22-03-2014, 04:03 PM
Game Theory and its Applications
Game Theory .ppt (Size: 1.19 MB / Downloads: 166)
Prisoner’s Dilemma
Two suspects arrested for a crime
Prisoners decide whether to confess or not to confess
If both confess, both sentenced to 3 months of jail
If both do not confess, then both will be sentenced to 1 month of jail
If one confesses and the other does not, then the confessor gets freed (0 months of jail) and the non-confessor sentenced to 9 months of jail
What should each prisoner do?
Battle of Sexes
A couple deciding how to spend the evening
Wife would like to go for a movie
Husband would like to go for a cricket match
Both however want to spend the time together
Scope for strategic interaction
Mixed strategies
A probability distribution over the pure strategies of the game
Rock-paper-scissors game
Each player simultaneously forms his or her hand into the shape of either a rock, a piece of paper, or a pair of scissors
Rule: rock beats (breaks) scissors, scissors beats (cuts) paper, and paper beats (covers) rock
No pure strategy Nash equilibrium
One mixed strategy Nash equilibrium – each player plays rock, paper and scissors each with 1/3 probability
Auctions
Games of incomplete information
First Price Sealed Bid Auction
Buyers simultaneously submit their bids
Buyers’ valuations of the good unknown to each other
Highest Bidder wins and gets the good at the amount he bid
Nash Equilibrium: Each person would bid less than what the good is worth to you
Second Price Sealed Bid Auction
Same rules
Exception – Winner pays the second highest bid and gets the good
Nash equilibrium: Each person exactly bids the good’s valuation
Bidding up to 50
Two-person game
Start with a number from 1-4
You can add 1-4 to your opponent’s number and bid that
The first person to bid 50 (or more) wins
Example
3, 5, 8, 12, 15, 19, 22, 25, 27, 30, 33, 34, 38, 40, 41, 43, 46, 50
Game theory tells us that person 2 always has a winning strategy
Bid 5, 10, 15, …, 50
Easy to train a computer to win