Naturally reminds one of the (Iterated) Prisoner's Dilemma.
Two other simple games are the Dollar Bill Auction and the St. Petersburg
Game.
In the dollar bill auction, one auctions off a dollar bill in the normal
fashion: increasing bids, top bid pays their bid and gets the bill. The
twist is that the second-highest bidder *also* has to pay their bid. What
happens in the regime where bidding is above 50 cents and below many
dollars?
In the St. Petersburg game, a coin is flipped repeatedly. You will win
$2^n, where n is the run-length of heads that show. How much would you pay
to play this game?
Greg forwards an article on startups:
>No news here, hi-risk, long hourse, great rewards.
If we believe Geoffrey Moore that making bank from high-tech products
involves a winner-take-all mainstream market dominance, then the industry
seems very much like playing poker: whoever has the strongest position at
the showdown (or achieves monopoly prior) takes the pot.
Fortunately or unfortunately, in business (especially at startup) we're
usually fairly ignorant both about the probable size of the pot (market
acceptance doesn't enter into poker) and about how many rounds of betting
may be required.
Therefore, a combination "St. Petersburg Auction" might be in order: the
players bid their "investment" (to the house) each round, then the coin is
flipped. When it comes up tails, the high bid of the previous round
receives the exponential payoff from the house., otherwise the game
continues. To model a market with barriers to entry, either some weighting
of the previous rounds should be used to determine the winner, or there
needs to be a mechanism for eliminating low bidders.
-Dave