Chapter 11 Game Theory and Strategic Behavior



Chapter 13. Game Theory and Competitive Strategy

Topics to be Discussed

Gaming and Strategic Decisions

Dominant Strategies

The Nash Equilibrium

Repeated Games

Maximin Strategy

Sequential Games : Moving First Advantage ( GRADUATES ONLY )

Gaming and Strategic Decisions

“If I believe that my competitors are rational and act to maximize their own profits, how should I take their behavior into account when making my own profit-maximizing decisions?”

Noncooperative versus Cooperative Games

Noncooperative Game

Negotiation and enforcement of a binding contract are not possible

Example:

Cooperative Game

Players negotiate binding contracts that allow them to plan joint strategies

Example: Buyer and seller negotiating the price of a good or service or a joint venture by two firms (i.e. Microsoft and Apple)

Binding contracts are possible

Gaming and Strategic Decisions

An Example

1) Auction a dollar bill

2) Highest bidder receives the dollar in return for the amount bid

3) Second highest bidder must pay the amount he or she bid

How much would you bid?

[pic]

Dominant Strategies

A and B are competitors and are deciding whether or not to advertise.

Firm A :Dominant strategy is to advertise

Firm B : Dominant strategy is to advertise

Outcome : Both advertise

Modified Advertising Game

The outcome without a dominant strategy for each firm is slightly different.

[pic]

Dominant Strategies

Observations

1) A has no dominant strategy.

2) B has a dominant strategy (advertise).

Should A choose to advertise?

Is this a Nash equilibrium?

The Nash Equilibrium

Dominant Strategies

“I’m doing the best I can no matter what you do.”

“You’re doing the best you can no matter what I do.”

Nash Equilibrium

“I’m doing the best I can given what you are doing”

“You’re doing the best you can given what I am doing.”

Product Choice Problem

Examples With A Nash Equilibrium

Two cereal companies

Market for one producer of crispy cereal

Market for one producer of sweet cereal

Each firm only has the resources to introduce on cereal

Noncooperative

[pic]

Questions

1) What is (are) the Nash Equilibrium(s)?

2) How could it (they) be reached?

Beach Location Game

Scenario

Two competitors, Y and C, selling soft drinks

Beach 200 yards long

Sunbathers are spread evenly along the beach

Price Y = Price C

Beach Location Game

Questions

1) Where will the competitors locate (i.e. where is the Nash equilibrium)?

Can you think of any examples of their decision problem?

Maximin Strategy

[pic]

Consider

If both are rational and informed

What is Player 2’s dominant strategy?

What is the Nash equilibrium?

Maximin Strategy

Maximizes the minimum gain that can be earned

Maximin Strategy

Consider

If Player 2 is not rational or completely informed

What would be Player 1’s maximin strategy?

What would be Player 2’s maximin strategy?

If 1 knows 2 is using a maximin strategy, what outcome would 1 choose?

Prisoners’ Dilemma

[pic]

Questions

1) What is the Nash Equilibrium?

2) What is the maximin solution?

Mixed Stragegies

Pure Strategies

Strategies in which player make a specific choice or take a specific action (e.g. advertise or do not advertise)

Pure strategy will not succeed for either player and there is not a Nash equilibrium.

Mixed Strategies

Strategies in which the player makes a random choice among two or more possible actions, based on a set of chosen probabilities.

Random choice is a Nash equilibrium because if any other choice is made there is an incentive for the other player to change.

Applications of mixed strategy are very limited and often unrealistic.

Pareto Efficient:

An allocation is Pareto Efficient if goods cannot be reallocated to make someone better off without making someone else worse off.

That is, a strategy is said to be pareto efficient if there is not other choice such that one is better off and the other is NOT worse.

Repeated Games

In real life, firms play a repeated game.

With each repetition of the Prisoners’ Dilemma, firms can develop reputations about their behavior and study the behavior of their competitors.

[pic]

In a non-repeated game the strategy is Low1 and Low2.

Question

How would this strategy change if the game repeated over a long period of time? (e.g. price announcements every month)

The optimum strategy is tit-for-tat.

By creating the possibility of tit-for-tat pricing, a cooperative price will be chosen.

Question

How would this strategy be impacted with a finite game?

Conclusion

Repeated game

The Prisoners’ Dilemma can have a cooperative outcome

This is most likely to occur in a market with:

Few firms, Stable demand, Stable cost

Cooperation is difficult at best since these factors may change in the long-run.

Sequential Games (GRADUATES ONLY)

Players move in turn

Players must think through the possible actions and rational reactions of each player

Examples

Stackelberg Model

Responding to a competitor’s ad campaign

Scenario

Two new (sweet, crispy) cereals

Successful only if each firm produces one cereal

Sweet will sell better

Both still profitable with only one producer

Question

What is the likely outcome if both make their decisions independently, simultaneously, and without knowledge of the other’s intentions?

Assume that Firm 1 will introduce its new cereal first (a sequential game).

Question

What will be the outcome of this game?

[pic]

The Advantage of Moving First

In this product-choice game, there is a clear advantage to moving first.

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download