Lecture 2 - 22/01
Prisoner's Dilemma
If agents do not cooperate, the best (global) outcome possible is missed.
COP 21 Game
N governments
2 actions per states
Do not pollute (Cost = 3)
Pollute (cost=1 and +1 for everyone)
What is the equilibrium?
Multi-Player Game
Siimultaneous move games
n players, each player pick a strat and occurs a loss.
Goal of the player: Minimize their loss
Zero-Sum Two-player Games
Zero-sum:
n=2
Action for each players: and
Game
Mix strategies
For example in the game of rock-paper-scissor
We have probabilities over actions of each player as and
Payoff:
Game:
Nash Equilibrium of a Game
Best worst-case move
Theorem
Any game with a finite set of players and a finite set of strategies has a Nash equilibrium of mixed strategies.
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