Game theory

Game Theory and Learning for Wireless Network

Author : Pooya Sagharchi Ha

• What is The Game Theory ?

• Nash Equilibrium

• Game Theory and Wireless Network

• Examples on Game Theory in Wireless Network

Agenda

• Developed in 1950 by mathematicians John von Neumann and economist Oskar Morgenstern.

• Game theory is concerned with situations in which decision-makers interact with one another.

• and in which the happiness of each participant with the outcome depends not just on his or her own decisions but on the decision made by everyone.

• A mathematical tool used to describe and solve games depending on 3 basic elements:

What is Game Theory?

Nash Equilibrium

• A Nash equilibrium is a situation in which none of them have dominant strategy and each player makes his or her best response.

• John Nash shared the 1994 Nobel prize in Economic for developing this idea!

• Players :

• Players are the decision takers in the game

• Strategies:

• Define a plan of action for every contingency

• Payoffs :

• a utility function decides the all possible outcomes for each player

Continue…

• Game theory has emerged in divers recent works related to communication networks, cognitive radio networks, wireless sensor networks, resource allocation and power control.

• Components of a wireless networking game :

Game Theory and Wireless Network

Components of a game Elements of a wireless network

Players Nodes in wireless network

A set of strategies A modulation scheme,coding rate, transmit etc.

A set of payoffs Performance metrics ( Delay, Throughput etc.)

Example 1: The Forwarder’s Dilemma

?

?

Blue Green

• Game formulation: G = (P,S,U) – P: set of players – S: set of strategy functions – U: set of payoff functions

• Strategic-form representation

Continue…

• Reward for packet reaching the destination: 1 • Cost of packet forwarding: c (0 < c << 1)

(1-c, 1-c) (-c, 1)

(1, -c) (0, 0)

Blue

Green

Forward

Drop

Forward Drop

Example 2 : The Multiple Access game

Time-division channel

Reward for successfultransmission: 1

Cost of transmission: c (0 < c << 1)

There is no strictly dominating strategy

(0, 0) (0, 1-c)

(1-c, 0) (-c, -c)

BlueGreen

Quiet

Transmit

Quiet Transmit

There are two Nash equilibria

Example 3 : The Joint Packet Forwarding Game

?Blue GreenSource Dest

?

No strictly dominated strategies !

• Reward for packet reaching the destination: 1 • Cost of packet forwarding: c (0 < c << 1)

(1-c, 1-c) (-c, 0)

(0, 0) (0, 0)

BlueGreen

ForwardDrop

Forward Drop

“Any Questions ?! .”