2. Game Theory
• What is Game Theory?
• What is strategic environment?
• What are the main assumptions in Game
Theory?
• How are games represented?
• What are the elements of Games ?
3. Game representations
Matrix form
Extensive form (aka normal form
aka strategic form)
player 2’s strategy
Up 1, 2
Up, Up Up, Down D, D
Down , Up
Up Coca Cola
Down 3, 4 Up 1, 2 1, 2 3, 4 3, 4
player 1’s
Pepsi strategy
Up 5, 6
Down 5, 6 7, 8 5, 6 7, 8
Down Coca Cola
Down 7, 8
5. Rules of the Game
• The strategic environment
– Players
– Strategies
– Payoffs
• The assumptions
– Rationality
– Common knowledge
• The rules
– Timing of moves
– Informational conditions
6. Formal definition
Definitions
• Let Ai be the set of actions available for player I
• a = (a1, a2, …, ai,…) be an action profile: An action for
each player in the game.
• write (ai', a-i) if i chooses ai', other players according to a
• ui (ai , a-i ): payoff for player i from playing action ai and
others playing a-i
8. Prisoner’s Dilemma
Not Confess Confess
Not Confess -2, -2 -5, -1
Confess -1, -5 -3,-3
9. Comments
• Simultaneous actions does not imply taking
actions at the same time.
• Rationality implies knowing the structure of
the game.
• It does not mean that there is coordination on
beliefs / cooperation
• Rationality is an assumption not necessary in
reality.
10. Comments
• (Not Confess, Not Confess) is a pareto optimal
outcome
• This is common knowledge
• Will Not Confess be chosen by both?
• Depends upon their beliefs about the actions
of other players
11. Prisoner’s Dilemma
Not Confess Confess
Not Confess -2, -2 -5, -1
Confess -1, -5 -3,-3
13. Nash Equilibrium
Nash Equilibrium:
• A set of strategies, one for each player, such
that each player’s strategy is a best response
to others’ strategies
Everybody is playing a best response
• No incentive to unilaterally change my strategy
14. Nash Equilibrium
• a* =( a* 1 , a* 2 , ……) = =( a* i , a* -i)
is a Nash equilibrium if for every player i and every
action, ai that is element of Ai:
ui(a*) ≥ ui (ai , a-i*)
where ui is the payoff function representing the
preferences of player I
15. L C R
U 8, 3 0, 4 4,4
M 8,5 1,5 5,3
D 3,7 0,1 2,0
18. SUV Price Wars
Discount No Discount
Discount 3,3 8, 0
No Discount 0, 8 5,5
19. Games of Chicken
• Entry into small markets
Firm 2
Stay Swerve
Stay -50 , -50 100 , 0
Firm 1
Swerve 0 , 100 50 , 50
20. Stag Hunt Game
• Each can individually hunt a stag or hunt a
hare together.
• You can hunt a stag alone.
• You can only hunt a hare when you hunt it
together.
• Hunting a hare alone means no dinner!
22. Games of Assurance
Joint research ventures
– Each firm may invest $50,000 into an R&D project
– Project succeeds only if both invest
– If successful, each nets $75,000
– Stag Hunt Firm 2
$50K $0
$50K 75 , 75 -50 , 0
Firm 1
$0 0 , -50 0 , 0
23. Nash Equilibrium
• May or may not have to exist in pure
strategies.
• Can be multiple in a single game.
Editor's Notes
In PD you know that Not confessing is a pareto optimal scenario, you know that everyone knows that Not Confessing is a pareto optimal scenario. However, this does not mean that Not Confessing will be chosen or is the best strategy to choose. Your optimal strategy depends upon your belief about the other players action. You could believe that the other player will choose Not Confess in which case it still will never be optimal for you to Not Confess.
Market worth of 10 which is split between the two players
Market worth of 10 which is split between the two players
