# Thursday, May 6th. BenJerry JaimieAmy JamieMasha TayoLisa AbbasSarah ChadKaty JTMatt.

## Presentation on theme: "Thursday, May 6th. BenJerry JaimieAmy JamieMasha TayoLisa AbbasSarah ChadKaty JTMatt."— Presentation transcript:

Thursday, May 6th

BenJerry JaimieAmy JamieMasha TayoLisa AbbasSarah ChadKaty JTMatt

 The Situation: ◦ Ben and Jerry are opening a new ice cream shop. ◦ You agree on everything except your elevation preferences are diametrically opposed: BenJerry Prefers low elevation “The lower the better!” Prefers high elevations “The higher the better!”

 Your Task: ◦ To maximize the number of customers you agree that the ice cream shop should be at the intersection of a route (A,B,C) and a highway (1,2,3). ◦ To determine the final location Ben will select the highway and Jerry will simultaneously choose a route. Route B Route Route C

 [Blank slide to thwart the smartboard from giving away the answer]

Three-dimensional road map of possible choices Ben Highways (Wants low) Routes123 Row Minima Jerry Routes (Wants high) A10464 B6595 C2372 Column Maxima 1059

 Players? –  Options? –  Strategies? -  Outcome? -

 Jerry has all of the candy, this time Jerry picks a column, and Ben simultaneously picks a row. The intersecting number is the number of candies that Jerry gives Ben. 372 851 694

Friday, May 7th

 In the above game the numbers in the middle represent the “batting averages” for the batter against the pitcher based on the pitch selected and the swing selected (.3 is a hit 30% of the time)  A) What is the maximin of this scenario?  B) What is the minimax of this scenario?  C) Does a saddle point exist? If not, what is the gap between the minimax and the maximin? Baseball duel (2-player game) Pitcher FastballCurve Batter Fastball0.3000.200 Curve0.1000.500

 What is the expected batting average? ◦ Expected Value:  When a player resorts to a mixed strategy, the resulting outcome of the game is no longer predictable.  Instead, the outcome must be described in terms of weighted probabilities.  We are essentially splitting up the gap between the maximin and minimax between the 2 players

Cory MatthewsShawn Hunter JaimieMasha JamieAmy TayoLisa AbbasSarah MattKaty JTChad ( Whoever’s partner bailed on them) Last week Dr. Feeney’s glasses were stolen after-class.

Cory Matthews DecisionSentenceShawn Hunter DecisionSentence JaimieMasha JamieAmy TayoLisa AbbasSarah MattKaty JTChad ( )

 A two-person variable sum game  Each player has two strategies  Deny (cooperate with other player)  Confess on partner (defect against other player)  Mutual defect is always worse than mutual cooperation (i.e. both confessing on the other is worse than both denying) (Snitch)

 When each person selects their own best individual strategy, both people suffer in the end. ◦ For both Shawn and Cory snitching strategy dominates denying ◦ But if both snitch, it’s worse than if both deny  For the best mutual outcome to be reached, cooperation is needed.

Scenario 1: Individual Strategies Scenario 2: Cooperation Corey ConfessesShawn Confesses Shawn Denies Both Receive 2 Weeks Both Receive 1 Week  In scenario where each selects their own best individual strategy, both suffer in the end.

 There are four possible outcomes:  Player 1 accelerates, Player 2 swerves Player 1 wins, both live  Player 2 accelerates, Player 1 swerves Player 2 wins, both live  Player 1 swerves, Player 2 swerves Both players lose-face, but both players live.  Player 1 accelerates, Player 2 accelerates Neither technically wins, both players die. Catastrophic outcome

 Activity: Assign point values to each of these outcomes in the table on your handout using values from 1-10 (with 1 being the worst).

Situation  Each person has one bullet.  Each decides whether to shoot or not shoot simultaneously  Two goals: #1 Survive #2 Kill as many others as possible *What should be the expected outcome?*

 How would the scenario be different if all decisions were not made simultaneously and all players must fire their gun?  Key Points to Remember: ◦ There is only 1 bullet in each gun ◦ A decides, then B, then C (but even if A shoots B, B still gets a shot in this scenario- simultaneous sequential) ◦ What should be the expected outcome?*

 How would the scenario be different if all decisions are not made simultaneously and players are not required to fire their gun? ◦  Note: If you fire your gun you must shoot someone *What should be the expected outcome?* Real Life Application: Is a truel mathematically a better model than a duel when aiming to prevent conflicts?

 Which of these activities could you use in your classroom? ◦ What would you modify?