Third price auction: the winner is the highest bidder but this time instead of paying the second highest bid, he would pay the third highest bid. -assume there are at least 3 bidders. -
Average price auction: the winner is the highest bidder but pays the average of his and the second highest bid.
For these,
How to show whether truthtelling is a dominant strategy or not? And how to show whether truthtelling is a nash equlibrium?