigarette Advertising on TV
      • All US tobacco companies advertised heavily on TV
      • Surgeon General issues official warning
          • Cigarette smoking may be hazardous
      • Cigarette companies fear lawsuits
          • Government may recover healthcare costs
      • Companies strike agreement
          • Carry the warning label and cease TV advertising in exchange for immunity from federal lawsuits.
      1964 1970
    • Strategic Interaction
      • Players: Reynolds and Philip Morris
      • Strategies: Advertise or Not Advertise
      • Payoffs: Companies’ Profits
      • Strategic Landscape:
        • 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?
    • Representing a Game PLAYERS STRATEGIES PAYOFFS 30 , 30 60 , 20 Ad 20 , 60 50 , 50 No Ad Reynolds Ad No Ad Philip Morris
    • What to Do?
      • If you are advising Reynolds, what strategy do you recommend?
      30 , 30 60 , 20 Ad 20 , 60 50 , 50 No Ad Reynolds Ad No Ad Philip Morris
    • Solving the Game
      • Best reply for Reynolds:
          • If Philip Morris advertises:
          • If Philip Morris does not advertise:
      30 , 30 60 , 20 Ad 20 , 60 50 , 50 No Ad Reynolds Ad No Ad Philip Morris
    • Dominance
      • A strategy is dominant if it outperforms all other choices no matter what opposing players do
      • Games with dominant strategies are easy to play
        • No need for “what if …” thinking
    • Dominance A Technical Point
      • Strict Dominance:
      • Advertise is strictly dominant for Reynolds if:
        • Profit ( Ad , Ad ) > Profit ( No , Ad )
        • Profit ( Ad , No ) > Profit ( No , No )
      • Weak Dominance:
      • Advertise is weakly dominant if:
        • Some inequalities are weak (  ),
        • At least one is strong(>)
      • By “dominant” we will mean “strictly dominant”
    • Dominance COMMANDMENT If you have a dominant strategy, use it. Expect your opponent to use her dominant strategy if she has one.
    • Prisoner’s Dilemma
      • Both players have a dominant strategy
      • The equilibrium results in lower payoffs for each player
      Equilibrium Optimal 30 , 30 60 , 20 Ad 20 , 60 50 , 50 No Ad Ad No Ad
    • Cigarette Advertising
      • After the 1970 agreement:
        • Cigarette advertising decreased by $63 million
        • Industry Profits rose by $91 million
      • Prisoner’s Dilemma
        • An equilibrium is NOT necessarily efficient
        • Players can be forced to accept mutually bad outcomes
        • Bad to be playing a prisoner’s dilemma, but good to make others play
    • How to Win a Bidding War by Bidding Less?
      • The battle for Federated (1988)
          • Parent of Bloomingdales
      • Current share price ≈ $60
      • Expected post-takeover share price ≈ $60
      • Macy’s offers $70/share
        • contingent on receiving 50% of the shares
      • Do you tender your shares to Macy’s?
    • How to Win a Bidding War (continued)
      • Robert Campeau bids $74 per share not contingent on amount acquired
      • Campeau’s Mixed Scheme:
        • If less than 50% tender their shares, each receives:
      • $74 per share
        • If more than 50% tender their shares, (if X% tender), each receives:
    • The Federated Game
      • To whom do you tender your shares?
      $74 $67 $74 Campeau $60 $60 Campeau $60 $60 Neither $60 $70 Macy’s You Neither Macy’s Majority of Others
    • How to Win a Bidding War
      • Each player has a dominant strategy: Tender shares to Campeau
      • Resulting Price:
        • (½ x 74) + (½ x 60) = $67
      • BUT: Macy’s offered $70 !
    • Dominant Strategies
      • “ The biggest, looniest deal ever. ”
      • – Fortune Magazine, July 1988
      • on Campeau’s acquisition of Federated Stores
      • What if players do not have dominant strategies?
    • Pricing without Dominant Strategies
      • Two bars (bar 1, bar 2) compete
        • Can charge price of $2, $4, or $5
      • Customer base consists of tourists and natives
        • 6,000 tourists pick a bar randomly
        • 4,000 natives select the lowest price bar
      • Marginal costs are close to zero
    • Tourists & Natives
      • Example scenario:
        • Bar 1 charges $4, Bar 2 charges $5
        • Bar 1 gets :
        • 3,000 tourists + 4,000 natives
        • = 7,000 customers x $4 = $28K
        • Bar 2 gets :
        • 3,000 tourists + 0 natives
        • = 3,000 customers x $5 = $15K
    • Tourists & Natives
      • in thousands of dollars
      Bar 2 25 , 25 28 , 15 14 , 15 $5 $4 15 , 28 15 , 14 $5 20 , 20 12 , 14 $4 Bar 1 14 , 12 10 , 10 $2 $2
    • Successive Elimination of Dominated Strategies
      • Does any player have a dominant strategy?
      • Does any player have a dominated strategy?
        • A strategy is dominated if there is some other strategy which always does better
          • Eliminate the dominated strategies
          • Reduce the size of the game
          • Iterate the above procedure
      • What is the equilibrium?
    • Successive Elimination of Dominated Strategies Bar 2 25 , 25 28 , 15 14 , 15 $5 $4 15 , 28 15 , 14 $5 20 , 20 12 , 14 $4 Bar 1 14 , 12 10 , 10 $2 $2
    • Dominance CAVEAT Expect your opponent to use her dominant strategy if she has one. BUT Be sure you understand your opponents’ true payoffs. (Do you know what really motivates them?)
    • No Dominated Strategies
      • Often there are no dominated strategies
      • Some games may have multiple equilibria
      • Equilibrium selection becomes an issue
      • Method :
      • For each player, find the best response to every strategy of the other player
      • Games of Coordination
      • Games of Assurance
      • Games of Chicken
    • Games of Coordination
      • Joint ventures and supplier choice
        • Two firms engaged in joint venture
        • Must use the same supplier, but each firm has a preferred supplier
      Firm 2 50 , 100 0 , 0 B A 0 , 0 B 100 , 50 A Firm 1
    • Games of Coordination
      • Solving:
      Firm 2 50 , 100 0 , 0 B A 0 , 0 B 100 , 50 A Firm 1
    • Games of Assurance
      • Joint research ventures
        • Each firm may invest $50,000 into an R&D project
        • Project succeeds only if both invest
        • If successful, each nets $75,000
      Firm 2 0 , 0 -50 , 0 $0 $50K 0 , -50 $0 75 , 75 $50K Firm 1
    • Games of Chicken
      • Entry into small markets
      Firm 2 50 , 50 100 , 0 Swerve Stay 0 , 100 Swerve -50 , -50 Stay Firm 1
    • The Right Game to Play
      • Why do we “solve” games?
      • To know which one to play!
        • How do internal corporate changes impact the outcome of strategic interaction?
      • Some games are better than others
    • Your Value to a Game
      • Your added value =
      • the size of the pie when you’re in the game
      • minus
      • the size of the pie when you are not
      • Added value limits how much you can get
          • You cannot receive much more than your added value
      • Added value provides benchmark
          • You should receive close to your added value
      • Change the Game!
          • You can increase your payoffs by increasing your added value OR decreasing the added value of other players.
    • Capacity Constraints
      • Can decreasing others’ added value increase our profits?
      • Can decreasing total industry value increase our profits?
    • Summary
      • Games have predictable outcomes
        • Notice dominant & dominated strategies
      • Select the right game to play
        • Seemingly internal corporate changes can impact the outcome of strategic interaction
      • Looking ahead:
        • Sequential Games:
        • How do games unfold over time?