Originally posted by talzamir
Oh. One thing was missing. Victory conditions.
First: Profit. Both spies seek to maximise their profit from the auction.
Second: Prestige. Each spy seeks to gain more profit than the other.
Do the different victory conditions cause the optimal strategy to change?
When Maximising profit the best strategy for the white spy (assuming bids must be integers) is as follows:
Bid 10,000 for codebook, black spy makes no profit overbidding on this so this is safe
Bid 17,500 for the Passport
Bid 32,499 for the sniper rifle
To overbid white on both the passport and the rifle would take 50001, which the black spy doesn't have, so he can only overbid on one of them
The black spy makes 7499 by overbidding for the passport
The black spy makes 7500 by overbidding for the sniper rifle
So the black spy bids for the sniper rifle only.
The white spy gets the codebook and the passport for $27,500 altogether and therefore makes a profit of $37,5000
The black spy gets the sniper rifle for 32500 and therefore makes a profit of $7,500
This "optimum" bidding strategy would completely fail if bidding for kudos, black would bid 10,001 for the codebook, let white win the sniper rifle and would win the passport for 17,501. Then black comes out with a $7,498 profit and white makes a -$22,499 loss, a relative difference of $29,997 in black's favour. As I have already shown that white can make a relative profit of at least $1 when bidding for kudos this proves that the optimum strategies for profit and kudos are completely different.