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Subject: The importance of two-thirds EV. rss

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Stephen Michael Hickey
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Based on the previous threads and some further thinking of my own I now believe the following to be true.

Situation A - As a general rule for players of equal wealth...

Observation 1 - The seller is always in a win/win situation because a painting is worth at least 1/3rd of Estimated Value to the seller.

Observation 2 - It is in the interests of experienced non-sellers to reduce their relative loss to the seller by offering up to 2/3rds EV and no more.

This situation can and does change for players of different wealth and I discuss this in situation B later.

This is my reasoning:

Consider a simplified scenario of 2 players both with 100 wealth. Player A has a painting to sell with an EV of 20.

I believe that Player A can always force at least 6 profit (33% EV). I also believe that Player B should not offer more than 13 (66% EV) to the seller in these circumstances and as a general rule.

Why?

Player A (as the seller) can afford to bid up to EV-1 and make a relative profit. Player B (as a non-seller) can only afford to bid EV/2 to maintain their relative position.

Thus Player A could bid 19 and sell for 20 for a net total of 101 versus player B's 100.
On the other hand Player B starts to lose once he offers more than 10 (EV/2). If B wins with a bid of 11, the net position is A=111 (100+11); B=109 (100-11+20).

Accepting that he must lose out to the seller, Player B's, optimal loss position is to bid no more than 13 (66% EV). If B wins the bid at 13 the result is a loss of 6 to B: A=113; B=107.

If player B offers any more or less than 66%EV his position worsens.
For example, if A wins with a bid of 13, B’s loss will be 7: A=107; B=100.
If B wins a bid of 114, B’s loss will be 8: A=114; B=106.

The optimal loss position for non sellers is 6 which equates to a bid up to 2/3EV and no more.


Of course things can change if the seller starts from a position of less wealth. A non-seller who wins an auction and sells for EV-1, or better, will always lose out to the seller but will always make a relative gain on the other non-sellers. See the previous thread.

However, if the non-seller is ahead of the Seller in current wealth, it makes sense for a non-seller to bid more than 2/3EV knowing that they will still be ahead of the seller at the end of the transaction and that they will also make relative gains on everyone else.

But this may only be true, when the non-seller is in first place and the seller is lower than second place. After all, if the seller is in second place, why throw away relative wealth to your nearest competitor.

The only exception I can think of would be this.

Based on players perceptions:
Player A is in second place and is the seller.
Player B is leading in first place and player C is in third.

Player C may be able afford to offer more than 2/3EV to player A even though he is losing to him. Player C can afford to improve player A's wealth up to the current leader's perceived wealth, knowing that if Player C wins the bid, he will close the gap on Player B as the current leader. So long as the improvement in A's wealth does not make A the new leader Player C can afford to keep bidding. This may mean a bid of more than 2/3EV bid is still possible. The gap in wealth between the leader and the seller becomes a crucial factor.

Ultimately, we also end up with an ingenious balancing mechanism whereby the more you are losing, the more you can afford to bid to close the gap on the leader, at least when the leader is not the seller.








 
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Mark McEvoy
Canada
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Steve99 wrote:
Consider a simplified scenario of 2 players both with 100 wealth.


This is where, I believe, the wheels come off your proof. Why assume there are only two players? There's always more than two players. And you're constantly jockeying for position relative to all of them. Sometimes you'll wilfully lose position to one to gain position on the others, and if you do this equally and well, you wind up gaining position on all of them.


I believe the 'ideal' ratio of EV is proportional to the number of players in the game. With more players, you're willing to give the auctioneer a higher 'cut' in order to gain a relative advantage over all the other would-be buyers.

In a 3 player game, offering 2/3 EV to each of the other 2 players gives you as much profit as them on their auctions (and then you surge ahead when one of them gives you 2/3 EV on your auction).

In a 5 player game, that 'balance' point happens at 4/5 EV. You pay 4/5 EV on each of your 4 opponents' auctions and you've made as much profit as them at their auctions - and again, you'll take the lead on your own auction.
 
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Stephen Michael Hickey
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Hi Mark,

Glad to see you've joined the debate again.

I'll come back to you later on this. I've got to go to work.

The 2 person scenario was to get the point across. It equally applies to more people as the comments at the bottom indicate. I'll come back with a more detailed responase later.
 
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Rod Spade
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I think a seller should bid half of EV on his own painting. Buying it at 1/2 EV gives him more profit than selling if for less than that.
 
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Kevin Brokish
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Steve, Mark, and Rod,
Steve, you're definitely right for a theoretical two-player game.
I actually showed that the ideal highest bid for auctioneers is EV*n/(2n-1) (where n is the total number of players) in my post http://www.boardgamegeek.com/thread/170393. The exception is when you're bidding against a losing player, in which case you should bid EV/2 (props fo Rod) because you don't care if they make money (http://www.boardgamegeek.com/thread/170556).
~Kevin
 
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