We generalise the classical implicit function theorem (IFT) for a family of Banach spaces, with the resulting implicit function having derivatives that are locally Lipschitz to very strong operator norms.

We introduce 2 parameter variants L_{p,q} of the Lebesgue spaces, to gain separate control on the asymptotic behaviour (p) and the local behaviour (q). Thus they behave with respect to p like the spaces ell_p and with respect to q like the spaces L_q on a probability space. Convolution behaves...

Do greater potential gains from trade enhance or erode contracting institutions? In an anonymous exchange environment traders can sign a contract, hence agreeing to interact with the assigned partner, or wait till the next match. Any contract can be endorsed (for a pay) by the enforcement...

A bargaining solution guarantees minimal equity if each player's payoff is at least as large as the minimum of the payoffs assigned to him by the equal-gain (i.e., egalitarian) and equal-loss solutions. The Kalai-Smorodinsky solution is the unique scale-invariant 2-person solution with this...

An IPV 2-bidder second-price auction is preceded by two rounds of bribing: prior to the auction each bidder can try to bribe his rival to depart from the auction, so that he (the briber) will become the sole participant and obtain the good for the reserve price. Bribes are offered sequentially...

We introduce a two-player, binary-choice game in which both players have a privately known incentive to enter, yet the combined surplus is highest if only one enters. Repetition of this game admits two distinct ways to cooperate: turn taking and cutoffs, which rely on the player's private value...

We analyze the loans that startup firms obtain from banks by testing our predictions on a set of small, young Italian companies founded during the 1992-2004 period. According to our investigation, the amount of borrowing is determined by (1) the size of the firm, (2), the ability to offer...

A bargaining solution balances fairness and efficiency if each player's payoff lies between the minimum and maximum of the payoffs assigned to him by the egalitarian and utilitarian solutions. In the 2-person bargaining problem, the Nash solution is the unique scale-invariant solution satisfying...

I study collusion between two bidders in a general symmetric IPV repeated auction, without communication, side transfers, or public randomization. I construct a collusive scheme, endogenous bid rotation, that generates a payoff larger than the bid rotation payoff.