Revenue guarantees in auctions with a (correlated) common prior and additional information

This paper considers auction environments with a (possibly correlated) common prior over bidders' values, where each bidder may have additional information (e.g., through information acquisition). Under certain conditions, we characterize the optimal mechanisms in terms of the expected revenue that is guaranteed given whatever additional information is available to the bidders. Even if the values are correlated,we do not necessarily have full-surplus extraction, and moreover, the optimal mechanism resembles those in the independently distributed cases. Specifically, we show that (i) a second-price auction is optimal among all the efficient mechanisms, and (ii) it is rate-optimal among all the mechanisms

Strategic and structural uncertainties in robust implementation

This paper discusses some connections among several robustness concepts of mechanisms in terms of agents' behaviors. Specifically, under certain conditions such as private values and ``rich'' interdependent values, we show that implementation in (one-round or iterative) undominated strategies, a solution concept robust to strategic uncertainty, is equivalent to Bayesian implementation with arbitrary type spaces, a solution concept robust to structural uncertainty

Optimal Public Information Disclosure by Mechanism Designer

We consider a mechanism design environment where a principal can partially control agents' information before they play a mechanism (e.g., a seller disclosing quality information). Assuming that the principal can ex ante commit to his disclosure policy, this is a Bayesian persuasion problem with an endogenous payoff function as a consequence of optimal mechanism design. Wefirst show that, if the principal's and agents' information are independent or affiliated, and if the implementable set of (non-monetary) allocation rules is invariant to disclosure policies, then it is optimal for the principal to disclose all the relevant information. In case of negative correlation or in case the set of implementable allocation rules varies with disclosure policies, then full disclosure is not necessarily optimal. We then characterize the optimal (non-full) disclosure policy under additional assumptions, which, viewed as a Bayesian persuasion problem, provides a solution to a novel class of environments

Implementation in Weakly Undominated Strategies, with Applications to Auctions and Bilateral Trade

We study the mechanism-design problem of guaranteeing desirable performances whenever agents are rational in the sense of not playing weakly dominated strategies. We first provide an upper bound for the best performance we can guarantee among all feasible mechanisms. We then prove the bound to be tight under certain conditions in auction and bilateral-trade applications. In particular, we find that a second-price auction is optimal in revenue with interdependent values, which is neither dominant-strategy nor ex post incentive compatible, but satisfies the novel incentive compatibility introduced in this analysis

Strategic and structural uncertainties in robust implementation

This paper discusses some connections among several robustness concepts of mechanisms in terms of agents' behaviors. Specifically, under certain conditions such as private values and ``rich'' interdependent values, we show that implementation in (one-round or iterative) undominated strategies, a solution concept robust to strategic uncertainty, is equivalent to Bayesian implementation with arbitrary type spaces, a solution concept robust to structural uncertainty

Double auction with interdependent values: incentives and efficiency

We study a double auction environment where buyers and sellers have interdependent valuations and multi-unit demand and supply. We propose a new mechanism which satisfies ex post incentive compatibility, individual rationality, feasibility, non-wastefulness, and no budget deficit. Moreover, this mechanism is asymptotically efficient in that the trade outcome in the mechanism converges to the efficient level as in a competitive equilibrium as the numbers of the buyers and sellers become large. Our mechanism is the first double auction mechanism with these properties in the interdependent values setting

Asymmetric information allocation to avoid coordination failure

In the context of team production, this paper studies the optimal (deterministic and stochastic) information allocation that implements desired effort levels as the unique Bayesian equilibrium. We show that, under certain conditions, it is optimal to asymmetrically inform agents even though they may be ex ante symmetric. The main intuition is that informing the agents asymmetrically can be effective in avoiding "bad" equilibria, that is, equilibria with coordination failure

Divergent Interpretation and Divergent Prediction in Communication

We consider a cheap-talk game à la Crawford and Sobel (1982) with almost-common interest players. The sender's bias parameter is only approximately common knowledge. Compared to the standard case where the structure of the bias parameter is (exactly) common knowledge, communication between the players is subject to divergent interpretation of the sender's messages by the receiver, and divergent prediction of the receiver's reaction by the sender. We show that the complementary nature of these phenomena can result in significant welfare consequences even with a \small" (in a certain sense) departure from (exact) common knowledge

On the Foundations of Ex Post Incentive Compatible Mechanisms

In private-value auction environments, Chung and Ely (2007) establish maxmin and Bayesian foundations for dominant-strategy mechanisms. We first show that similar foundation results for ex post mechanisms hold true even with interdependent values if the interdependence is only cardinal. This includes, for example, the one-dimensional environments of Dasgupta and Maskin (2000) and Bergemann and Morris (2009b). Conversely, if the environment exhibits ordinal interdependence, which is typically the case with multi-dimensional environments (e.g., a player’s private information)