Nash Equilibrium-Game Theory For Managers-Lecture Slides, Slides of Game Theory

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Lecture 3 Game Plan^ „^

Nash equilibrium^ „^

… in pure strategies & mixed strategies „ … how NE play arises from rationality „ … how NE play can arise from evolution

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Nash Equilibrium „^ Nash Equilibrium:

• A set of strategies, one for each player, such thateach player’s strategy is a best response to others’strategies

„^

Best Response

• The strategy that maximizes my payoff given others’strategies.

„^

Everybody is playing a best response

• No incentive to unilaterally change my strategy

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Some Prototypical Games

„^

Prisoners’ Dilemma

„^

price war

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Example: SUV Price Wars “General Motors Corp. and Ford Motor Co.slapped larger incentives on popular sport-utility vehicles, escalating a

discounting

war in the light-truck category

… Ford

added a $500 rebate on SUVs, boosting cashdiscounts to $2,500. The Dearborn, Mich.,auto maker followed GM, which earlier in theweek began offering $2,500 rebates onmany of its SUVs.”

-- Wall Street Journal,

January 31, 2003

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SUV Price Wars: Outcome^ „^

Each firm has a unilateral incentiveto discount but neither achieves apricing advantage.

GM

Discount

Don’t

Discount

Ford

Don’t

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“Red Queen Effect”^ “It takes all the running you can do to keep in the same

place” – Red Queen to Alice

From Carroll, Lewis.

Alice’s Adventures in Wonderland.

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Prisoners’ Dilemma Game

Prisoner 2

Don’t

Confess

Confess

Prisoner 1

Don’t

„^

Key features:

• Both players have a dominant strategy to Confess• BUT both players better off if they

both

Don’t

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Prisoners’ Dilemma Game

Prisoner 2

Confess

Don’t

Confess

Prisoner 1

Don’t

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Evolution in Prisoners’Dilemma (One Population)

Prob. of Confess in population

„^

Row and Col players are drawn from thesame population

„^

Those who Confess get higher payoff, soConfess dominates the population

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Some Prototypical Games

„^

Prisoners’ Dilemma

„^

Loyal Servant

„^

price war

„^

defensive innovation

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Soft & Chewy Cookies „^ Supermarket cookies tend to becrispy, not chewy „^ Duncan Hines (owned by P&G)entered with a chewy cookie [1984] „^ How did Nabisco and Keeblerrespond?

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Soft & Chewy Wars^ „^

Nabisco and Keebler rolled out theirown soft and chewy varieties:^ „^

Keebler Soft Batch „ Nabisco Chips Ahoy! Chewy

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Soft & Chewy Retreat

„^

P&G sells Duncan Hines to Aurora [1997] “This agreement is a win-win. Consumerswill still be able to buy great DuncanHines products, now through AuroraFoods, and we can focus on the strategicopportunities we've established for ourfood and beverage business.”

-Steve Donovan, P&G VP, food and beverages.

Source: Larkin, Patrick. “Duncan Hines Sold: Columbus Firm Buys P&G Brand.”

The

Cincinnati Post

. 8 December 1997,

http:/

/www.cincypost.com/business/1997/pg120897.html (accessed July 14, 2004).

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Defensive Innovation^ „^

A monopolist’s incentive to innovateincreases as it faces innovative entrants.

„^

Consider case of

product variety

• consumers represented as points in a square • they buy whichever product is closest

represents

consumers who buyfrom monopolist^ represents aproduct of monopolist

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