Oligopoly & Game Theory Lecture 26 Dr. Jennifer P. Wissink ©2017 John M. Abowd and Jennifer P. Wissink, all rights reserved. May 8, 2017

WISSINK Econ 1110 FINAL EXAM INFO & OTHER GRADING POLICY: Please see class syllabus (on our web page), Bb announcements and Bb FAQs. And all the best to everyone! Final is cumulative but will stress material since prelim 2 a little more than all the other material. Lecture content since prelim 2 is worth taking a real good look at. Especially all the graphs. See link below for great study guide of questions you should be able to answer. https://courses.cit.cornell.edu/econ1110jpw/review%201110.pdf Check https://courses.cit.cornell.edu/econ1110jpw/help.htm for office hour info. Final Exam is Saturday May 20 from 2pm-4:30pm in Barton Hall Center and East (near Teagle Gym side). People w/extra time or quiet conditions will start at 12pm in Uris 498. Make sure you bring your Cornell Student ID to the exam or some other picture ID. Everyone will be individually checked in with the TA that Student Center has you attached to. PLEASE make sure you KNOW this information BEFORE you arrive at the final so you can get to the correct TA table to check in quickly. When you check in you will get an index card. You should immediately find a seat and fill out the card. Place the completed card and your ID out in front of you. In Barton: Only sit 2 people to a table at either ends of the table. Make sure to bring a simple calculator, a ruler and a couple/three pens & pencils. The format for the final will be similar to the prelims. Multiple Choice (and maybe a few just fill in the blank in the m.c. section). Then multi-part problems. And maybe something a little different. The final is 2.5 hours long and usually students have plenty of time. I don't have any more finals to post. There is plenty of sample stuff already up there on the web site. Don't forget to get to the exam location early and KNOW WHAT SECTION YOU ARE OFFICIALLY REGISTERED IN, so you can check in quickly at the correct TA's table. Make sure you bring a photo ID. Make sure you bring a simple calculator. I think that covers it for now... Thanks! The Make-Up Final is Monday May 22 from 2:00-4:30pm in Uris 262. People w/extra time or quiet conditions will start at 12pm in Uris 438. Make sure you bring picture ID to the makeup final so you can be checked in.

The Prisoners’ Dilemma Game & Dominant Strategy Equilibrium Roger and Chris have been accused of a major crime (which they committed). They also have outstanding warrants based on minor crimes, too. They are held in isolated cells and offered the choice to either Lie or Confess. The payoff matrix shows the number of years of prison Roger (the row player) and Chris (the column player) will receive depending upon who confesses and who lies as (Roger’s prison time, Chris’ prison time). The game is played one-shot, simultaneously and non-cooperatively with full information.

The Prisoners’ Dilemma Is Very Distressing..., Or Is It? In the Prisoners’ Dilemma game, the “superior” outcome is when both prisoners lie – but that requires cooperation. When the game is only played once, simultaneously and non-cooperatively, (confess, confess) is the dominant strategy equilibrium and (-5, -5) is the dominant strategy equilibrium outcome. Could Roger & Chris sustain the (lie, lie) outcome of (-1, -1) somehow? change the payoffs in the matrix play the game repeatedly Do all games have at least one dominant strategy equilibrium? NO! Then what?

Nash Equilibrium Named after John Nash - a Nobel Prize winner in Economics. Did you read or see A Beautiful Mind? A Nash Non-cooperative Strategy (Best Response) for player “i” is a strategy such that player’s i’s payoff from playing that strategy is at least as large as the payoff player i would get from playing any other strategy, given the strategies the others are playing. A Nash Non-cooperative Equilibrium is a set of (Nash) strategies for all players, such that, when played simultaneously, they have the property that no player can improve his payoff by playing a different strategy, given the strategies the others are playing.

Hotelling's Location Game (Nash Equilibrium in Location) Emmanuel Macron Marine Le Pen

The Price Game Chris Low High Low 20, 20 60, 0 Roger High 0, 60 100, 100 i>clicker question: Are there any dominant strategy equilibria? Yes No. i>clicker question: Are there any Nash equilibria? Yes No. i>clicker question: Which Nash equilibrium do you think is more likely? Low, Low High, High

Maximin Equilibrium Chris Low High Low 20, 20 60, 0 Roger High 0, 60 More proactive than reactive. Pessimistic? The “min” part of maximin: for each of his options the player determines his worst outcome(s). The “max” part of maximin: the player then looks over all his worst case scenarios for each strategy and picks the best of the worst. The equilibrium part of maximin: When each player has a maximin strategy and when played against each other they are a Nash equilibrium. So all maximin equilibria are Nash equilibria. Not all Nash equilibria are maximin equilibria. Chris Low High Low 20, 20 60, 0 Roger High 0, 60 100, 100

Consider the following game between Roger and Chris Consider the following game between Roger and Chris. It is played one shot, simultaneously and non-cooperatively. CHRIS Left Right ROGER Top 10, 2 22, 2 Middle 20, 20 10, 20 Bottom 10, 5 5, 20 i>clicker question: Is there a dominant strategy equilibrium? Yes No i>clicker question: Is there a Nash equilibrium? Yes No i>clicker question: Is there a maximin equilibrium? Yes No

Another Game To Try Player 1 is the row player and can select numbers. 10, 20 30, 15 10, 15 16, 12 2 20, 10 30, 40 20, 25 8, 24 3 20, 20 12, 20 15, 10 25, 29 4 10, 10 15, 24 11, 27 Player 1 is the row player and can select numbers. Player 2 is the column player and can select letters. The payoffs are (Player 1, Player 2) Game is one-shot, simultaneous, non-cooperative, full information. Are there any… Dominant strategy equilibriums? Nash? Maximin?