Game Theory question

[Dari]

I was asked this question at a recent seminar and it stuck with me. I took GT a long time ago and don't remember all of it. Here is the problem:

100 people must decide simultaneously whether to contribute a non-refundable amount to build a new road. The road can only be built if at least 51 people contribute. The preferences are such
1) He does not contribute but the road is built
2) He contributes and the road is built
3) He does not contribute and the road is not built
4) He contributes but the road is not built

Is there a Nash Eq. in which
a) more than 51 contribute?
b) exactly 51 contribute?
c) less than 51 contribute?

 

[The Boston Dangler]

when i read "game theory" i was hoping the issue would be something like:

"do i invade kamchatka, or do i sit and hold alaska?"

 

[mundane]

I come from Ukraine. You not say Ukraine is weak. Ukraine is game to you? How about I take your little game and smash!

 

[sandorski]

Originally posted by: The Boston Dangler
when i read "game theory" i was hoping the issue would be something like:

"do i invade kamchatka, or do i sit and hold alaska?"

Invade Kamchatka. Maintain a large Force, but keep a Large Force in Alaska as well.

 

[Fayd]

it's impossible to set up the problem without knowing the relative values of people having the road vs not having the road.

EDIT:

and the problem represents a free-rider problem anyways.

it's been awhile since i did this kind of game theory.

 

[sandorski]

Games are Created, you get them at a Store. You're dealing with just a THEORY!!!!

 

[Fayd]

Originally posted by: sandorski
Games are Created, you get them at a Store. You're dealing with just a THEORY!!!!

you keep saying that when i solve chess.

 

[grrl]

Originally posted by: Fayd
it's impossible to set up the problem without knowing the relative values of people having the road vs not having the road.

EDIT:

and the problem represents a free-rider problem anyways.

How does it being a free-rider problem change things?

 

[Fayd]

Originally posted by: grrl

Originally posted by: Fayd
it's impossible to set up the problem without knowing the relative values of people having the road vs not having the road.

EDIT:

and the problem represents a free-rider problem anyways.

How does it being a free-rider problem change things?

the problem wasnt framed very well.

my questions:

A: can the people who pay in recoup their costs if the action is not taken? (not enough people pay in)
B: does everybody get the same payoff from the action being taken? (also, is the payoff greater than the amount necessary to contribute?)
C: are the participants using a blended strategy?

EDIT:

assuming everybody has the same payoff, we can represent a player's responses on a 2x2 grid...

there's no dominant strategy.

without knowing the relative payoffs, we cant do minimax or maximin.

the only "solution" i can think of in this situation is a blended strategy.

 

[Dari]

Originally posted by: Fayd

Originally posted by: grrl

Originally posted by: Fayd
it's impossible to set up the problem without knowing the relative values of people having the road vs not having the road.

EDIT:

and the problem represents a free-rider problem anyways.

How does it being a free-rider problem change things?

the problem wasnt framed very well.

my questions:

A: can the people who pay in recoup their costs if the action is not taken? (not enough people pay in)
B: does everybody get the same payoff from the action being taken? (also, is the payoff greater than the amount necessary to contribute?)
C: are the participants using a blended strategy?

EDIT:

assuming everybody has the same payoff, we can represent a player's responses on a 2x2 grid...

there's no dominant strategy.

without knowing the relative payoffs, we cant do minimax or maximin.

the only "solution" i can think of in this situation is a blended strategy.

Right. My primary problem with this question was the lack of values. But perhaps there is another way?

 

[nineball9]

Originally posted by: The Boston Dangler
when i read "game theory" i was hoping the issue would be something like:

"do i invade kamchatka, or do i sit and hold alaska?"

:laugh:

 

[Dari]

Anyone? I've gotten it down to a probability p = (y-x)/y, where why is the preferred outcome and x is the contribution. However, I don't know how 51% can be achieved.