Game Theory Week #4
Outline:
Zero sum games
Maximin & minimax: Pure actions
Maximin & minimax: Mixed strategies
Linear programming
Fictitious play
Zero-sum games
Matching pennies:
H
T
H 1, 1 1, 1
T 1, 1 1, 1
Rock-paper-scissors:
R
P
S
R 0, 0 1, 1 1
ECEN 4018/5018 Game Theory and Multiagent Systems
Homework #3
1. Recall BoS, Stag hunt, and Typewriter games from HW#2. Compute all of the NE for these games
(including mixed strategy NE). Note that at the mixed strategy equilibrium, both players are indi
Game Theory Week #8
Outline:
Single agent learning
Regret matching
Multiagent learning
Better reply graphs
Potential games
Weakly acyclic games
Recap
Ingredients:
Players: N = cfw_1, 2, ., n
Action: Ai
Utility functions: ui : A R
Social Science
Game Theory Week #7
Outline:
Cost Sharing Problems
The Core
Shapley Value
Auctions
Mechanism Design
Vickrey-Clarke-Groves Mechanism
Example: A cost sharing problem among two towns
Two nearby towns are considering building a joint water distribution
Game Theory Week #5
Outline:
Imperfect information
Bayesian game
Bayes-Nash equilibrium
Examples
Imperfect information
Motivation: Uncertain environment
Example: Poker
Underlying truth (state): Opponents cards
Available information (signal): Own c
Game Theory - Week #2
Outline:
Review
Dominated strategies
Iterated dominated strategy elimination
Random models
Probability basics
Expected payo
Recap
Set up:
Set of players, cfw_1, ., n
For each player, a set of actions, Ai .
For each player,
Game Theory Week #1
Outline:
Optimization vs game theory
Game theory vs multiagent systems
Players, actions, preferences
Nash equilibrium
Best response function
Examples
Models & issues
Optimization vs game theory
High road
c(x) = x
S
D
c(x) = 1
Lo
ECEN 4018/5018 Game Theory and Multiagent Systems
Homework #2 Solutions
1. Craps: To evaluate the probability of winning on the pass line in craps we have the following:
pwin = Pr (7, 11) + Pr (win|4) + . + Pr (win|10)
where Pr (win|10) indicates the prob
ECEN 4018/5018 Game Theory and Multiagent Systems
Homework #1 Solutions
1. Tragedy of the Commons: The social planners optimization equates to
N
max N e1 10
N
which is maximized at N = 10. Therefore, the optimization leads to 1 goat/family which
produces