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.
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