Game Theory Exercises

Solving Structured Games The underlying principle is to –look forward to determine the outcomes that will result from your own and competitors’ actions –Reason backward to find the best decision In all of these games it is best to play the game as it is written (not assuming some other conditions than those which are given) After you have played the game, then you can start to think about how the game could be changed to get a more favorable result.

Group paper instructions This group exercise is due on October 27 –You should choose your own group (about 4- 5 member teams seem to work best) –Solve each of the following game situations Tell how the game will turn out (Nash equilibrium) Explain how you got your answer –Each of the game solutions should only require about one page –Have fun!

Hot Dog Stands on a Beach Oscar and Meyer decide to sell hot dogs on a beach. They are required to sell the hot dogs at the same price and the hot dogs are undifferentiated. The sunbathers are distributed equally along the beach. Where should Oscar and Meyer locate their hot dog stands?

The Prisoner’s Dilemma Al JoeTalkDon’t talk Talk(-8, -8)(0, -15) Don’t talk(-15, 0)(-1, -1) How will the game turn out? Two vagrants, Al and Joe, have been arrested for vagrancy. The DA suspects them of complicity in a robbery, but she doesn’t have enough evidence to convict them. (Al and Joe don’t know this for sure.) The DA interrogates each of them separately and offers the following deal: “If you implicate your friend, I’ll reduce your charge to being an accomplice. If you don’t, I will throw the book at you.” Assume the relevant prison times (in months) are as follows:

The Rational Pigs Big Pig: Little Pig:PressDon’t Press Press(1.5, 3.5)(-0.5, 6) Don’t Press(5, 0.5)(0, 0) A big pig and a little pig are in a long, narrow pen. There is a lever at one end of the pen which, when pressed, dispenses 6 units of food into a trough at the other end of the pen. Thus, if either pig presses the lever it must run to the other end of the pen before it can eat. By the time it gets there, the other pig may have eaten some or most of the food. The big pig is able to prevent the little pig from getting any of the food when both are at the trough. Assume it requires energy equivalent to ½ unit of food for either pig to run from one end of the pen to the other. If both of the pigs press the lever, the subordinate pig is faster than the dominant pig and can eat two units of food before the dominant pig gets to the food. The rest of payoffs are listed below. How will this game turn out?

Boeing, Airbus and the Super- jumbo Aircraft Boeing and Airbus are considering building a super- jumbo aircraft seats) It is a very expensive and risky proposition. All the numbers in the following payoff matrix are $billions Boeing must pay all of its own development costs Airbus will receive a development subsidy of $5 billion from the European Union The introduction of a super-jumbo aircraft (by either firm) will impact the companies current product lines –Boeing will lose about half of its 747 sales (- $6 billion) –Airbus will lose less (-$2 billion) The forecasted market for the super-jumbo is $15 billion The payoff matrix is computed on the next slide.

Boeing, Airbus and the super-jumbo airframe (1991) Boeing Airbus Develop Doesn’t Develop Doesn’t Develop (A/B)(A/B) (6-8+5=3 / 9-8=1) (-1/12) (15-3=12/ -6) (-2/15-8=7) Market =$15b, Development Cost=$8b, Airbus subsidy=$5b