We show that with complete information, there exists a single, detail-free mechanism that can implement any social choice function whenever agents regard its value as being socially desirable. Even non-monotonic social choice rules can be implemented using Nash equilibrium refinements. Within economic environments, the gap after Palfrey and Srivastava's work between necessary and sufficient conditions was closed by Jackson 1991 with a strengthening of Bayesian monotonicity. We investigate the collective decision with incomplete information and side payments. In this paper, we introduce a notion of continuous implementation and characterize when a social choice function is continuously implementable. In section 4, we illustrate the di¢ culties in economies with non-exclusive information introduced by Postlewaite and Schmeidler 1986.
Though some new sufficient conditions accompanying incentive compatibility were identified incentive consistency in Duggan 1997 , measurability in Abreu and Matsushima 1992 , they were not necessary conditions, and not even logically weaker than Bayesian monotonicity as shown in Serrano and Vohra 2001. The task was to reconcile the Utopian and Hobbesian traditions, using game theory to find ways to organise the society that are both socially optimal and incentive compatible. An astronomer as well as an essayist on numerous scientific topics, Lardner often took side trips into other fields. We show that a general procedure is to start with an incentive-compatible revelation mechanism, and then augment agents' message spaces in order to eliminate undesired equilibria. I survey the theory of implementation in this article, emphasizing the results based on two behavioral assumptions for the agents dominant strategies and Nash equilibrium. Introduction The problem of social decision making when information is decentralized has occupied economists since the days of Adam Smith. In contrast with the standard models, we construct only mechanisms that are universal, i.
It is shown that, in environments with at least three agents, mixed Bayesian implementation is equivalent to mixed Bayesian monotonicity, incentive compatibility and closure. I consider robust virtual implementation in iteratively undominated strategies under complete information, where robustness is the requirement that the mechanism depends only on the payoff type. It is well known that a social choice function is truthfully imple- mentable in Bayesian Nash equilibrium if and only if it is incentive compatible. The implementation problem lies at the heart of a theory of institutions. We show also that in the incomplete information environments with two or more agents, every Bayesian incentive compatible social choice function can be implemented in Bayesian Nash equilibrium by a mechanism that is universal in the sense that it does not depend on the detail of the private signal structure. With the complementary probability we actuate a mechanism that may be typically far from optimal but is incentive compatible. We show that a direct mechanism associated with the social choice function that satisfies budget balancing, incentive compatibility, and interim individual rationality exists for generic prior distributions.
An example shows that there are virtually in fact, exactly Bayesian implementable social choice functions that are not virtually implementable in iteratively undominated strategies. If a mechanism has the property that, in each possible state of the world, the set of equilibrium outcomes equals the set of optimal outcomes identified by the social choice rule, then the social choice rule is said to be implemented by this mechanism. This result is independent of the presence of monetary transfers or assumptions alike, made in previous studies. In conjunction with a second condition, Bayesian incentive consistency, incentive compatibility is also sufficient. The Bayesian incentive-compatible interim core may be empty, as pointed out by Hahn and Yannelis 1997. This is in contrast to the well-known negative result for complete information environments. A resource allocation mechanism is thus essentially a system for communicating and processing information.
Jevons, who claimed that a reading of Railway Economy in 1857 led him to investigate economics in mathematical terms. A social choice function is robustly implemented if every equilibrium on every type space achieves outcomes consistent with it. We define iterative honesty-proofness by iteratively removing messages dominated by more honest messages. In their example, every individually rational social choice function is non-constant, and therefore, is normative in our sense. This observation means that the gap between the solution concepts of pure strategy Bayesian Nash equilibrium Serrano and Vohra 2001 , Serrano and Vohra 2005 and iterated deletion of interim strictly dominated strategies Abreu and Matsushima 1992c in incomplete information virtual implementation disappears in our robust approach.
Implicitly, it is assumed that the mechanism designer does not know the true θ, and this lack of information makes it impossible for her to directly choose an outcome in F θ. Examples discussed include voting, and the allocation of private and public goods under complete and incomplete information. For instance, Serrano and Vohra 2001 investigated the economic environments where agents' preferences are the same across states but their initial endowments depend on the state. He studied railway engineering in Paris, and was probably well acquainted with the econo-engineering work at the Ecole des Ponts et Chaussées at a time when Jules Dupuit was actively pursuing economic topics. We also provide a necessary and sufficient condition - type diversity with respect to deceptions -f or virtual Bayesian implementation in economic environments. In doing so, the paper takes a unified approach to exact and approximate implementation, and considers general social choice sets in economic environments with incomplete information — outside of economic environments, tight characterizations are generally not available, even for pure-strategy equilibria.
The paper by Glazer and Rubinstein 1998 is more closely related to the present paper, where agents are allowed to have preference for anything non-consequential. Typically, the underlying parameters e. Type diversity is a con- dition with a simple economic interpretation compared to Bayesian monotonicity, and the mechanism we construct is also simple. This observation means that the gap between the solution concepts of pure strategy Bayesian Nash equilibrium Serrano and Vohra 2001 , Serrano and Vohra 2005 and iterated deletion of interim strictly dominated strategies Abreu and Matsushima 1992c in incomplete information virtual implementation disappears in our robust approach. An important issue is whether simple and intuitively appealing mechanisms can be optimal.
Our results characterize both exact and virtual mixed implementation. Most of the papers on implementation that use equilibrium concepts have confined their scope to the case of pure strategies. Several papers on implementation Postlewaite and Schmeidler 1986 , Palfrey and Srivastava 1989 , Serrano and Vohra 2001 assume that the aggregate initial endowment P i e i t i does not depend on t, i. This lacuna is troubling as consumers have much control over the data being collected. The Bayesian incentive-compatible coarse core is nonemepty. The present-day corporations are interdependent, so the required game theory needs to model an environment in which the feasibility and implications of coordinated strategy choice within a coalition are influenced by the outsiders of strategy choice.
In particular, it is weaker than Abreu-Matsushima's measurability, thereby implying that: 1 virtual implementation in Bayesian equilibrium is more permissive than virtual implementation in iteratively undominated strategies, and 2 non-regular mechanisms may be important for virtual implementation in Bayesian equilibrium. It is equivalent to Bayesian monotonicity on all type spaces. This paper constructs a two-country Home and Foreign general equilibrium model of Schumpeterian growth without scale effects. The mechanism we design is optimal up to an additive factor of the order of magnitude of one over the square root of the number of agents and involves no utility transfers. The implementation problem can be made more challenging by imposing additional requirements on the mechanisms, such as robustness to renegotiation and collusion. We show that in the incomplete information environments, every incentive compatible social choice function can be implemented by the mechanism that is universal in the sense that it does not depend on the private signal structure. The first part of the paper provides the key ingredients.
Mechanism design concerns the reverse question: given some desirable outcome, can we design a game which produces it? The descriptive theory of cooperative game with incomplete information developed to date is surveyed. The following generalization of the irrelevance theorem is shown here: indescribability does not matter even in the presence of asymmetric information at the trading stage, as long as there is symmetric information at the contracting stage. Journal of Economic Literature Classification Numbers: 025, 026. An inuential article by Hayek crystallized the problem. This implies that in most environments virtual Bayesian implementation is as successful as it can be incentive compatibility is the only condition needed. This paper studies implementation in a principal—agent model of adverse selection. We introduce an easily verifiable condition, Condition 1, which is equivalent to Bayesian monotonicity under strict self selection.