CMSC Lecture Notes 5
Road Networks and Braess's Paradox
Example:
Road Networks
Suppose 1,000 drivers wish to travel from S (start) to D (destination)
Two possible paths: SAD and SBD
The road from S to A is long: t = 50 minutes but very wide, t=50 no m

Lecture Notes 7
Rationalizability and Price of Anarchy
Rationalizability
A strategy is rationalizable if a perfectly rational agent could justifiably play it against perfectly
rational opponents
A strategy for agent i is rationalizable if its a best res

Ganbott Voey
CMSC 474
Lecture Notes 2
Normal Form Games
Games in Normal Form
A (finite, n-person) normal-form game includes the following:
1. An ordered set N = (1, 2, 3, ., n) of agents or players:
2. Each agent i has a finite set Ai of possible actions

Lecture Notes 8
Maxmin and Minmax Strategies
Worst-Case Expected Utility
For agent i, the worst-case expected utility of a strategy si is the minimum over all possible
combinations of strategies for the other agents
A maxmin strategy for agent i
A stra

Ganbott Voey
CMSC 474
Lecture Notes 1
Introduction to Game Theory
Game theory- self interested players
different players have different preferences on outcomes
Algorithmic Game Theory
incentive-aware algorithm design or Mechanism Design
Combines:
Algo

Ganbott Voey
CMSC 474
Lecture Notes 3
Important Normal Form Games
Examples
Which of the following lotteries would you choose?
A: 100% chance of receiving $3000
B: 80% chance of receiving $4000; 20% chance of receiving nothing
Which of the following lo

Lecture Notes 6
Finding Nash Equilibria
Finding Mixed-Strategy Nash Equilibria
In general, its tricky to compute mixed-strategy Nash equilibria
But easier if we can identify the support of the equilibrium strategies
In 2x2 games, we can do this easily

Lecture Notes 10
Epsilon-Nash Equilibria
e-Nash Equilibrium
Reflects the idea that agents might not change strategies if the gain would be very small
Let e > 0. A strategy profile s = (s1, . . . , sn ) is an e-Nash equilibrium if for every agent i and
f

Lecture Notes 9
Dominant Strategies and Correlated Equilibrium
Dominant Strategies
Let si and si be two strategies for agent i
Intuitively, si dominates si if agent i does better with si than with si for every strategy
profile si of the remaining agents

CMSC 474 Lecture 4
Analyzing Normal Form Games
How to Reason about Games
In single-agent decision theory, look at an optimal strategy
Maximize the agents expected payoff in its environment
With multiple agents, the best strategy depends on others choic