MicroEconomics 5e by besanko braeutigam chapter 14

Chapter Fourteen Overview 1.Motivation: Honda and Toyota 3.Nash Equilibrium 5.The Prisoner's Dilemma 6.Dominant Strategy Equilibrium 7.Limitations of the Nash Equilibrium 8.Sequential Mo

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Chapter Fourteen Overview

1.Motivation: Honda and Toyota

3.Nash Equilibrium 5.The Prisoner's Dilemma 6.Dominant Strategy Equilibrium 7.Limitations of the Nash Equilibrium

8.Sequential Moves Games

• The Value of Limiting One’s Opinion

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Honda

Toyota

Capacity Expansion Game

What is the likely outcome of this game?

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Game Elements

Players: agents participating in the game (Toyota, Honda)

Strategies: Actions that each player may take under any possible

circumstance (Build, Don't build)

Outcomes: The various possible results of the game (four, each

represented by one cell of matrix)

Payoffs: The benefit that each player gets from each possible

outcome of the game (the profits entered in each cell of the matrix)

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Information: A full specification of who knows what when (full information)

Timing: Who can take what decision when and how often the game is repeated (simultaneous, one-shot)

Solution concept of the game: "What is the likely outcome"? (Dominant Strategy Equilibrium, Nash Equilibrium)

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Nash Equilibrium

Definition: A Nash Equilibrium occurs when each player chooses a strategy that gives him/her the highest payoff, given the strategy chosen by the other

player(s) in the game ("rational

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Nash Equilibrium

• Given Toyota builds a new plant, Honda's best response is to build a new plant

• Given Honda builds a new plant, Toyota's

best response is to build a plant

• Why is the Nash Equilibrium plausible?

• It IS "self enforcing” Even though it DOES NOT necessarily maximise collective interest

Why?

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Other Considerations

Nash Equilibrium: both confess Pareto Dominant Point: Neither confesses

Definition: A dominant strategy is a strategy that is better

than any other strategy that a player might choose, no

matter what strategy the other player follows.

Note: When a player has a dominant strategy, that strategy will be the player's Nash Equilibrium strategy.

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Dominant Strategy Equilibrium

Definition: A Dominant Strategy Equilibrium occurs when each

player uses a dominant strategy.

Honda

Toyota

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Dominated Strategy

Definition: A player has a dominated strategy when the player has another

strategy that gives it a higher payoff no matter what the other player does

Honda

Toyota

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Dominant or Dominated Strategy

Why look for dominant or dominated strategies?

A dominant strategy equilibrium is particularly compelling as a "likely" outcome

Similarly, because dominated strategies are unlikely

to be played, these strategies can be eliminated from consideration in more complex games This can make solving the game easier.

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Honda

Dominated Strategy

Toyota Game Matrix 4: Dominated Strategies

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Slick

Luke

Nash Equilibrium Limitations

Game Matrix 4: Dominated Strategies Limitations of Nash Equilibrium

The Nash Equilibrium need not be unique

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Depositor 1

Depositor 2

Example: Bank Runs

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Nash Equilibrium need not exist

Example: Matching Pennies Game Matrix 6: Non-existence of Nash Equilibrium

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Mixed Strategies

Pure Strategy – A specific choice of a strategy

from the player’s possible strategies in a game.

Mixed Strategy – A choice among two or more

pure strategies according to pre-specified probabilities.

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Repeated Prisoner’s Dilemma

Cooperation can result from self-interested behavior on the part of each player under certain circumstances:

“Grim Trigger” Strategy – one episode of cheating

by one player triggers the grim prospect of a permanent breakdown in cooperation for the remainder of the game.

“Tit-for-Tat” Strategy – A strategy in which you do

to your opponent in this period what your opponent did to you in the last period.

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Repeated Prisoner’s Dilemma

Likelihood of cooperation increases under these conditions:

1.The players are patient.

2.Interactions between the players are frequent.

3.Cheating is easy to detect.

4.The one-time gain from cheating is relatively small.

Likelihood of cooperation diminishes under these conditions:

5.The players are impatient.

6.Interactions between the players are infrequent.

7.Cheating is hard to detect.

8.The one-time gain from cheating is large in comparison to the

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Sequential Move Games

Games in which one player (the first mover) takes an action before another player (the second mover) The second mover observes the action taken by the first mover before deciding what action

it should take.

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Sequential Move Games - Terms

A game tree shows the different strategies that each player can

follow in the game and the order in which those strategies get chosen.

Backward induction is a procedure for solving a sequential-move

game by starting at the end of the game tree and finding the optimal decision for the player at each decision point.

Strategic moves are actions that a player takes in an early stage of

a game that alter the player’s behavior and the other players’ behavior later in the game in a way that is favorable to the first player.

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Sequential Move Games – Game Tree

Game Tree 1: Toyota and Honda, Revisited

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Game trees often are solved by starting at the end of the tree and, for each decision point, finding the optimal decision for the player at that point

Keeps analysis manageable Ensures optimality at each point

The solution to the revisited game differs from that of the

simultaneous game Why – the first mover can force second mover's hand Illustrates the value of commitment (i.e limiting

one's own actions) rather than flexibility

Example: Irreversibility of Business Decisions in the Airline Industry.

Sequential Move Games – Game Tree

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1 Game Theory is the branch of economics concerned with the analysis of optimal decision making when all decision makers are presumed to be rational, and each is attempting to anticipate the actions and reactions of the competitors

2 A Nash Equilibrium in a game occurs when each player chooses a strategy that gives him/her the highest payoff, given the strategies chosen by the other players

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