We characterize belief-free equilibria in infinitely repeated games with incomplete information with N \ge 2 players and arbitrary information structures. This characterization involves a new type of individual rational constraint linking the lowest equilibrium payoffs across players. The...

We compare the seller's expected revenue in a second price sealed bid auction for a single object in which bidders receive multidimensional signals. Bidders' valuations for the object depend on their signals and a signal observed privately by the seller. We show in various examples that the...

We let "Algorithmic Market-Makers" (AMMs), using Q-learning algorithms, choose prices for a risky asset when their clients are privately informed about the asset payoff. We find that AMMs learn to cope with adverse selection and to update their prices after observing trades, as predicted by...