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Robust Mechanism Design and Robust Prediction in Games

Periodic Reporting for period 4 - ROBUST (Robust Mechanism Design and Robust Prediction in Games)

Reporting period: 2021-06-01 to 2022-08-31

The main objectives of the projects are two-fold: (i) to develop new theoretical methodology of robust mechanism design and apply it to various economic problems; and (ii) to study robust predictions in game theory and assess its economic significance. Conceptually, the robustness in these projects are achieved by imposing much less assumptions on the behaviors of economic agents in predicting their behaviors. This is an important direction of the economics researches, since the analyses under ``too strong'' assumptions have been criticized for long time. It would provide more sensible and relevant analyses of economic problems both in economic theory and application, whereby contributing to the society.
Along the line of research proposed in the original proposal, I have developed necessary analytical tools and apply those tools in some applications. The conclusion of the action is three-fold: First, in certain environments, robustness concerns in mechanism design necessitates the use of ``classical’’ robust concepts such as dominant-strategy incentive compatibility, though not always. In particular, with common/interdependent-values, alternative notions of robustness would be necessary. Also, other kinds of robustness (than informational robustness) would be relevant depending on the applications. Second, if the designer can actively control certain aspect of the agents’ information, that could benefit the principal significantly, and the form of optimal information design can be analyzed with the developed tools. Third, robust predictions in general game settings can be analyzed with the developed tools. Interestingly, it seems to have a close connection with the robust mechanism design problem in terms of the methodology (this last observation is briefly discussed in one of the papers with Shintaro Miura, ``Robust prediction in games with uncertain parameters’’, and its further investigation is left for future research).
As explained above, along the line of research proposed in the original proposal, I have developed necessary analytical tools and apply those tools in some applications. Regarding the projects related to information in mechanism design, I have approached the problems from two perspectives. One concerns informational robustness in the sense that the principal has little idea about the agents’ information in designing a mechanism. For example, in ``On the foundations of ex post incentive compatible mechanisms'' with Zhu, I consider the situation where the principal’s information about the agent’s estimate about relevant future events is limited, and yet desires to write a contract contingent on those future events. The key is how to extract the agent’s private information about those events. This is an instance of interdependent-value settings, and as described above, the main result shows that ex post incentive compatible mechanisms can be strictly improved under mild assumptions. In ``Auction Design with Approximate Common Prior'' with Pham, we show that dominant-strategy auction mechanisms are optimal in private-value auction environments, even if both the seller and buyers have almost common knowledge about the value prior. These findings are in line with the general conjecture that the nature of uncertainty (whether it is private-value environments or common-/interdependent-value environments) is crucial in determining whether the classical notion of robustness would have appropriate worst-case-based foundations or not.

The other perspective concerns the design of information in principal-agent relationships. Related to the recent trend of research in Bayesian persuasion / information design, I have developed this line of research signigicantly. For example, ``Optimal Persuasion via Bi-Pooling'' with Arieli, Babichenko, and Smorodinsky develop novel theoretical tools in complex (in the sense of a continuum state space and action space) Bayesian persuasion environments; and ``Information Design in Concave Games'' with Smolin develop the duality-based machinery for information design in game environments. In terms of applications, ``Optimal public information disclosure by mechanism designer'' and ``Type-contingent information disclosure'' with Zhu consider seller-buyer trading, ``A Mediator Approach to Mechanism Design with Limited Commitment'' with Lomys study dynamic mechanism design with limited commitment, and ``On the Veil-of-Ignorance Principle: Welfare-Optimal Information Disclosure in Voting'' with Van der Straeten apply some of these techniques in voting environments.

Regarding the robust prediction, ``Robust prediction in games with uncertain parameters'' with Miura develop the notion of robust equilibrium prediction without a common prior. Different from the existing studies which usually concern both robustness with respect to information and with respect to equilibrium selection, we focus on robustness with respect to information only. This adds flexibility in the obtained prediction, and is more suitable in certain applications such as robust mechanism design, where one is often interested in partial (or the ``best equilibrium’’) implementation. In ``Order on types based on monotone comparative statics'' with Kunimoto, we develop the notion of robust comparative statics with respect to the players’ information, and show that the ``higher-order’’ stochastic ordering (which we call common certainty of optimism) captures the appropriate idea of robust comparative statics in the class of supermodular games.