fa25-cs540 cs540
Lecture 21: Games I Lecture 21: Games I
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Introduction
Course Context
Agent-World Interaction Model
Games: Multiple Agents
Properties of Games
Property 1: Number of Players
Property 2: Action Space
Property 3: Deterministic or Random
Property 4: Sum of Payoffs
Property 5: Sequential or Simultaneous Moves
Normal Form Game
Example: Prisoner’s Dilemma
Strictly Dominant Strategies
Prisoner’s Dilemma Analysis
Dominant Strategy Equilibrium
Dominant Strategy as Best Response
DSE Does Not Always Exist
Nash Equilibrium
Nash Equilibrium: Best Response to Each Other
Pure Nash Equilibrium
Finding Pure Nash Equilibria by Hand
Pure Nash Equilibrium May Not Exist
Mixed Strategies
Mixed Strategy Nash Equilibrium
Example: Rock-Paper-Scissors
Finding Mixed NE: Two Finger Morra
Properties of Nash Equilibrium
The Tragedy of the Commons
Setup
Continuous Action Game
Finding g^*
The Tragedy
Lessons from the Tragedy
Practice Problems
Key Takeaways
Suggested Reading