Robust Implementation in General Mechanisms

A social choice function is robustly implemented if every equilibrium on every type space achieves outcomes consistent with it. We identify a robust monotonicity condition that is necessary and (with mild extra assumptions) sufficient for robust implementation. Robust monotonicity is strictly stronger than both Maskin monotonicity (necessary and almost sufficient for complete information implementation) and ex post monotonicity (necessary and almost sufficient for ex post implementation). It is equivalent to Bayesian monotonicity on all type spaces.Mechanism design, Implementation, Robustness, Common knowledge, Interim equilibrium, Dominant strategies

Robust Implementation in General Mechanisms

A social choice function is robustly implemented if every equilibrium on every type space achieves outcomes consistent with it. We identify a robust monotonicity condition that is necessary and (with mild extra assumptions) sufficient for robust implementation. Robust monotonicity is strictly stronger than both Maskin monotonicity (necessary and almost sufficient for complete information implementation) and ex post monotonicity (necessary and almost sufficient for ex post implementation). It is equivalent to Bayesian monotonicity on all type spaces.Mechanism design, Implementation, Robustness, Common knowledge, Interim equilibrium, Dominant strategies

Supermodular mechanism design

This paper introduces a mechanism design approach that allows dealing with the multiple equilibrium problem, using mechanisms that are robust to bounded rationality. This approach is a tool for constructing supermodular mechanisms, i.e. mechanisms that induce games with strategic complementarities. In quasilinear environments, I prove that if a social choice function can be implemented by a mechanism that generates bounded strategic substitutes - as opposed to strategic complementarities - then this mechanism can be converted into a supermodular mechanism that implements the social choice function. If the social choice function also satisfies some efficiency criterion, then it admits a supermodular mechanism that balances the budget. Building on these results, I address the multiple equilibrium problem. I provide sufficient conditions for a social choice function to be implementable with a supermodular mechanism whose equilibria are contained in the smallest interval among all supermodular mechanisms. This is followed by conditions for supermodular implementability in unique equilibrium. Finally, I provide a revelation principle for supermodular implementation in environments with general preferences.Implementation, mechanisms, learning, strategic complementarities, supermodular games

Marginal Abatement Cost Curves in General Equilibrium: The Influence of World Energy Prices

Marginal abatement cost curves (MACCs) are one of the favorite instruments to analyze the impacts of the implementation of the Kyoto Protocol and emissions trading. As shown in this paper one important factor that influences MACCs are energy prices. This leads to the question of how to define MACCs in a general equilibrium context where the overall abatement level world wide influences energy prices and thus national MACCs. We first discuss the mechanisms theoretically and then use the CGE model DART to quantify the effects. The result is, that changes in energy prices resulting from different world wide abatement levels do indeed affect the national MACCs. Also, we compare different possibilities of defining MACCs - of which some turn out to be robust against changes in energy prices while others vary considerably.Climate change, Marginal abatement cost, Energy price, Computable general equilibrium model

Continuous Implementation

It is well-known that mechanism design literature makes many simplifying infor- mational assumptions in particular in terms of common knowledge of the environment among players. In this paper, we introduce a notion of continuous implementation and characterize when a social choice function is continuously implementable. More specif- ically, we say that a social choice function is continuously (partially) implementable if it is (partially) implementable for types in the model under study and it continues to be (partially) implementable for types "close" to this initial model. We ?rst show that if the model is of complete information a social choice function is continuously (partially) implementable only if it satis?es Maskin?s monotonicity. We then extend this result to general incomplete information settings and show that a social choice function is continuously (partially) implementable only if it is fully implementable in iterative dominance. For ?nite mechanisms, this condition is also su¢ cient. We also discuss implications of this characterization for the virtual implementation approach.High order beliefs, robust implementation

The Power of Simple Menus in Robust Selling Mechanisms

We study a robust selling problem where a seller attempts to sell one item to a buyer but is uncertain about the buyer's valuation distribution. Existing literature indicates that robust mechanism design provides a stronger theoretical guarantee than robust deterministic pricing. Meanwhile, the superior performance of robust mechanism design comes at the expense of implementation complexity given that the seller offers a menu with an infinite number of options, each coupled with a lottery and a payment for the buyer's selection. In view of this, the primary focus of our research is to find simple selling mechanisms that can effectively hedge against market ambiguity. We show that a selling mechanism with a small menu size (or limited randomization across a finite number of prices) is already capable of deriving significant benefits achieved by the optimal robust mechanism with infinite options. In particular, we develop a general framework to study the robust selling mechanism problem where the seller only offers a finite number of options in the menu. Then we propose a tractable reformulation that addresses a variety of ambiguity sets of the buyer's valuation distribution. Our formulation further enables us to characterize the optimal selling mechanisms and the corresponding competitive ratio for different menu sizes and various ambiguity sets, including support, mean, and quantile information. In light of the closed-form competitive ratios associated with different menu sizes, we provide managerial implications that incorporating a modest menu size already yields a competitive ratio comparable to the optimal robust mechanism with infinite options, which establishes a favorable trade-off between theoretical performance and implementation simplicity. Remarkably, a menu size of merely two can significantly enhance the competitive ratio, compared to the deterministic pricing scheme