Monotone Pure Strategy Equilibria in First Price Menu Auctions

Monotone Pure Strategy Equilibria in First Price Menu Auctions

This paper studies the first-price menu auctions, with asymmetric bidders, interdependent values, and affiliated signals, in which bidders submit menus of multidimensional contracting decisions and the decision maker (DM) chooses a contracting decision from a menu that she accepts. The interdependent values generically induces a continuum of continuation equilibria, one of which the DM chooses to follow for her contracting decision choice. It establishes the existence of a continuum of monotone pure-strategy equilibria, each of which depends on bidders’ beliefs on the continuation equilibrium that the DM chooses to follow. The continuum of monotone pure-strategy equilibria is characterized in terms of how sensitive it is to bidders’ beliefs on the continuation equilibrium. It identifies a belief-free monotone pure-strategy equilibrium that survives in any continuation equilibrium upon any bidder’s deviation.