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## Question

Sean wants to attend a basketball game. Unfortunately, he could not get tickets before it was sold out, but he has located someone that has an extra ticket which he is willing to sell to Sean. The seller begins by asking \$100 for the ticket. Sean counters by offering \$50. The seller always counters by asking the average of the two offers. Sean always counters by the average of his previous offer and the sellerâ€™s new offer.

At what price will Sean and the seller finally agree upon?

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\$67.30 It could also be off a penny or two for rounding.

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Price = 100*(1 - 1/2 + 1/4 - 1/8 + 1/16 - ...) which = \$66.67

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By the time they reach an agreement, the game would have been played and the ticket rendered worthless

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never!

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following this method, they will eventally make a deal at \$66.666666666 or \$66 and 2/3 or just plain \$66.67

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Actually, if you assume that offers are made only to the nearest one cent, they agree on \$66.74, as it doesnt make sence to have an offer with a fraction of a penny.!

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Maybe I'm wrong here, but if the seller offers 100 and then Sean offers 50 it is stated that the seller offers the average of those offers thus:

(100+50)/2 = 75

Next Sean counters with the average of his previous offer (50) and the sellers new offer (75) so:

(75+50)/2 =

\$62.50

If that's wrong can someone explain to me what I'm doing wrong here?

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Actually, if you assume that offers are made only to the nearest one cent, they agree on \$66.74, as it doesnt make sence to have an offer with a fraction of a penny.!

I found it to be \$66.69 on the 8th offer made by the seller, yet the seller stopped at this price on the 7th offer. This was with rounding to the nearest penny for each offer. It also seems to depend on when the rounding is done. If the rounding is done after determining all the offers (unlikely) then you end up with \$66.67 on the 8th offer.

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If seller 1 always offers the average of the first two offers, he'll always counter w/ \$75...and since the second guy counters with the average, eventually he'll pay the \$75 (extremely frustrated). If they both are splitting the difference rounding to the nearest penny he'll pay 66.69. If they aren't rounding to the nearest cent he'll pay 66.66 and one will have to budge about the 2/3 of a cent...probably the guy owing 2/3...so he'll play 66.67...

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\$83.33 (rounded to the nearest penny from \$[250/3])

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\$83.33 (rounded to the nearest penny from \$[250/3])

Ooops!

\$66.67 (rounded to the nearest penny from \$[200/3])

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Ooops!

\$66.67 (rounded to the nearest penny from \$[200/3])

Rule #1:

Never be the first to go for the average in your counter offer!!!!

In the previous solutions, it was assumed that the seller would start by asking for \$75

In my opinion, the seller being more professional and experienced would have waited untill Sean agreed on paying \$75, then he would ask for the new average.

superprismatic was right on both accounts I think.

Edited by roolstar
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Rule #1:

Never be the first to go for the average in your counter offer!!!!

In the previous solutions, it was assumed that the seller would start by asking for \$75

In my opinion, the seller being more professional and experienced would have waited untill Sean agreed on paying \$75, then he would ask for the new average.

superprismatic was right on both accounts I think.

The first answer I gave was done by making the assumption that the seller would always raise the low value and the buyer would always lower the high value. Since this is a ridiculous way to haggle, the opposite was probably meant in the OP.

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\$66.67

Sean wants to attend a basketball game. Unfortunately, he could not get tickets before it was sold out, but he has located someone that has an extra ticket which he is willing to sell to Sean. The seller begins by asking \$100 for the ticket. Sean counters by offering \$50. The seller always counters by asking the average of the two offers. Sean always counters by the average of his previous offer and the sellerâ€™s new offer.

At what price will Sean and the seller finally agree upon?

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66.67

Edited by joepan29

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\$66.67

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the two thirds has to be rounded up

Edited by teekayla

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68.75

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Edited by blair

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