22-08-2013, 03:29 PM
Game Theory in Wireless and Communication Networks: Theory, Models, and Applications
Game Theory .pptx (Size: 549.77 KB / Downloads: 19)
Overview of Bayesian Game
Static Bayesian Game
Extensive Form
Detailed Example: Cournot Duopoly with incomplete information
Application in wireless networks
Packet Forwarding
K-Player Bayesian Water-filling
Channel Access
Bandwidth Auction
Summary
What is Bayesian Game?
Game in strategic form
Complete information(each player has perfect information
regarding the element of the game)
Iterated deletion of dominated strategy, Nash equilibrium:
solutions of the game in strategic form
Bayesian Game
A game with incomplete information
Each player has initial private information, type.
- Bayesian equilibrium: solution of the Bayesian game
Simple Example
Information is imperfect since player 2 does not know what player 1 does when he comes to play. If both players are rational and both know that both players are rational, play in the game will be as follows according to perfect Bayesian equilibrium:
Player 2 cannot observe player 1's move. Player 1 would like to fool player 2 into thinking he has played U when he has actually played D so that player 2 will play D' and player 1 will receive 3. In fact, there is a perfect Bayesian equilibrium where player 1 plays D and player 2 plays U' and player 2 holds the belief that player 1 will definitely play D (i.e player 2 places a probability of 1 on the node reached if player 1 plays D). In this equilibrium, every strategy is rational given the beliefs held and every belief is consistent with the strategies played. In this case, the perfect Bayesian equilibrium is the only Nash equilibrium.
Summary
Games with incomplete information (i.e., Bayesian game) can be used to analyze situations where a player does not know the preference (i.e., payoff) of his opponents.
This is a common situation in wireless communications and networking where there is no centralized controller to maintain the information of all users. Also, the users may not reveal the private information to others.
The detail of Bayesian game framework was studied in detail.
Examples of this game are given