Game theory basics
• A Game describes situations of strategic
interaction, where the payoff for one
agent depends on its own actions as well
as on the actions of other agents.
• Example. In an industry with two firms,
each firm’s profit depends not only on its
own price but also on the price charged by
the other firm.
Game theory basics
Ingredients of a simple game (with
complete information):
• The players.
• The actions. feasible courses of actions for
each player
• The rules. who moves and when.
• The payoffs. the utility each player gets for
every possible combination of the players’
actions
Game A
Strategy sets for
each player
Players
Column Player 
Red
Black
Red
2,2
5,0
Black
0,5
3,3
Row Player 
Payoff to Row
Payoff to Column
Dominant strategies
• A strategy s'i for player i is dominant if, regardless
of the other players’ strategies, player i’s payoff
from playing s'i is larger than his payoff from playing
any other strategy
• A rational player will choose his dominant strategy
(if there is one!)
• Dominant strategies in Game A (Red for player
Row and Red for Player Column) give us a unique
pair of strategies (Red, Red)
Game B: The Prisoners dilemma
Prisoner 2 
Mum
Confess
Mum
-1,-1
-9,0
Confess
0,-9
-6,-6
Prisoner 1 
Prisoner’s dilemma
• Game B (Prisoners dilemma): same logic as
in Game A with different payoffs
• Players have a dominant strategy
• Conflict between individual goals and social
goals
Game C: no Dominant strategies
Player 2 
L
C
R
T
1,1
2,0
1,1
M
0,0
0,1
0,0
B
2,1
1,0
2,2
Player 1 
Dominated strategies
• A strategy s'i for player i is dominated by another
strategy s''i if for each feasible combination of the
other players’ strategies, player i’s payoff from
playing s'i is smaller than his payoff from playing s''i.
• A rational player will not choose a dominated
strategy
• So, we can eliminate dominated strategies in a
successive manner.
• Game C: successive (iterated) elimination of
dominated strategies leaves a unique pair of
strategies (B,R).
Game D:
no dominant or dominated Strategies
Player 2 
L
C
R
T
0,4
4,0
5,3
M
4,0
0,4
5,3
B
3,5
3,5
6,6
Player 1 
Nash Equilibrium
• For games A, B, and C, we can use dominant
strategies and iterated elimination of
dominated strategies to find unique solutions
(we could say something definite about how
players will choose): these are the equilibrium
of these Games!
• For Game D, we need the concept of Nash
Equilibrium
Nash Equilibrium (NE)
• A pair of strategies is a Nash Equilibrium
if no player can improve his payoff by
unilaterally changing his strategy.
• A pair of strategies is a Nash Equilibrium,
if each player’s strategy is a best
response to the other player’s strategy
• Game D: Nash Eq. leads to a unique pair
of strategies (B,R)
Game E: The battle of the sexes
Man 
Friends
Football
game
Friends
2,1
0,0
Football game
0,0
1,2
Woman 
Game E has two Nash Equilibria (multiple equilibria)
Existence of Nash Equilibrium is guaranteed: if the
number of players is finite and the number of
available strategies for every player is also finite, then
there exists at least one equilibrium.