Construct a two player extensive form game with perfect information
that has a subgame perfect equilibrium in (weakly) dominated
strategies. |
Request for Question Clarification by
rbnn-ga
on
09 Nov 2002 17:06 PST
There are several different definitions of "weakly dominated" in the
literature. Can you specify the definition of "weakly dominated" that
you are using with respect to this question?
Also, I am interpreting "equilibrium in weakly dominated strategies"
to mean an equilibrium each constituent strategy of which is weakly
dominated by some other strategy; if there is a specific definition
for this term as well that you are using, please delineate it.
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Clarification of Question by
vitaminc-ga
on
10 Nov 2002 13:14 PST
Fr example:
Bob
L R
Alice T 10,10 0,0
B 10,10 1,0
A pure strategy s weakly dominate a pure strategy s' for Alice, if
payoff A(s,t)>=payoff A(s',t) for all strategies t for Bob. And
payoff A(s,t)>payoff A(s',t) for some t.
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Clarification of Question by
vitaminc-ga
on
13 Nov 2002 16:38 PST
The tree has 5 nodes(from 0 to 4).
The root is 0.(player 1)
The player 1 moves from the root are as follows:
There is an edge labeeled l from 0 to 1.
There is an edge labelled r from 0 to 2.
The player 2 moves are as follows:
There is an edge labelled L from 2 to 3
There is an edge labelled R from 2 to 4
The payoffs for:
Node 1 is (a1,b1)
Node 3 is (a2,b2)
Node 4 is (a3,b3)
Remark: Don't mix up dominateED and dominANT strategies.
Suppose a3>a1=a2=b1=b2=b3, then the subgame perfect equilibrium(l,L)
is in dominated strategies.
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Clarification of Question by
vitaminc-ga
on
13 Nov 2002 16:40 PST
Above is the solution.
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