Olivier Bochet

Nash Implementation with Lottery Mechanisms

Consider the problem of exact Nash Implementation of social choice correspondences. Define a lottery mechanism as a mechanism in which the planner can randomize on alternatives out of equilibrium while pure alternatives are always chosen in equilibrium. When preferences over alternatives are strict, we show that Maskin monotonicity (Maskin in Rev Econ stud 66: 23–38, 1999) is both necessary and sufficient for a social choice correspondence to be Nash implementable. We discuss how to relax the assumption of strict preferences. Next, we examine social choice correspondences with private components. Finally, we apply our method to the issue of voluntary implementation (Jackon and Palfrey in J Econ Theory 98: 1–25, 2001).

Preference Manipulations Lead to the Uniform Rule

In the division problem with single-peaked preferences, it is well known that the uniform rule is robust to strategic manipulation. Furthermore, under efficiency and symmetry, it is the unique strategy-proof rule (Sprumont, 1991; Ching, 1994). We conversely analyze the consequences of strategic manipulation for a wide class of rules. Given a rule, we interpret its associated direct revelation game as a manipulation game, and we characterize its equilibrium allocations. We establish a strong connection between outcomes of manipulation and the uniform rule itself. For every rule that belongs to the class, the uniform allocation (i) is the unique strong Nash equilibrium allocation and the unique Pareto-efficient Nash equilibrium allocation, and (ii) is the unique Nash equilibrium allocation under an additional strict monotonicity condition. Thus, attempts to manipulate each of our rule lead to the recommendation made by the uniform rule. A by-product of our results is the identification of a large class of direct revelation mechanisms that doubly implement the uniform rule in Nash and strong Nash equilibria.

The relation between monotonicity and strategy-proofness

The Muller–Satterthwaite Theorem (J Econ Theory 14:412–418, 1977) establishes the equivalence between Maskin monotonicity and strategy-proofness, two cornerstone conditions for the decentralization of social choice rules. We consider a general model that covers public goods economies as in Muller–Satterthwaite (J Econ Theory 14:412–418, 1977) as well as private goods economies. For private goods economies, we use a weaker condition than Maskin monotonicity that we call unilateral monotonicity. We introduce two easy-to-check preference domain conditions which separately guarantee that (i) unilateral/Maskin monotonicity implies strategy-proofness (Theorem 1) and (ii) strategy-proofness implies unilateral/Maskin monotonicity (Theorem 2). We introduce and discuss various classical single-peaked preference domains and show which of the domain conditions they satisfy (see Propositions 1 and 2 and an overview in Table 1). As a by-product of our analysis, we obtain some extensions of the Muller–Satterthwaite Theorem as summarized in Theorem 3. We also discuss some new “Muller–Satterthwaite preference domains” (e.g., Proposition 3).

Maximal Domains for Strategy-Proof or Maskin Monotonic Choice Rules

Domains of individual preferences for which the well-known impossibility Theorems of Gibbard-Satterthwaite and Muller-Satterthwaite do not hold are studied. First, we introduce necessary and sufficient conditions for a domain to admit non-dictatorial, Pareto efficient and either strategy-proof or Maskin monotonic social choice rules. Next, to comprehend the limitations the two Theorems imply for social choice rules, we search for the largest domains that are possible. Put differently, we look for the minimal restrictions that have to be imposed on the unrestricted domain to recover possibility results. It turns out that, for such domains, the conditions of inseparable pair and of inseparable set yield the only maximal domains on which there exist non-dictatorial, Pareto efficient and strategy-proof social choice rules. Next, we characterize the maximal domains which allow for Maskin monotonic, non-dictatorial and Pareto-optimal social choice rules.

Strategic manipulations of multi-valued solutions in economies with indivisibilities

This paper studies strategic manipulations of multi-valued solutions in the problem of fairly allocating homogeneous indivisible objects with monetary transfers. We provide various extensions of strategy-proofness to multi-valued solutions and examine their impact on standard solutions. We show that some efficient and fair solutions, such as the envy-free solution, satisfy certain extensions of strategy-proofness. We also establish an impossibility result on extended strategy-proofness that is defined in terms of expected utility.

Switching from complete to incomplete information

We construct an elementary mechanism (Dutta, Sen and Vohra (1995)) that Nash implements the Constrained Walrasian correspondence. We extend it to incomplete and non-exclusive information economies by enlarging the message space of agents. We characterize the set of Bayesian equilibrium outcomes of the mechanism, and thus characterize an extension of the Constrained Walrasian correspondence when one switches from complete to incomplete information. First, measurability restrictions on allocations do not emerge from the strategic behavior of agents: there exist simple economies for which the set of Constrained Rational Expectations equilibrium allocations is not contained in the set of equilibrium outcomes of the mechanism. Next, by imposing measurability restrictions on allocations, the mechanism globally implements the Constrained Rational Expectations Equilibrium correspondence. This result shows game-theoretic connections between these two market equilibrium concepts. However, it is obtained at the price of strong restrictions on the behavior of agents.price of strong restrictions on the behavior of agents.We construct an elementary mechanism (Dutta-Sen-Vohra, 1995) that Nash implements the Constrained Walrasian correspondence. We extend it to incomplete and non-exclusive information economies by enlarging the message space of agents. We characterize the set of Bayesian equilibrium outcomes of the mechanism, and thus characterize an extension of the Constrained Walrasian correspondence when one switches from complete to incomplete information. First, measurability restrictions on allocations do not emerge from the strategic behavior of agents: there exist simple economies for which the set of Constrained Rational Expectations equilibrium allocations is not contained in the set of equilibrium outcomes of the mechanism. Next, by imposing measurability restrictions on allocations, the mechanism globally implements the Constrained Rational Expectations Equilibrium correspondence. This result shows game-theoretic connections between these two market equilibrium concepts. However, it is obtained at the price of strong restrictions on the behavior of agents.

Better Later than Never? An Experiment on Bargaining under Adverse Selection

A central result in the literature on bargaining with asymmetric information is that the uninformed party (buyer) can screen the informed party (seller) over time. Screening eliminates trade failures that are otherwise common in the presence of adverse selection, but the downside of the bargaining institution is the cost associated with repeated offers and time frictions. This paper reports an experimental test of these predictions. We find that rates of trade are substantially higher in the bargaining institution than in control treatments in which we remove the possibility to make repeated offers (take-it-or-leave-it offer) or the time frictions. However, we also observe a persistent over-delay before agreements are reached, i.e., bargaining takes longer than theoretically predicted. This lowers efficiency below its predicted level and below the level observed in the take-it-or-leave-it offer institution. We identify possible channels for over-delay in the form of fairness preferences and loss aversion, concluding that there are important behavioral deviations from the standard model that are detrimental to the efficiency of bargaining under incomplete information.

Subgame Perfect Implementation and the Walrasian Correspondence

Consider a class of exchange economies in which preferences are continuous, convex and strongly monotonic. It is well known that the Walrasian correspondence defined over this class violates Maskin Monotonicity (Maskin, 1999) and is thus not Nash implementable. However, contrary to a result in Moore-Repullo (1988), it is not implementable in subgame perfect equilibrium (and, in fact, in any solution concept). Indeed, the assumption of differentiability cannot be relaxed unless one imposes parametric restrictions on the environment, like assumption EE.3 in Moore-Repullo (1988). Nest, assuming differentiability, we construct a sequential mechanism that fully implements the Walrasian correspondence in subgame perfect and strong subgame perfect equilibrium. We take of the boundary problem that was prominent in the Nash implementation literature. Moreover, our mechanism is based on price-allocation announcements and fits the very description of Walrasian equilibrium.

BETTER LATER THAN NEVER? AN EXPERIMENT ON BARGAINING UNDER ADVERSE SELECTION: BETTER LATER THAN NEVER?

A central result in the literature on bargaining with asymmetric information is that the uninformed party (buyer) can screen the informed party (seller) over time. Screening eliminates trade failures that are otherwise common in the presence of adverse selection, but the downside of the bargaining institution is the cost associated with repeated offers and time frictions. This paper reports an experimental test of these predictions. We find that rates of trade are substantially higher in the bargaining institution than in control treatments in which we remove the possibility to make repeated offers (take-it-or-leave-it offer) or the time frictions. However, we also observe a persistent over-delay before agreements are reached, i.e., bargaining takes longer than theoretically predicted. This lowers efficiency below its predicted level and below the level observed in the take-it-or-leave-it offer institution. We identify possible channels for over-delay in the form of fairness preferences and loss aversion, concluding that there are important behavioral deviations from the standard model that are detrimental to the efficiency of bargaining under incomplete information.

Incentive compatible and stable trade mechanisms on networks

We study a network of buyers and sellers where each seller owns an indivisible object and has no incentive to keep it, while each buyer has a downward sloping demand curve which is private information. Only the connected buyer-seller pairs can engage in trade. We search for trade mechanisms that are efficient, strategy-proof, bilateral trade stable and individually rational. In general, there does not exist a trade mechanism simultaneously satisfying these properties. The tension between strategy-proofness and bilateral trade stability is generated by the intersection between sets of competitors of a buyer at different sellers. Such intersections often allow the buyer to manipulate (via demand reductions) the prices paid in the network. The observed tension can be resolved if and only if the underlying network is cycle-free. In such a case, there is a unique trade mechanism which satisfies our four properties, a generalized Vickrey auction.