Social and Behavioral Sciences Commons^™

Continuous Implementation With Payoff Knowledge, Yi-Chun Chen, Takashi Kunimoto, Yifei Sun

Research Collection School Of Economics

The literature on robust mechanism design assumes players' knowledge about a fixed payoff environment and investigates global robustness of optimal mechanisms to large changes in the information structure. Acknowledging global robustness as a demanding requirement, we propose continuous implementation as a notion of local robustness. Keeping the assumption of payoff knowledge, we say that an SCF is continuously implementable if there exists a mechanism which yields the outcome close to the desired one for all types close to the planner's initial model. We show that when a generic correlation condition is imposed on the class of interdependent-value environments, any (interim) …

On Incentive Compatible, Individually Rational Public Good Provision Mechanisms, Takashi Kunimoto, Cuiling Zhang

Research Collection School Of Economics

This paper characterizes mechanisms satisfying incentive compatibility and individual rationality in the classical public good provision problem. Many papers in the literature obtain the results in the so-called standard model of ex ante identical agents with a continuous, closed interval of types. The main contribution of this paper is the characterization of the budget-surplus maximizing mechanism satisfying incentive compatibility and individual rationality (Theorem 1 for Bayesian implementation and Theorem 3 for dominant strategy implementation) that applies to a finite discretization over the standard model. Making use of the proposed budget-surplus maximizing mechanisms, we show that some known results do not …

Robust Virtual Implementation With Almost Complete Information, Takashi Kunimoto

Research Collection School Of Economics

Artemov, Kunimoto, and Serrano (2013a,b, henceforth, AKS) study a mechanism design problem where arbitrary restrictions are placed on the set of first-order beliefs of agents. Calling these restrictions Δ, they adopt Δ-rationalizability (Battigalli and Siniscalchi, 2003) and show that Δ-incentive compatibility and Δ-measurability are necessary and sufficient conditions for robust virtual implementation, which implies that virtual implementation is possible uniformly over all type spaces consistent with Δ-restrictions. By appropriately defining Δ in order to restrict attention to complete information environments and thereafter explicitly modelling the assumption of complete information in the language of type spaces, I re-establish the permissive implementation …

Essays On A Mechanism Design Approach To The Problem Of Bilateral Trade And Public Good Provision, Cuiling Zhang

Dissertations and Theses Collection (Open Access)

The dissertation consists of three chapters which studies a mechanism design approach to the problem of bilateral trade and public good provision.

Chapter 1 characterizes mechanisms satisfying Bayesian incentive compatibility (BIC) and interim individual rationality (IIR) in the classical public good provision problem. We propose a stress test for the results in the standard continuum type space by subject- ing them to a finite type space. The main contribution of this paper is to propose a set of techniques that allow us to characterize the efficient and optimal mechanisms in a discrete setup. Using these techniques, we conclude that many …

Continuous Implementation With Small Transfers, Yi-Chun Chen, Takashi Kunimoto, Yifei Sun

Research Collection School Of Economics

The robust mechanism design literature investigates the global robustness of op-timal mechanisms to large changes in the environment. Acknowledging the global robustness as an overly demanding requirement, we propose continuous implementa-tion as a local robustness of optimal mechanisms to small changes in the environment. We say that a social choice function is continuously implementable “with small trans-fers” if there exists a mechanism which yields the outcome close to the desired one for all types close to the designer’s initial model. We show that when a generic cor-relation condition is imposed on the class of interdependent values environments, any incentive compatible …

Mixed Bayesian Implementation In General Environments, Takashi Kunimoto

Research Collection School Of Economics

A social choice rule is said to be mixed Bayesian implementable if one can design a mechanism (or institution) in which the set of all mixed Bayesian Nash equilibrium outcomes coincides with that specified by the rule. The objective of this paper is to generalize the results of mixed Bayesian implementation. By means of example, I first assess the implication of common priors in Bayesian implementation. Second, I identify a mild condition that fills the gap between the necessity and sufficiency for mixed Bayesian implementation in general environments including non-economic ones. Third, I establish some new results to unify the …

On Incentive Compatible, Individually Rational Public Good Provision Mechanisms, Takashi Kunimoto, Cuiling Zhang

Research Collection School Of Economics

This paper characterizes mechanisms satisfying Bayesian incentive compatibility (BIC) and interim individual rationality (IIR) in the classical public good provision problem. Many papers in the literature obtain the results in the so-called standard model of ex ante identical agents with a continuous, closed interval of types. Although the standard model and more generally a continuum type space are widely used in the literature, it is nonetheless an abstraction of reality. Given that the public good provision problem has occupied a central application in the theory of mechanism design, we propose a "stress test" for the results in the standard model …

Efficient Dynamic Mechanisms With Interdependent Valuations, Wei He, Jiangtao Li

Research Collection School Of Economics

This paper considers a dynamic environment with interdependent valuations and evolving private information. Under the assumption of “independent types”, we construct an efficient, incentive-compatible mechanism that is also budget-balanced in every period of the game. Our mechanism works in environments where in each period, each agent observes her own realized outcome-decision payoff from the previous period. This extends the insight of Mezzetti (2004) to the dynamic setting.

Implementation With Transfers, Yi-Chun Chen, Takashi Kunimoto, Yifei Sun

Research Collection School Of Economics

We say that a social choice rule is implementable with (small) transfers if one candesign a mechanism whose set of equilibrium outcomes coincides with that speciÖed bythe rule but the mechanism allows for (small) ex post transfers among the players. Weshow in private-value environments that any incentive compatible rule is implementablewith small transfers. We obtain this permissive implementation result by proposinga natural extension of Abreu and Matsushima (1994) to incomplete information environments.Furthermore, in order to showcase the applicability of our results, we relatethem to the recent developments in implementation theory. Next we revisit the conjectureby Abreu and Matsushima (1994), who …

Robust Virtual Implementation With Almost Complete Information, Takashi Kunimoto

Research Collection School Of Economics

Artemov, Kunimoto, and Serrano (2013a,b, henceforth, AKS) study amechanism design problem where arbitrary restrictions are placed on the setof first-order beliefs of agents. Calling these restrictions Δ, they adopt Δ-rationalizability (Battigalli and Siniscalchi (2003)) and show that Δ-incentivecompatibility and Δ-measurability are necessary and sufficient conditions forrobust virtual implementation. By appropriately defining Δ in order to restrictattention to complete information environments, I exploit the implicationsof AKS and show that the permissive implementation result of Abreu andMatsushima (1992a) is robust to how the underlying type space is specified.However, AKS need to fix a complete information environment throughouttheir analysis and therefore does not …

Robust Virtual Implementation: Toward A Reinterpretation Of The Wilson Doctrine, Georgy Artemov, Takashi Kunimoto, Roberto Serrano

Research Collection School Of Economics

We study a mechanism design problem where arbitrary restrictions are placed on the sets of first-order beliefs of agents. Calling these restrictions Δ, we use Δ-rationalizability (Battigalli and Siniscalchi, 2003, [5]) as our solution concept, and require that a mechanism virtually implement a socially desirable outcome. We obtain two necessary conditions, Δ-incentive compatibility and Δ-measurability and show that the latter is satisfied as long as a particular zero-measure set of first-order beliefs is ruled out. In environments allowing small transfers of utility among agents, these two conditions are also sufficient.

A New Necessary Condition For Implementation In Iteratively Undominated Strategies, Takashi Kunimoto, Roberto Serrano

Research Collection School Of Economics

We uncover a new necessary condition for implementation in iteratively undominated strategies by mechanisms that satisfy the “best element property” where for each agent, there exists a strategy profile that gives him the highest payoff in the mechanism. This class includes finite and regular mechanisms. We conclude that either the quasilinearity-like assumptions of available sufficiency results cannot be completely dispensed with or some mechanisms that do not satisfy the best element property must be employed. We term the condition “restricted deception-proofness.” It requires that, in environments with identical preferences, the social choice function be immune to all deceptions, making it …

Indescribability And Its Irrelevance For Contractual Incompleteness, Takashi Kunimoto

Research Collection School Of Economics

The incomplete contracts literature often cites indescribable contingencies as a major obstacle to the creation of completecontracts. Using agents’ minimum foresight concerning possible future payoffs, Maskin and Tirole (Rev Econ Stud 66:83–114, 1999) show that indescribability does not matter for contractual incompletenessas long as there is symmetric information at both the contracting stage and the trading stage. This is called the irrelevance theorem. The following generalization of the irrelevance theorem is shown here: indescribability does not matter even in the presenceof asymmetric information at the trading stage, as long as there is symmetric information at the contracting stage. This isan …

Indescribability And Asymmetric Information At The Contracting Stage, Takashi Kunimoto

Research Collection School Of Economics

Maskin and Tirole [Maskin, E., Tirole, J., 1999. Unforeseen contingencies and incomplete contracts. Review of Economic Studies, 66, 83–114] show that indescribability does not matter for contractual incompleteness when there is symmetric information both at the contracting stage and at the trading stage. Following their setup, I show that with asymmetric information at both stages, indescribability can matter.