Chapter 11 Game Theory and Strategic Behavior
Topics to be Discussed
n Gaming and Strategic Decisions
n Dominant Strategies
n The Nash Equilibrium
n Repeated Games
n Maximin Strategy
n Sequential Games : Moving First Advantage ( GRADUATES ONLY )
Gaming and Strategic Decisions
n “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?”
n 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
n 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
4) How much would you bid?
Dominant Strategies
n A and B are competitors and are deciding whether or not to advertise.
•
•
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Firm A :Dominant strategy is to advertise
Firm B : Dominant strategy is to advertise
Outcome : Both advertise
Modified Advertising Game
n The outcome without a dominant strategy for each firm is slightly different.
Dominant Strategies
n 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
n 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.”
n 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
n 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
n Questions
1) What is (are) the Nash Equilibrium(s)?
2) How could it (they) be reached?
Beach Location Game
n 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
n Questions
1) Where will the competitors locate (i.e. where is the Nash equilibrium)?
2) Can you think of any examples of their decision problem?
Maximin Strategy
n Consider
• If both are rational and informed
– What is Player 2’s dominant strategy?
– What is the Nash equilibrium?
n Maximin Strategy
• Maximizes the minimum gain that can be earned
Maximin Strategy
n 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
n Questions
1) What is the Nash Equilibrium?
2) What is the maximin solution?
Mixed Stragegies
n Pure Strategies
• Strategies in which player make a specific choice or take a specific action (e.g.
advertise or do not advertise)
n Pure strategy will not succeed for either player and there is not a Nash equilibrium.
n 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.
Repeated Games
n In real life, firms play a repeated game.
n With each repetition of the Prisoners’ Dilemma, firms can develop reputations about
their behavior and study the behavior of their competitors.
n In a non-repeated game the strategy is Low1 and Low2.
n Question
• How would this strategy change if the game repeated over a long period of time?
(e.g. price announcements every month)
n The optimum strategy is tit-for-tat.
• By creating the possibility of tit-for-tat pricing, a cooperative price will be chosen.
n Question
• How would this strategy be impacted with a finite game?
n 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)
n Players move in turn
n Players must think through the possible actions and rational reactions of each player
n Examples
• Stackelberg Model
• Responding to a competitor’s ad campaign
n 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
n Question
• What is the likely outcome if both make their decisions independently,
simultaneously, and without knowledge of the other’s intentions?
n Assume that Firm 1 will introduce its new cereal first (a sequential game).
n Question
• What will be the outcome of this game?
n The Advantage of Moving First
• In this product-choice game, there is a clear advantage to moving first.