Extensive and Strategic Form Games Econ 171. Reminder: Course requirements Class website Go to...
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Transcript of Extensive and Strategic Form Games Econ 171. Reminder: Course requirements Class website Go to...
![Page 1: Extensive and Strategic Form Games Econ 171. Reminder: Course requirements Class website Go to economics department home page. Under Links, find Class.](https://reader030.fdocuments.net/reader030/viewer/2022032701/56649c7f5503460f949361f6/html5/thumbnails/1.jpg)
Extensive and Strategic Form Games
Econ 171
![Page 2: Extensive and Strategic Form Games Econ 171. Reminder: Course requirements Class website Go to economics department home page. Under Links, find Class.](https://reader030.fdocuments.net/reader030/viewer/2022032701/56649c7f5503460f949361f6/html5/thumbnails/2.jpg)
Reminder: Course requirements
• Class website Go to economics department home page. Under Links, find Class pages, then click on Econ 171
• Textbook: Games, Strategies, and Decision Making by Joseph E. Harrington, Jr.
• Clicker: Available at campus bookstore i>clicker Register your clicker at www.i>clicker.com/registration
![Page 3: Extensive and Strategic Form Games Econ 171. Reminder: Course requirements Class website Go to economics department home page. Under Links, find Class.](https://reader030.fdocuments.net/reader030/viewer/2022032701/56649c7f5503460f949361f6/html5/thumbnails/3.jpg)
Rock, Paper, Scissors
![Page 4: Extensive and Strategic Form Games Econ 171. Reminder: Course requirements Class website Go to economics department home page. Under Links, find Class.](https://reader030.fdocuments.net/reader030/viewer/2022032701/56649c7f5503460f949361f6/html5/thumbnails/4.jpg)
Rock-Paper-Scissors
First let’s draw the game tree on the blackboard for the game played with full information, where Player A moves first.
How would we draw the game tree for this game when players move simultaneously?
![Page 5: Extensive and Strategic Form Games Econ 171. Reminder: Course requirements Class website Go to economics department home page. Under Links, find Class.](https://reader030.fdocuments.net/reader030/viewer/2022032701/56649c7f5503460f949361f6/html5/thumbnails/5.jpg)
Vocabulary for Extensive form games
• Decision Tree• Decision Node-Specifies whose turn• Branches-Options• Terminal Node—End of play• Payoffs—For each person at each terminal
node.• Strategy—What will you do at each decision
node where it is your turn
![Page 6: Extensive and Strategic Form Games Econ 171. Reminder: Course requirements Class website Go to economics department home page. Under Links, find Class.](https://reader030.fdocuments.net/reader030/viewer/2022032701/56649c7f5503460f949361f6/html5/thumbnails/6.jpg)
Clicker Question
How many strategies are possible for Player B in the perfect information version of Rock-Paper-ScissorsA) 3B) 6C) 9D) 12E) 27
![Page 7: Extensive and Strategic Form Games Econ 171. Reminder: Course requirements Class website Go to economics department home page. Under Links, find Class.](https://reader030.fdocuments.net/reader030/viewer/2022032701/56649c7f5503460f949361f6/html5/thumbnails/7.jpg)
What is a strategy?
• “A strategy is not a sequence of actions, but rather a catalog of contingency plans, what to do in every situation. ‘’ Harrington, page 34.
(Read this section with extra care.)
• A strategy is a list stating what you would do at each possible decision node where it is your turn.
![Page 8: Extensive and Strategic Form Games Econ 171. Reminder: Course requirements Class website Go to economics department home page. Under Links, find Class.](https://reader030.fdocuments.net/reader030/viewer/2022032701/56649c7f5503460f949361f6/html5/thumbnails/8.jpg)
Details of strategic form game
• Set of Players• For each player a strategy set—list of all the
strategies that the player could choose. Remember that a strategy tells everything you would on any occasion when its your turn.
• Strategy profile: List of strategies chosen by every player.
• Payoff to each player depends on the strategy profile that was chosen.
![Page 9: Extensive and Strategic Form Games Econ 171. Reminder: Course requirements Class website Go to economics department home page. Under Links, find Class.](https://reader030.fdocuments.net/reader030/viewer/2022032701/56649c7f5503460f949361f6/html5/thumbnails/9.jpg)
Strategies for B in perfect information rock, paper, scissors game
• A strategy for B in perfect rock, paper, scissors answers 3 questions: – what will I do if I see rock?, – what will I do if I see paper? – What will I do if I see scissors?
• There are 3 possible answers to each question. Hence there are 3x3x3=27 possible strategies.
• Examples: – Paper if rock, rock if paper, rock if scissorrs– Or Rock if rock, scissors if paper, paper if scissors And so on… 27 possibilities
![Page 10: Extensive and Strategic Form Games Econ 171. Reminder: Course requirements Class website Go to economics department home page. Under Links, find Class.](https://reader030.fdocuments.net/reader030/viewer/2022032701/56649c7f5503460f949361f6/html5/thumbnails/10.jpg)
Two player game matrix in strategic form
Make a two-by-two table with one row for each strategy that player 1 could choose and one column for every strategy that player 2 could choose.
Enter payoffs to players 1 and 2 in appropriate spots.
![Page 11: Extensive and Strategic Form Games Econ 171. Reminder: Course requirements Class website Go to economics department home page. Under Links, find Class.](https://reader030.fdocuments.net/reader030/viewer/2022032701/56649c7f5503460f949361f6/html5/thumbnails/11.jpg)
Example: Matching Pennies
• In this case each player has only two possible strategies. Choose Heads, Choose tails.
• Payoff to Player 1 (row chooser) is written first, then payoff to Player 2.
![Page 12: Extensive and Strategic Form Games Econ 171. Reminder: Course requirements Class website Go to economics department home page. Under Links, find Class.](https://reader030.fdocuments.net/reader030/viewer/2022032701/56649c7f5503460f949361f6/html5/thumbnails/12.jpg)
Matching PenniesStrategic Form of Game
-1, 1 1,-1
1,-1 -1,1
Heads Tails
Heads
Tails
Player 2
Player 1
![Page 13: Extensive and Strategic Form Games Econ 171. Reminder: Course requirements Class website Go to economics department home page. Under Links, find Class.](https://reader030.fdocuments.net/reader030/viewer/2022032701/56649c7f5503460f949361f6/html5/thumbnails/13.jpg)
Rock, Paper, Scissors—Simultaneous Move
0,0 1,-1Rock Paper Scissors
Rock
Paper
Scissors
![Page 14: Extensive and Strategic Form Games Econ 171. Reminder: Course requirements Class website Go to economics department home page. Under Links, find Class.](https://reader030.fdocuments.net/reader030/viewer/2022032701/56649c7f5503460f949361f6/html5/thumbnails/14.jpg)
More complicated gamePlayer 1
Player 1
Player 220
31
00
12
DC
FE
G H
4 Possible Strategies for Player 1 : What are they?
2 Possible Strategies for Player 2:What are they?
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Strategic Form
1, 2 3, 1
0, 0 3, 1
2, 0 2, 0
2, 0 2, 0
Player 2E F
Player 1
C,G
C,H
D,G
D,H
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WMDs: What are the strategies?
![Page 17: Extensive and Strategic Form Games Econ 171. Reminder: Course requirements Class website Go to economics department home page. Under Links, find Class.](https://reader030.fdocuments.net/reader030/viewer/2022032701/56649c7f5503460f949361f6/html5/thumbnails/17.jpg)
Prisoners’ Dilemma Game
10, 10 0, 11
11, 0 1, 1
Cooperate Defect
Cooperate
Defect
PLAyER 1
Player 2
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Clicker Question 2
Players A and B play two rounds of simultaneous move prisoners’ dilemma. They don’t get to see how the other player played until both rounds are over. How many strategies are possible for each player?A) 2B) 4C) 8D) 16E) 32
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Clicker Question 3Players A and B play two rounds of simultaneous move prisoners’ dilemma. Each gets to see the other’s move in round 1 before choosing an action for round 2. How many strategies are possible for each player?A) 2B) 3C) 4D) 8E) 16
![Page 20: Extensive and Strategic Form Games Econ 171. Reminder: Course requirements Class website Go to economics department home page. Under Links, find Class.](https://reader030.fdocuments.net/reader030/viewer/2022032701/56649c7f5503460f949361f6/html5/thumbnails/20.jpg)
The game of Chicken
James Dean story.Alternatively—Two animals both want a resource. Each has two possible strategies. Fight or give up. A fight is very bad for both of them. How do we make an interesting game of this?
![Page 21: Extensive and Strategic Form Games Econ 171. Reminder: Course requirements Class website Go to economics department home page. Under Links, find Class.](https://reader030.fdocuments.net/reader030/viewer/2022032701/56649c7f5503460f949361f6/html5/thumbnails/21.jpg)
0 , 0 0 , 1
1, 0 -10, -10
Swerve
Swerve
Don’t Swerve
Don’t Swerve
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So long…at least for now.