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Title: Postgraduate: Strategic Form games - Note from WARWICK UNIVERSITY
Description: Economics graduate study note on strategic form games exclusively availble at Warwick University.
Description: Economics graduate study note on strategic form games exclusively availble at Warwick University.
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Problem Set 1: Strategic Form Games
Here are lots of easy problems to give you some practice at using the concepts
...
Where possible apply the iterated elimination of strictly dominated strategies to
the following strategic forms
(-1,-1) (1,-2)
(-2,1) (0,0)
Prisoners' Dilemma,
(0,0)
(1,2)
(0,-1)
(-1,-1)
(-2,1)
(1,1)
(0,0)
(3,0)
(1,-2)
(0,0)
(0,-2)
(10,0) ,
(2,1)
(3,-1)
(3,2)
...
)
2
...
The
set of pure strategies for each player is the unit interval [0,1]
...
If player 1 sets x and player 2
sets y then player 1's payoff is given by the function π1(x,y) below and player
2's payoff is given by π2(x,y)
1-c x>y
π1(x,y)
=
1/2 x=y
where 1>c>1/2
c
x
=
1-c
1/2
c
y>x
y=x
y
Does any value of x for player 1 strictly dominate any other value?
Does any value of x for player 1 weakly dominate any other value?
What happens if you iteratively eliminate all strict (weak) dominated
strategies?
3
...
Suppose player 1, 2, 3 are on a committee and
must choose between three alternatives α,β,γ
...
If
there is a 3-way tie, player 1 then gets to choose the outcome
...
Analyse this game using iterative elimination of dominated strategies
...
Find all the Nash equilibria for the following games in strategic form
...
As the parameter ‘a’ varies explain how the set of Nash equilibria for the game
below alters
...
Consider the following Bayesian game
...
And Player 2 is a seller with a use value of the good
c that is distributed U(0,1)
...
When trade
occurs it is arranged by an intermediary at the average of the two values
...
Seller
Trade
Trade
( v-½(v+c), ½(v+c)-c)
No trade
(0,0)
No Trade
(0,0)
(0,0)
Buyer
Assume they follow cut-off strategies so that low value buyers do not trade and high
cost sellers do not trade
...
Title: Postgraduate: Strategic Form games - Note from WARWICK UNIVERSITY
Description: Economics graduate study note on strategic form games exclusively availble at Warwick University.
Description: Economics graduate study note on strategic form games exclusively availble at Warwick University.