This Segment:
Techniques for solving games
Lecture 1: Game representations,
game-theoretic solution concepts, and complexity
Tuomas Sandholm
Computer Science Department
Carnegie Mellon University
The heart of the problem
In a 1-agent setting, agents expe
Algorithms for solving twoplayer normal form games
Tuomas Sandholm
Carnegie Mellon University
Computer Science Department
Recall: Nash equilibrium
Let A and B be |M| x |N| matrices.
Mixed strategies: Probability distributions over M and N
If player 1 p
Resolu'on Proof Example
Prateek Tandon, John Dickerson
Robot Doom Domain
1.
2.
3.
4.
Jack owns a roomba
Every roomba owner is a robot enthusiast.
No robot enthusiast breaks a robot.
Either Jack or SENSOR MALFUNCTION b
Graduate AI Midterm SOLUTIONS
March 6, 2012.
10:3011:50am.
Name:
Andrew ID:
Read all of the following information before starting the exam:
Please clearly write your name and Andrew ID in the spaces above.
For full credit, please show all work clearly a
Graduate Articial Intelligence 15-780
Homework #1: Knowledge Representation,
SAT, and CSPs
SOLUTIONS
Out on January 28
Due on February 11
Homework #1
Graduate Articial Intelligence 15-780
Problem 1: Knowledge Representation [20 pts.]
In the not too distan
Midterm Review
Prateek Tandon, John
Dickerson
Basic Uninformed
Search (Summary)
b = branching factor
d = depth of shallowest goal state
m = depth of the search space
l = depth limit of the algorithm
CSP Solving - Backtracking
search
Depth-first search for
Constraint Satisfaction Problems
Tuomas Sandholm
Carnegie Mellon University
Computer Science Department
Read Chapter 6 of Russell & Norvig
Constraint satisfaction problems (CSPs)
Standard search problem: state is a "black box any data
structure that supp
Advanced informed search
Tuomas Sandholm
Computer Science Department
Carnegie Mellon University
Read: Optimal Winner Determination Algorithms.
Sandholm, T. 2006.
Chapter 14 of the book Combinatorial Auctions,
Cramton, Shoham, and Steinberg, editors, MIT P
Algorithms for solving sequential
(zero-sum) games
Main case in these slides: chess
Slide pack by
Tuomas Sandholm
Rich history of cumulative ideas
Game-theoretic perspective
Game of perfect information
Finite game
Finite action sets
Finite length
Che
Algorithms for Large Sequential Incomplete-Information
Games
Tuomas Sandholm
Professor
Carnegie Mellon University
Computer Science Department
Most real-world games are incomplete-information
games with sequential (& simultaneous) moves
Negotiation
Multi-s
Search I
Tuomas Sandholm
Carnegie Mellon University
Computer Science Department
Read Russell & Norvig Sections 3.1-3.4.
(Also read Chapters 1 and 2 if you havent already.)
Next time well cover topics related to Section 6.
Search I
Goal-based agent (proble
Informed search methods
Tuomas Sandholm
Computer Science Department
Carnegie Mellon University
Read Section 3.5-3.7 of Russell and Norvig
Informed Search Methods
Heuristic = to find, to discover
Heuristic has many meanings in general
How to come up with