Knowledge that Transforms

The main contribution of this paper is the development and application of cryptographic techniques to the design of strategic communication mechanisms. One of the main assumptions in cryptography is the limitation of the computational power available to agents. We introduce the concept of limited computational complexity, and by borrowing results from cryptography, we construct a communication protocol to establish that every correlated equilibrium of a two-person game with rational payoffs can be achieved by means of computationally restricted unmediated communication. This result provides an example in game theory where limitations of computational abilities of players are helpful in solving implementation problems. More specifically, it is possible to construct mechanisms with the property that profitable deviations are too complicated to compute. Copyright The Econometric Society 2002.

This paper investigates the design of seller–optimal auctions when winning bidders can attempt to resell the good. In that case, the optimal allocation characterized by Myerson (1981) cannot be achieved without resale. I find a sufficient and necessary condition for sincere bidding given the possibility of resale. In two–bidder cases, I prove that the Myerson allocation can be achieved under standard conditions supplemented with two assumptions. With three or more bidders, achieving the Myerson allocation is more difficult. I prove that it can be implemented in special cases. In those cases, the Myerson allocation is generated through a sequence of resale auctions, each optimally chosen by a reseller.

Self–selected migration presents one potential explanation for why observed returns to a college education in local labor markets vary widely even though U.S. workers are highly mobile. To assess the impact of self–selection on estimated returns, this paper first develops a Roy model of mobility and earnings where workers choose in which of the 50 states (plus the District of Columbia) to live and work. Available estimation methods are either infeasible for a selection model with so many alternatives or place potentially severe restrictions on earnings and the selection process. This paper develops an alternative econometric methodology that combines Lee's (1983) parametric maximum order statistic approach to reduce the dimensionality of the error terms with more recent work on semiparametric estimation of selection models (e.g., Ahn and Powell (1993)). The resulting semiparametric correction is easy to implement and can be adapted to a variety of other polychotomous choice problems. The empirical work, which uses 1990 U.S. Census data, confirms the role of comparative advantage in mobility decisions. The results suggest that self–selection of higher educated individuals to states with higher returns to education generally leads to upward biases in OLS estimates of the returns to education in state–specific labor markets. While the estimated returns to a college education are significantly biased, correcting for the bias does not narrow the range of returns across states. Consistent with the finding that the corrected return to a college education differs across the U.S., the relative state–to–state migration flows of college– versus high school–educated individuals respond strongly to differences in the return to education and amenities across states.

Iterated elimination of strictly dominated strategies is an order dependent procedure. It can also generate spurious Nash equilibria, fail to converge in countable steps, or converge to empty strategy sets. If best replies are well–defined, then spurious Nash equilibria cannot appear; if strategy spaces are compact and payoff functions are uppersemicontinuous in own strategies, then order does not matter; if strategy sets are compact and payoff functions are continuous in all strategies, then a unique and nonempty maximal reduction exists. These positive results extend neither to the better–reply secure games for which Reny has established the existence of a Nash equilibrium, nor to games in which (under iterated eliminations) any dominated strategy has an undominated dominator.

This paper offers a new approach to the study of economic problems usually modeled as games of incomplete information with discontinuous payoffs. Typically, the discontinuities arise from indeterminacies (ties) in the underlying problem. The point of view taken here is that the tie-breaking rules that resolve these indeterminacies should be viewed as part of the solution rather than part of the description of the model. A solution is therefore a tie-breaking rule together with strategies satisfying the usual best-response criterion. When information is incomplete, solutions need not exist; that is, there may be no tie-breaking rule that is compatible with the existence of strategy profiles satisfying the usual best-response criteria. It is shown that the introduction of incentive compatible communication (cheap talk) restores existence. Copyright The Econometric Society 2002.

How can diversity be measured? What does it mean to value biodiversity? Can we assist Noah in constructing his preferences? To address these questions, we propose a multi-attribute approach under which the diversity of a set of species is the sum of the values of all attributes possessed by some species in the set. We develop the basic intuitions and requirements for a theory of diversity and show that the multi-attribute approach satisfies them in a flexible yet tractable manner. A natural starting point is to think of the diversity of a set as an aggregate of the pairwise dissimilarities between its elements. The multi-attribute framework allows one to make this program formally precise. It is shown that the program can be realized if and only if the family of relevant attributes is well-ordered (“acyclic”). Moreover, there is a unique functional form aggregating dissimilarity into diversity, the length of a minimum spanning tree. Examples are taxonomic hierarchies and lines representing uni-dimensional qualities. In multi-dimensional settings, pairwise dissimilarity information among elements is insufficient to determine their diversity. By consequence, the qualitative and quantitative behavior of diversity differs fundamentally.

This paper presents an algorithm for computing an equilibrium of an extensive two-person game with perfect recall. The method is computationally efficient by virtue of using the sequence form, whose size is proportional to the size of the game tree. The equilibrium is traced on a piecewise linear path in the sequence form strategy space from an arbitrary starting vector. If the starting vector represents a pair of completely mixed strategies, then the equilibrium is normal form perfect. Computational experiments compare the sequence form and the reduced normal form, and show that only the sequence form is tractable for larger games.