Ludovic Renou

Mechanism Design With Ambiguous Communication Devices

This paper considers mechanism design problems in environments with ambiguity-sensitive individuals. The novel idea is to introduce ambiguity in mechanisms so as to exploit the ambiguity sensitivity of individuals. Deliberate engineering of ambiguity, through ambiguous mediated communication, can allow (partial) implementation of social choice functions that are not incentive compatible with respect to prior beliefs. We provide a complete characterization of social choice functions partially implementable by ambiguous mechanisms.

Minimax Regret and Strategic Uncertainty

This paper introduces a new solution concept, a minimax regret equilibrium, which allows for the possibility that players are uncertain about the rationality and conjectures of their opponents. We provide several applications of our concept. In particular, we consider pricesetting environments and show that optimal pricing policy follows a non-degenerate distribution. The induced price dispersion is consistent with experimental and empirical observations (Baye and Morgan (2004)).

More Strategies, More Nash Equilibria

This short paper isolates a non-trivial class of games for which there exists a monotone relation between the size of pure strategy spaces and the number of pure Nash equilibria (Theorem). This class is that of two- player nice games, i.e., games with compact real intervals as strategy spaces and continuous and strictly quasi-concave payoff functions, assumptions met by many economic models. We then show that the sufficient conditions for Theorem to hold are tight.

Mechanism design and communication networks

This paper characterizes the communication networks (directed graphs) for which, in any environment (utilities and beliefs), every incentive compatible social choice function is implementable. We show that any incentive compatible social choice function is implementable on a given communication network, in all environments with either common independent beliefs and private values or a worst outcome, if and only if the network is strongly connected and weakly 2-connected. A network is strongly connected if for each player, there exists a directed path to the designer. It is weakly 2-connected if each player is either directly connected to the designer or indirectly connected to the designer through two disjoint paths not necessarily directed. We couple encryption techniques together with appropriate incentives to secure the transmission of each players private information to the designer.

Repeated Nash Implementation

This paper studies repeated implementation of social choice functions in environments with complete information and changing preferences. We introduce the condition of dynamic monotonicity and show that it is necessary for repeated implementation in finite as well as infinite horizon problems. With at least three agents, the conditions of dynamic monotonicity and no-veto power are sufficient. In infinite horizon problems with high enough discount factors, dynamic monotonicity implies weak efficiency in the range (Lee and Sabourian, 2011), while Maskin monotonicity implies dynamic monotonicity in finite horizon problems.

Implementation in Mixed Nash Equilibrium

A mechanism implements a social choice correspondence f in mixed Nash equilibrium if at any preference profile, the set of all pure and mixed Nash equilibrium outcomes coincides with the set of f-optimal alternatives at that preference profile. This definition generalizes Maskin’s definition of Nash implementation in that it does not require each optimal alternative to be the outcome of a pure Nash equilibrium. We show that the condition of weak set-monotonicity, a weakening of Maskin’s monotonicity, is necessary for implementation. We provide sufficient conditions for implementation and show that important social choice correspondences that are not Maskin monotonic can be implemented in mixed Nash equilibrium.

Implementation in mixed Nash equilibrium

A mechanism implements a social choice correspondence f in mixed Nash equilibrium if at any preference profile, the set of all pure and mixed Nash equilibrium outcomes coincides with the set of f-optimal alternatives at that preference profile. This definition generalizes Maskin’s definition of Nash implementation in that it does not require each optimal alternative to be the outcome of a pure Nash equilibrium. We show that the condition of weak set-monotonicity, a weakening of Maskin’s monotonicity, is necessary for implementation. We provide sufficient conditions for implementation and show that important social choice correspondences that are not Maskin monotonic can be implemented in mixed Nash equilibrium.

Rent Extraction and Uncertainty

This note revisits the problem of rent extraction in situations where agents are uncertain about the private information of others, represented by multiple probabilistic assessments. A generalization of convex independence (Cremer and McLean, 1985 and 1988) is necessary and sufficient for full rent extraction. Full rent extraction is not generically possible.

Mixed Nash Implementation with Finite Mechanisms

This paper studies full implementation problems in (pure and mixed) Nash equilibrium in finite environments. We restrict the designer to adoptfinite mechanisms, thus ruling out integer games. We provide a condition, top-D inclusiveness, that together with set-monotonicity is sufficient for mixed Nash implementation with finite mechanisms in separable environments. Top-D inclusiveness is an efficiency condition.

Ordients: Optimization and Comparative Statics without Utility Functions ∗

This paper introduces the concept of ordient for binary relations (prefer- ences), a relative of the concept of gradient for functions (utilities). The main motivation for this study is to replace the binary relation at the center stage of economic analysis, rather than its representation (whenever it exists). Ordi- ents have a natural economic interpretation as marginal rates of substitution. Some examples of ordientable binary relations include the lexicographic order, binary relations resulting from the sequential applications of multiple rationales or binary relations with differentiable representations. We characterize the con- strained maxima of binary relations through ordients and provide an implicit function theorem and an envelope theorem.