Game Theory
 Game Theory encompasses a wide variety of games, but they all have a common factor: They all have situations of conflict or cooperation
 2 or more parties will interact with each other
Topics
 Impartial Combinatorial Games
 Zerosum Games
 General sum games
 Nash equilibria
 Evoluationary games, ESs, correlated equilibria
 Mechanism Design
A GeneralSum Game
 (Taken from Ben Polak’s class at Yale)
 Take a paper and write your name on it. Then, write either or .
 Here are the payoffs:
 and : Both get B
 and : Both get B+
 and : gets A, gets C.
 There is a dominant strategy: Picking .
Nimble
 Game rules:
 Board with 8 spaces, numbered 1~8. There is 1 coin on the first space, 2 on the third, and 1 on the sixth.
 Each turn, one coin can be moved any number of spaces to the left.
 When a coin is moved off the board, it is removed from play.
 Win condition: Last player to move a coin wins.
 Solution: This problem reduces to a Tweedledum & Tweedledee Strategy
 Player first reduces to Tweedledum & Tweedledee
 Can computer first win?
Impartial/Partial Games (??)
 Games that ahve the same options available to both players
 Examples: Chess, Checkers, etc.
Combinatorial Games
 No randomness (Chess, Go, Tictactoe)
Payoff Diagram Syntax
Row \ Column 



(B, B) 
(A, C) 

(C, A) 
(B+, B+) 