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Introduction to Microeconomics Game theory Chapter 9

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Introduction to Microeconomics. Game theory Chapter 9. Elements of a Game. Basic elements The players. The strategies. The payoffs. Payoff matrix A table that describes the payoffs in a game for each possible combination of strategies. Strategy. Dominant strategy - PowerPoint PPT Presentation

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Page 1: Introduction to Microeconomics

Introduction to Microeconomics

Game theoryChapter 9

Page 2: Introduction to Microeconomics

• Basic elements– The players.– The strategies.– The payoffs.

• Payoff matrix– A table that describes the payoffs in a game for

each possible combination of strategies.

LO1: Basic Elements of A Game

Elements of a Game

© 2012 McGraw-Hill Ryerson Limited Ch9 -2

Page 3: Introduction to Microeconomics

Strategy

Dominant strategy – One that yields the highest payoff no matter what

the other players in the game chooseDominated strategy

– Any other strategy available to a player that has a dominant strategy

Page 4: Introduction to Microeconomics

• The Prisoner’s Dilemma– A classic example of potential conflict between the

narrow self-interest of individuals and the broader interest of larger communities.

• The Prisoner’s Dilemma– Each player has a dominant strategy.– The dilemma is: Payoffs are smaller than they

would be if each player had played a dominated strategy.

Lo4: The Effect of Dominant Strategy

Prisoner’s Dilemma

© 2012 McGraw-Hill Ryerson Limited Ch9 -4

Page 5: Introduction to Microeconomics

• Will the prisoners confess?– Two prisoners, Horace and Jasper, are being held in separate cells for a serious

crime that they did in fact commit.– The prosecutor, has only enough hard evidence to convict them of a minor

offence.

The Payoff Matrix for the original Prisoner’s Dilemma

© 2012 McGraw-Hill Ryerson Limited Ch9 -5Lo4: The Effect of Dominant

Strategy

Page 6: Introduction to Microeconomics

• Example 9.3: Will the prisoners confess?– The dominant strategy for each prisoner is to confess.

Table 9.3: The Payoff Matrix for the original Prisoner’s Dilemma

© 2012 McGraw-Hill Ryerson Limited Ch9 -6

Dominate strategy

Lo4: The Effect of Dominant Strategy

Page 7: Introduction to Microeconomics

• Will the prisoners confess?– The dominant strategy for each prisoner is to confess.

The Payoff Matrix for the original Prisoner’s Dilemma

© 2012 McGraw-Hill Ryerson Limited Ch9 -7

√ √Dominate strategy

Lo4: The Effect of Dominant Strategy

Page 8: Introduction to Microeconomics

• Will the prisoners confess?– When each follows his dominant strategy and confesses,

both will do worse than if each had shown restraint.

Table 9.3: The Payoff Matrix for the original Prisoner’s Dilemma

© 2012 McGraw-Hill Ryerson Limited Ch9 -8

Nash Equilibrium

Better Outcome

Lo4: The Effect of Dominant Strategy

Page 9: Introduction to Microeconomics

• ..\..\..\..\..\..\Users\gmason.PRAINC\Documents\Pavtube\youtube_converter\Nash Equilibrium - YouTube.mp4

Page 10: Introduction to Microeconomics

TerminologyWhen a player tries to choose the "best" strategy among a multitude of options, that player may compare two strategies A and B to see which one is better. The result of the comparison is one of:• B dominates A: choosing B always gives as good as or a better outcome than choosing A. There are 2

possibilities:– B strictly dominates A: choosing B always gives a better outcome than choosing A, no matter what the other player(s)

do.– B weakly dominates A: There is at least one set of opponents' action for which B is superior, and all other sets of

opponents' actions give B at least the same payoff as A.• B and A are intransitive: B neither dominates, nor is dominated by, A. Choosing A is better in some cases,

while choosing B is better in other cases, depending on exactly how the opponent chooses to play. For example, B is "throw rock" while A is "throw scissors" in Rock, Paper, Scissors.

• B is dominated by A: choosing B never gives a better outcome than choosing A, no matter what the other player(s) do. There are 2 possibilities:

– B is weakly dominated by A: There is at least one set of opponents' actions for which B gives a worse outcome than A, while all other sets of opponents' actions give A at least the same payoff as B. (Strategy A weakly dominates B).

– B is strictly dominated by A: choosing B always gives a worse outcome than choosing A, no matter what the other player(s) do. (Strategy A strictly dominates B).

• This notion can be generalized beyond the comparison of two strategies.– Strategy B is strictly dominant if strategy B strictly dominates every other possible strategy.– Strategy B is weakly dominant if strategy B dominates all other strategies, but some are only weakly dominated.– Strategy B is strictly dominated if some other strategy exists that strictly dominates B.– Strategy B is weakly dominated if some other strategy exists that weakly dominates B.

Source: Wikipedia

Page 11: Introduction to Microeconomics

• ThePrisonersDilemma.cdf

Page 12: Introduction to Microeconomics

• Imagine that Pepsi and Coca Cola are the only makers of cola drinks. Both are earning economic profits of $6000/day.

• Assume the following: – If Pepsi increases its advertising expenditures by $1000/day and

Coca Cola spends no more on advertising , Pepsi’s profit will increase to $8000/day and Coca Cola’s will decrease to $2000.

– If both spend $1000 on advertising, each will earn an economic profit of $5500/day.

– If Pepsi stands pat while Coca Cola increases its spending by $1000, Pepsi’s economic profit will fall to $2000/day, and Coca Cola’s will increase to $8000.

– The payoffs are symmetric.

Will Pepsi spend more money on advertising?

LO1: Basic Elements of A Game Ch9 -12© 2012 McGraw-Hill Ryerson Limited

Page 13: Introduction to Microeconomics

The Payoff Matrix for an Advertising Game

© 2012 McGraw-Hill Ryerson Limited Ch9 -13LO1: Basic Elements of A Game

Page 14: Introduction to Microeconomics

Table 9.1: The Payoff Matrix for an Advertising Game

© 2012 McGraw-Hill Ryerson Limited Ch9 -14

Suppose Coca Cola assumes that Pepsi will raise its spending on advertising, in that case, Coca Cola’s best option would be to follow suit.

Payoff is higher

LO1: Basic Elements of A Game

Page 15: Introduction to Microeconomics

Table 9.1: The Payoff Matrix for an Advertising Game

© 2012 McGraw-Hill Ryerson Limited Ch9 -15

Suppose Coca Cola assumes that Pepsi will do nothing, in that case, Coca Cola’s best option would be to raise its spending on advertisements.

Payoff is higher

LO1: Basic Elements of A Game

Page 16: Introduction to Microeconomics

Table 9.1: The Payoff Matrix for an Advertising Game

© 2012 McGraw-Hill Ryerson Limited Ch9 -16

No matter which strategy Pepsi chooses, Coca Cola will earn a higher economic profit by increasing its spending on advertising.

Nash equilibrium

Since this game is perfectly symmetric, a similar conclusion holds for Pepsi: No matter which strategy Coca Cola chooses, Pepsi will do better by increasing its spending on advertisements.

Dominate strategy

LO2: Identifying Dominant StrategyLO3: Find an Equilibrium for a Game

Page 17: Introduction to Microeconomics

• Dominant strategy:– A strategy that yields a higher payoff no matter what

the other players in a game choose.• Dominated strategy:

– Any other strategy available to a player who has a dominant strategy.

• Nash Equilibrium:– Any combination of strategies in which each player’s

strategy is his best choice, given the other players’ strategies.

LO2: Identifying Dominant Strategy

Strategies

© 2012 McGraw-Hill Ryerson Limited Ch9 -17

Page 18: Introduction to Microeconomics

Example 9.2: The Payoff Matrix for an Advertising Game When One Player Lacks a Dominant Strategy

© 2012 McGraw-Hill Ryerson Limited Ch9 -18

No matter what Pepsi does, Coca Cola will do better to increaseits advertising, so raising the advertising budget is a dominant strategy for Coca Cola.

Payoff is higher

Payoff is higher

Dominate strategy

LO3: Find an Equilibrium for a Game

Page 19: Introduction to Microeconomics

Example 9.2: The Payoff Matrix for an Advertising Game When One Player Lacks a Dominant Strategy

© 2012 McGraw-Hill Ryerson Limited Ch9 -19

Pepsi does not have a dominate strategy in this game.

Payoff is higher

Payoff is higher

LO3: Find an Equilibrium for a Game

Page 20: Introduction to Microeconomics

Example 9.2: The Payoff Matrix for an Advertising Game When One Player Lacks a Dominant Strategy

© 2012 McGraw-Hill Ryerson Limited Ch9 -20

Nash equilibrium: If Pepsi believes that Coca Cola will spend more on advertisements, Pepsi’s best strategy is to keep its own spending constant.

Dominate strategy

Nash Equilibrium

LO3: Find an Equilibrium for a Game

Page 21: Introduction to Microeconomics

• Cartel:– A coalition of firms that agree to restrict output for the purpose

of earning an economic (excess) profit.– Normally cartels involve several firms.

• This makes retaliation against a dissenter difficult.– Agreements are not legally enforceable and hence may be

unstable.– Constant temptation for each participant to cheat on the

agreement.• Example: OPEC oil cartel production quotas.

– Economic naturalist 9.1: Why might cartel agreements be unstable?

LO5: Games with Equilibrium Like Prisoner’s Dilemma

Cartels

© 2012 McGraw-Hill Ryerson Limited Ch9 -21

Page 22: Introduction to Microeconomics

– Faced with the demand curve shown, a monopolist with zero marginal cost would produce 1000 bottles/day (the quantity at which marginal revenue equals zero) and sell them at a price of $1.00/bottle.

FIGURE 9.1: The Market Demand for Mineral Water

DMR

© 2012 McGraw-Hill Ryerson Limited Ch9 -22LO5: Games with Equilibrium Like Prisoner’s

Dilemma

Page 23: Introduction to Microeconomics

– By cutting its price from $1/bottle to $0.90/bottle, Aquapure can sell the entire market quantity demanded at that price, 1100 bottles/day, rather than half the monopoly quantity of 1000 bottles/day.

FIGURE 9.2: The Temptation to Violate a Cartel Agreement

DMR

0.90

1100

© 2012 McGraw-Hill Ryerson Limited Ch9 -23LO5: Games with Equilibrium Like Prisoner’s

Dilemma

Page 24: Introduction to Microeconomics

– Each firm’s dominant strategy is to sell at the lower price, yet in following that strategy, each earns a lower profit than if each had sold at the higher price.

TABLE 9.4: The Payoff Matrix for a Cartel Agreement

© 2012 McGraw-Hill Ryerson Limited Ch9 -24

Nash Equilibrium

LO5: Games with Equilibrium Like Prisoner’s Dilemma

Page 25: Introduction to Microeconomics

• ..\..\..\..\..\..\Users\gmason.PRAINC\Documents\Pavtube\youtube_converter\Game Theory 101 What Is a Nash Equilibrium (Stoplight Game) - YouTube_0.mp4