Knightian Auctions

We study single-good auctions in a setting where each player knows his own valuation only within a constant multiplicative factor \delta{} in (0,1), and the mechanism designer knows \delta. The classical notions of implementation in dominant strategies and implementation in undominated strategies are naturally extended to this setting, but their power is vastly different. On the negative side, we prove that no dominant-strategy mechanism can guarantee social welfare that is significantly better than that achievable by assigning the good to a random player. On the positive side, we provide tight upper and lower bounds for the fraction of the maximum social welfare achievable in undominated strategies, whether deterministically or probabilistically

Knightian Analysis of the Vickrey Mechanism

We analyze the Vickrey mechanism for auctions of multiple identical goods when the players have both Knightian uncertainty over their own valuations and incomplete preferences. In this model, the Vickrey mechanism is no longer dominant-strategy, and we prove that all dominant-strategy mechanisms are inadequate. However, we also prove that, in undominated strategies, the social welfare produced by the Vickrey mechanism in the worst case is not only very good, but also essentially optimal.Comment: To appear in Econometric

Uncertainty Aversion, Robust Control and Asset Holdings

Optimal portfolio rules are derived under uncertainty aversion by formulating the portfolio choice problem as a robust control problem. The robust portfolio rule indicates that the total holdings of risky assets as a proportion of the investor’s wealth could increase as compared to the holdings under the Merton rule, which is the standard risk aversion case. With two risky assets an increase in the holdings of the one risky asset is accompanied by a reduction in the holdings of the other asset. Furthermore, in the optimal robust portfolio the investor may increase the holdings of the asset for which there is or less ambiguity, and reduce the holding of the asset for which there is more ambiguity, a result that might provide an explanation of the home bias puzzle.Uncertainty aversion, Model misspecification, Robust control, Portfolio choice models

A Social-Welfare Optimal Probabilistic Mechanism for Knightian Single-Good Auctions

We provide an optimal probabilistic mechanism for maximizing social welfare in single-good auctions when each player does not know his true valuation for the good, but only a set of valuations that is guaranteed to include his true one

An overview of economic applications of David Schmeidler`s models of decision making under uncertainty

This paper surveys some economic applications of the decision theoretic framework pioneered by David Schmeidler to model effects of ambiguity. We have organized the discussion principally around three themes: financial markets, contractual arrangements and game theory. The first section discusses papers that have contributed to a better understanding of financial market outcomes based on ambiguity aversion. The second section focusses on contractual arrangements and is divided into two sub-sections. The first sub-section reports research on optimal risk sharing arrangements, while in the second sub-section, discusses research on incentive contracts. The third section concentrates on strategic interaction and reviews several papers that have extended different game theoretic solution concepts to settings with ambiguity averse players. A final section deals with several contributions which while not dealing with ambiguity per se, are linked at a formal level, in terms of the pure mathematical structures involved, with Schmeidler`s models of decision making under ambiguity. These contributions involve issues such as, inequality measurement, intertemporal decision making and multi-attribute choice.Ellsberg Paradox, Ambiguity aversion, Uncertainty aversion

Portfolio Inertia and [Epsilon]-Contaminations,

This paper analyzes platforms and rejections in two-sided markets with network externalities, using the specific context of a payment card association. We study the cooperative antitrust determination of the interchange fee by member banks. We use a framework in which banks and merchants may have market power and consumers and merchants decide rationally on whether to buy or accept a payment card developed by Rochet and Tirole (2002). After drawing the welfare implications of a cooperative determination of the interchange fee and antitrust conducts, we describe in detail the factors affecting merchant resistance, compare cooperative and for-profit business models, and make a first cut in the analysis of system competition.