We show that a mechanism that robustly implements optimal outcomes in a one-dimensional supermodular environment continues to robustly implement "-optimal outcomes in all close-by environments. Robust implementation of "-optimal outcomes is thus robust to small perturbations of the environment. This is in contrast to ex-post implementation which is not robust in this sense as only trivial socia...

A dataset is a list of observed factor inputs and prices for a technology; profits and production levels are unobserved. We obtain necessary and sufficient conditions for a dataset to be consistent with profit maximization under a monotone and concave revenue based on the notion of cyclic monotonicity. Our result implies that monotonicity and concavity cannot be tested, and that one cannot deci...

Given two sets of random variables, how can one determine whether the former variables are more interdependent than the latter? This question is of major importance to economists, for example, in comparing how various policies affect systemic risk or income inequality. Moreover, correlation is ill-suited to this task as it is typically not justified by any economic objective. Economists’ intere...

Abstract The inequalities of Hardy-Littlewood and Riesz say that certain integrals involving products of two or three functions increase under symmetric decreasing rearrangement. It is known that these inequalities extend to integrands of the form F (u1, . . . , um) where F is supermodular; in particular, they hold when F has nonnegative mixed second derivatives ∂i∂jF for all i 6= j. This paper...

This paper develops a general theory of sequential irreversible investments in capital where a firm has the option to expand its current capacity or just wait for better time. Facing economic uncertainty, the firm has an operating function of the current capacity and an exogenous stochastic factor modelled by semimartingale. This general model encompasses all previously studied models, includin...

We reconsider Stackelberg’s classical critique of the Cournot duopoly, in the framework of endogenous timing for two-player games. For quantity duopoly we provide different sets of minimal conditions, directly on the demand and cost functions, yielding respectively the simultaneous and the two sequential modes of play. While our findings essentially confirm the predominance of the former, they ...

We consider four models of evolution and learning in games which rely on perturbations of payoffs, including stochastic fictitious play. In all cases, we establish global stability results for zerosum games, games with an interior ESS, potential games, and supermodular games.

In perfect foresight dynamics, an action is linearly stable if expectation that people will always choose the action is self-fulfilling. A symmetric game is a PIM game if an opponent’s particular action maximizes the incentive of an action, independently of the rest of the players. This class includes supermodular games, games with linear incentives and so forth. We show that, in PIM games, lin...

We propose two characteristics of players’ beliefs and study their role in shaping the set of rationalizable strategy profiles in games with incomplete information. The first characteristic, type-sensitivity, is related to how informative a player thinks his type is. The second characteristic, optimism, is related to how “favorable” a player expects the outcome of the game to be. The paper has ...

This paper establishes a necessary and sufficient condition for the convexity (or supermodularity) in oligopoly games.  1999 Elsevier Science B.V. All rights reserved.