Game Theory Question

[viciouspenguin]

There are two firms in a market that produce an identical product. Each firm has either one or zero units to sell. The probability of having a unit to sell is q and the probability of having no units to sell is 1-q. There is a single consumer interested in buying only one unit of the good at a price not to exceed $1. If both firms have capacity available, it will buy from the lowest priced. If only one firm has capacity, it buys from that firm provided its price does not exceed $1. You must decide what price to charge for the good if you were to have a unit available to sell. Note that at the time of making this decision you do not know whether your competitor will have a unit of capacity to sell or not and what price it will choose.

What are the optimal price choices for the following 3 cases?

1. q = 1/4
2. q = 1/2
3. q = 3/4

[bisonbison]

This question sucks dyke balls.

[THAY3R]

I would probably SIIHP, but since you're not sure if she has the herp or AIDS, maybe just a titty [censored] followed by a facial.

[dchz]

[ QUOTE ]
I would probably SIIHP, but since you're not sure if she has the herp or AIDS, maybe just a titty [censored] followed by a facial.

[/ QUOTE ]

this is the nash equilibrium

[xorbie]

at q = 1/2, price of 1 has EV of .25, thus nobody should ever charge < .5. however, (.5,.5) gives each an EV of < .25, so it is not a NE. BR(.5) = 1. however, BR(1) = .99 and this continues down to BR(.51) = .5. thus no NE, not for any of these.

you may want to verify, this was just a quick sketch.

[tabako]

I don't think there are any NE in pure strategy.

For q = .5, I think the mixed strategy p = U~[.5,1] might work, though I am not sure how to verify if it does.

[adsman]

This question reminds me why I spent most of my final school years going surfing.

[Nick B.]

$100. no wait $99!

[dchz]

OP:

i just made an A in game theory this semester...

i don't see how the probability has any effect on competitive pricing for the firms because it's the same for both firm, so when you optimize the price the probability of having the quantity cancels out

but if you do a rollback equilibrium, i think the greater the probability the more you wanna shave off from $1, but i still fail to see how the probabilities matter, am i getting leveled?

[FatalError]

[ QUOTE ]
$100. no wait $99!

[/ QUOTE ]

i'm going to bid 1$ bob