Help me reason through these incentives.
There are two critical parameters at play, let's call them R (above 0) and D (between 0 and 1).
The rules for an auction are:
1) The initial required bid is 0.
2) Your required_bid is equal to (previous_bid + (R*(previous_bid - previous_required_bid))
3) When you place a bid, (D*(your_bid - previous_bid)) goes to dividends and (previous+bid + (1 - D)*(your_bid - previous_bid)) goes to previous bidder.
An example: suppose R = 1 and D = 0.5
Brand new auction.
I bid 100. My required bid was 0, so the next person must bid 200. (100 goes to dividends as there is no previous bidder)
Next person bids 210. His required bid was 200, so next required bid is 220. (Previous bidder gets 150, 50 goes to dividends)
Next person bids 300. His required bid was 220, so next required bid is 380. (Previous bidder gets 255, 45 goes to dividends).
* R needs to be high enough to realistically motivate people to bid as high as they would be willing to pay right form the start. I'm thinking this might happen even with a value less than 1.
* D needs to be low enough to motivate people to call people out on low bids, but high enough to make outbidding yourself not worth it (extra price buffer more worthwhile than money you save from your own kickback).