We study a problem of optimal auction design in the realistic case in which the players can collude both on the way they play in the auction and on their participation decisions. Despite the fact that the principal's opportunities for extracting payments from the agents in such a situation are...

We study cheap-talk pre-play communication in the static all-pay auctions. For the case of two bidders, all correlated and communication equilibria are payoff equivalent to the Nash equilibrium if there is no reserve price, or if it is commonly known that one bidder has a strictly higher value....