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Game Theory. Mike Shor Lecture 3. “Loretta’s driving because I’m drinking and I’m drinking because she’s driving.”. - The Lockhorns. Review. Understanding the game Noting if the rules are flexible Anticipating our opponents’ reactions Thinking one step ahead

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Game Theory

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Game Theory

Mike ShorLecture 3

“Loretta’s driving because I’m drinking and I’m drinking because she’s driving.”

- The Lockhorns


  • 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


  • 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.

  • 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



    What to Do?

    If you are advising Reynolds, what strategy do you recommend?

    Solving the Game

    • Best reply for Reynolds:

      • If Philip Morris advertises:

      • If Philip Morris does not advertise:


    • A strategy is dominantif 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

    DominanceA Technical Point

    • Strict Dominance:

      Advertise is strictly dominant forReynoldsif:

      • 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”



    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



    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?

    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

    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



    Expect your opponent to use her dominant strategy if she has one.


    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

    Games of Coordination

    • Solving:

    Firm 2

    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

    Games of Chicken

    • Entry into small markets

    Firm 2

    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


      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?


    • 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?

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