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The website www.bitcoinauction.us hosts a bidding game with a prize. Note that it's not a real auction because you don't get your bid back if you're outbid.

The game works as follows:

  • The game starts with a specified prize, let's call it P
  • A fixed closing time is specified
  • "Bidding" starts at 0
  • Players make "bids" to win. Each bid (let's call the most recent bid B) must be higher than the previous bid. Each bid also increases the prize amount P; let's assume P is increased by a fixed proportion (let's call it G for Generosity) of B each time a bid is made. So P would increase by G*B.
  • Whoever has the highest bid when the game ends wins the prize P.
  • It's complicated by the fact that "bids" are paid in bitoins and need to be confirmed prior to the auction finish. The amount of time to confirm a bitcoin transaction in this case is 10 mins on average, but follows a poisson distribution so could be an hour or more occasionally, and frequently is much less than 10 mins. This makes it a matter of luck if a "bid" is left to the last minutes of the auction.

Example:

  1. The game starts with a prize P=2, Bidding is at 0, Generosity (G) is 0.9
  2. Player A pays a "bid" of 0.5, which increases P by 0.45 (ie 0.9*0.5) to 2.45
  3. Player B pays a "bid" of 0.8, which increases P by 0.72 (ie 0.9*0.8) to 3.17
  4. Player A pays a "bid" of 1, which increases P by 0.9 (ie 0.9*1) to 3.35
  5. Player C pays a "bid" of 1.1 in the final 5 mins, but unfortunately for them it's not confirmed in time so it doesn't count. Player C gets their 1.1 bitcoins refunded when the confirmation comes through after the closing time, and player A wins the prize of 3.35 bitcoins.

What is an optimal strategy for playing the game, if any? Note that I do understand there's no guaranteed way to win every time, but perhaps there is a way to break even by adding another "bid" of a particular amount when you're outbid?

Disclaimer: I have no affiliation with the website, nor do I actually intend to play it.

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But how do you win? –  Pedro Tamaroff Feb 15 '12 at 21:43
    
Good point! Have clarified above - whoever has the highest bid when the game ends wins the prize P. I should add there's obviously no guaranteed way of winning, since you can ALWAYS be outbid - perhaps I should rephrase the question to take that into account. –  Highly Irregular Feb 15 '12 at 21:49
1  
With your definition of winning, isn't the answer simply "don't bid until the last minute and make the last bid as long as the prize is greater than the required bid?" All earlier bids just cost without gain. –  Ross Millikan Feb 15 '12 at 22:29
    
Yes, though there's still the question of what amount to bid. Also, it's complicated by the fact that bids are paid in bitoins and need to be confirmed prior to the auction finish. The amount of time to confirm a bitcoin transaction is 10 mins on average, but follows a poisson distribution so could be an hour or more occasionally, and frequently is much less than 10 mins. I suppose this is another constraint that should really be added to the list of game rules... –  Highly Irregular Feb 15 '12 at 22:43
    
Without the time limit, this is a standard example of a game with no winners. The greedy strategy at each point is to bid, but given that everyone is bidding, each bid lowers the expected payoff. If players follow the greedy strategy then the result is all but one player is bankrupt, and the last player loses (some fraction near to 1, dependent on G) as much money as the second to last surviving player. The only winner is the house, and the winning strategy is not to play. With the time limit, Ross Millikan's strategy is the best. –  Jack Schmidt Feb 16 '12 at 16:30

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