Lecture 18: Multiagent Decision Making

Lecture 18: Multiagent Decision Making¶

AIMA Chapter 18 — 1 hour¶

Learning Objectives¶

• Define normal-form and extensive-form games

• Find Nash equilibria

• Understand cooperative game theory

• Apply auctions, voting, bargaining

Normal-Form Games¶

• Players: N agents

• Actions: A_i for each

• Payoffs: u_i(a₁,...,aₙ)

• Matrix: 2-player, 2-action

Nash Equilibrium¶

• No player wants to deviate unilaterally

• Mixed strategy: Probability over actions

• Existence: Every finite game has mixed Nash

Repeated Games¶

• Stage game: Played repeatedly

• Strategies: Tit-for-tat, grim trigger

• Folk theorem: Many equilibria

Extensive Form¶

• Game tree: Sequential moves

• Information sets: What players know

• Subgame perfect: Nash in every subgame

Cooperative Games¶

• Coalitions: Subsets of players

• Characteristic function: v(S) = value of coalition S

• Core, Shapley value: Solution concepts

Auctions¶

• English auction: Ascending

• Vickrey: Second-price, truthful

• Combinatorial: Multiple items

Voting¶

• Social choice: Aggregate preferences

• Arrow’s theorem: No perfect system

• Strategic voting: Manipulation

Summary¶

• Nash: No unilateral deviation

• Repeated: Cooperation possible

• Cooperative: Coalitions

• Mechanisms: Auctions, voting

References¶

• AIMA Ch. 18

• Russell & Norvig, AIMA 4e, Ch. 18

• Chapter PDF: chapters/chapter-18.pdf

Questions?¶

Next lecture: Learning from Examples (Chapter 19)