If you have a high signal you should bid a very, very high amount of money, because if the other received a low-signal he will offer 12.5m and you only have to pay his offer because its a second bid auction and in that case you are in positive since you only pay 12.5m and you receive 25m. If the other received a high signal the same applies
I should bid $0 for the low signal (either the other player got the low signal and it means the field values 0, either it received the high signal and he will bid more anyway), and I should bid $50m for the high signal (either the other player received the low signal, and I am indifferent about any value above 0$; or the other player received the high signal in which case any bid different from $50m would not be optimal).
I should bid $1 regardless if the signal is high or low. 1/2 of the time you will overbid me with a wide marigin. 1/4 of the time I win the worthless oilfields. But 1/4 of the time I win the 25m oilfield. If you received a high signal you have negative expected payoff according to your strategy.
sume dokin, Lets assume the oilfield was $25m. If you got the lower signal, then you bid $1. BUT, if you received the lower signal, the other player received the higher signal. Then he will bid higher than $1, and get the field. You loose all the same as if you decided to bid $0 as I suggested. So it is a tie in this situation. If you got the higher signal, you ALSO bid $1. If you received the higher signal, the other player received the lower signal. Thus you will bid more than the other player and get the field. How much do you pay for the field? The amount that the other player decided to bid while having the lower signal. This is the same amount as you would pay as if you decided to bid $50m as I suggested. Again, a tie. So, why is my proposal better if it performs the same in both cases? Because so far I only considered the $25m oilfield. Assume for a moment that the oilfield values $0. If the other player follows my lead, he will bid 0$ (because both of you will receive the low signal), and you will be $1 short. So, that was a bad move. Assume of a moment that the oilfield values $50m. If the other players follows my lead, he will bid $50m (both of you will receive the high signal) and you will bid $1, thus he will get the oilfield and pay only $1. That is a profit of $49999999. Thus, my strategy is in some occasions the same as yours (when the field values $25m all outcomes are the same), and in some occasions better (you avoid loosing $1) and in other occasions much better ($49999999 better).
You're right! I was considering a strategy for a first price auction. Still, would it really turn into a first price auction if you bid $0? It would make sense from the auctioner's perspective not to include $0 bids, but is it really how it will work in this case? That is a question which will determine if this strategy is really a Nash equilibrium.
The problem here is that if the other player is rational and you get the lower signal, than you can only win the auction if the field values $0. So in that case you don't want to participate if you have to pay. (Since if the oilfield was valuing $25m and you get the lower signal, then the other player got the high signal and will always outbid you). Any bid other than $0 would have a profitable deviation (just make a smaller bid).
If you have a high signal you should bid a very, very high amount of money, because if the other received a low-signal he will offer 12.5m and you only have to pay his offer because its a second bid auction and in that case you are in positive since you only pay 12.5m and you receive 25m. If the other received a high signal the same applies
I should bid $0 for the low signal (either the other player got the low signal and it means the field values 0, either it received the high signal and he will bid more anyway), and I should bid $50m for the high signal (either the other player received the low signal, and I am indifferent about any value above 0$; or the other player received the high signal in which case any bid different from $50m would not be optimal).
I should bid $1 regardless if the signal is high or low. 1/2 of the time you will overbid me with a wide marigin. 1/4 of the time I win the worthless oilfields. But 1/4 of the time I win the 25m oilfield. If you received a high signal you have negative expected payoff according to your strategy.
sume dokin,
Lets assume the oilfield was $25m.
If you got the lower signal, then you bid $1. BUT, if you received the lower signal, the other player received the higher signal. Then he will bid higher than $1, and get the field.
You loose all the same as if you decided to bid $0 as I suggested. So it is a tie in this situation.
If you got the higher signal, you ALSO bid $1. If you received the higher signal, the other player received the lower signal. Thus you will bid more than the other player and get the field.
How much do you pay for the field? The amount that the other player decided to bid while having the lower signal. This is the same amount as you would pay as if you decided to bid $50m as I suggested. Again, a tie.
So, why is my proposal better if it performs the same in both cases? Because so far I only considered the $25m oilfield.
Assume for a moment that the oilfield values $0.
If the other player follows my lead, he will bid 0$ (because both of you will receive the low signal), and you will be $1 short. So, that was a bad move.
Assume of a moment that the oilfield values $50m.
If the other players follows my lead, he will bid $50m (both of you will receive the high signal) and you will bid $1, thus he will get the oilfield and pay only $1. That is a profit of $49999999.
Thus, my strategy is in some occasions the same as yours (when the field values $25m all outcomes are the same), and in some occasions better (you avoid loosing $1) and in other occasions much better ($49999999 better).
You're right! I was considering a strategy for a first price auction. Still, would it really turn into a first price auction if you bid $0? It would make sense from the auctioner's perspective not to include $0 bids, but is it really how it will work in this case? That is a question which will determine if this strategy is really a Nash equilibrium.
The problem here is that if the other player is rational and you get the lower signal, than you can only win the auction if the field values $0. So in that case you don't want to participate if you have to pay.
(Since if the oilfield was valuing $25m and you get the lower signal, then the other player got the high signal and will always outbid you).
Any bid other than $0 would have a profitable deviation (just make a smaller bid).
Thank you.
Winner’s Curse? More like “Whoa, this could fill your purse!”…if you have a purse and use the lessons gained from these videos to make more money.
Really useful video William. Here is an explanation of the Winner's Curse in Spanish: th-cam.com/video/K6Pm0aYZiIU/w-d-xo.html