We study the design of mechanisms under asymmetric awareness and information. While the mechanism designer cannot necessarily commit to a particular social choice function in the face of unawareness, she can at least commit to properties of social choice functions such as efficiency given ex post awareness. Assuming quasi-linear utilities and private values, we show that we can implement in conditional dominant strategies a social choice function that is utilitarian ex post efficient under pooled awareness without the need of the social planner being fully aware ex ante. To this end, we develop novel dynamic versions of Vickrey-Clarke-Groves mechanisms in which true types are revealed and subsequently elaborated at endogenous higher awareness levels. We explore how asymmetric awareness affects budget balance and participation constraints. We show that ex ante unforeseen contingencies are no excuse for deficits. Finally, we propose a dynamic elaboration reverse second price auction for efficient procurement of complex incompletely specified projects with budget balance and participation constraints.

Additional Feedback: 49, 59, 74 – The discussion here talks a bit loosely about certifying the strategyproofness of auctions. However, this is not quite what gets certified, and this is an important caveat that should be made more explicit. In particular, what gets certified is the amount by which agents can manipulate on particular type profiles. This makes no guarantees about the incentives on any other type profile, so it is a bit misleading to describe the approach as certifying the extent of strategyproofness full stop. The abstract (11) is more careful and explicit about this. Based on the description of the 3 trained networks (225-230), none of them seem to use it.

We study worst-case VCG redistribution mechanism design for the public project problem. We use a multilayer perceptron (MLP) with ReLU activation to model the payment function and use mixed integer programming (MIP) to solve for the worst-case type profiles that maximally violate the mechanism design constraints. We collect these worst-case type profiles and use them as training samples to train toward better worst-case mechanisms. In practice, we require a tiny network structure for the above approach to scale. The Lottery Ticket Hypothesis states that a large network is likely to contain a "winning ticket" -- a much smaller subnetwork that "won the initialization lottery", which makes its training particularly effective. Motivated by this hypothesis, we train a large network and prune it into a tiny subnetwork. We run MIP-based worst-case training on the drawn subnetwork and evaluate the resulting mechanism's worst-case performance. If the subnetwork does not achieve good worst-case performance, then we record the type profiles that cause the current draw to be bad. To draw again, we restore the large network to its initial weights and prune using recorded type profiles from earlier draws, therefore avoiding drawing the same ticket twice. We expect to eventually encounter a tiny subnetwork that leads to effective training for our worst-case mechanism design task. Lastly, a by-product of multiple ticket draws is an ensemble of mechanisms with different worst cases, which improves the worst-case performance further. Using our approach, we find previously unknown optimal mechanisms for up to 5 agents. Our results confirm the tightness of existing theoretical upper bounds. For up to 20 agents, we derive significantly improved worst-case mechanisms, surpassing a long list of existing manual results.

Bayesian persuasion studies how an informed sender should partially disclose information to influence the behavior of a self-interested receiver. Classical models make the stringent assumption that the sender knows the receiver's utility. This can be relaxed by considering an online learning framework in which the sender repeatedly faces a receiver of an unknown, adversarially selected type. We study, for the first time, an online Bayesian persuasion setting with multiple receivers. We focus on the case with no externalities and binary actions, as customary in offline models. Our goal is to design no-regret algorithms for the sender with polynomial per-iteration running time. First, we prove a negative result: for any $0 < \alpha \leq 1$, there is no polynomial-time no-$\alpha$-regret algorithm when the sender's utility function is supermodular or anonymous. Then, we focus on the case of submodular sender's utility functions and we show that, in this case, it is possible to design a polynomial-time no-$(1 - \frac{1}{e})$-regret algorithm. To do so, we introduce a general online gradient descent scheme to handle online learning problems with a finite number of possible loss functions. This requires the existence of an approximate projection oracle. We show that, in our setting, there exists one such projection oracle which can be implemented in polynomial time.

Obvious strategyproofness (OSP) is an appealing concept as it allows to maintain incentive compatibility even in the presence of agents that are not fully rational, e.g., those who struggle with contingent reasoning (Li 2015). However, it has been shown to impose some limitations, e.g., no OSP mechanism can return a stable matching (Ashlagi and Gonczarowski 2015). We here deepen the study of the limitations of OSP mechanisms by looking at their approximation guarantees for basic optimization problems paradigmatic of the area, i.e., machine scheduling and facility location. We prove a number of bounds on the approximation guarantee of OSP mechanisms, which show that OSP can come at a significant cost. However, rather surprisingly, we prove that OSP mechanisms can return optimal solutions when they use monitoring — a novel mechanism design paradigm that introduces a mild level of scrutiny on agents’ declarations (Kovacs, Meyer, and Ventre 2015).

The family of Groves mechanisms, which includes the well-known VCG mechanism (also known as the Clarke mechanism), is a family of efficient and strategy-proof mechanisms. Unfortunately, the Groves mechanisms are generally not budget balanced. That is, under such mechanisms, payments may flow into or out of the system of the agents, resulting in deficits or reduced utilities for the agents. We consider the following problem: within the family of Groves mechanisms, we want to identify mechanisms that give the agents the highest utilities, under the constraint that these mechanisms must never incur deficits. We adopt a prior-free approach. We introduce two general measures for comparing mechanisms in prior-free settings. We say that a non-deficit Groves mechanism M individually dominates another non-deficit Groves mechanism M' if for every type profile, every agent's utility under M is no less than that under M', and this holds with strict inequality for at least one type profile and one agent. We say that a non-deficit Groves mechanism M collectively dominates another non-deficit Groves mechanism M' if for every type profile, the agents' total utility under M is no less than that under M', and this holds with strict inequality for at least one type profile. The above definitions induce two partial orders on non-deficit Groves mechanisms. We study the maximal elements corresponding to these two partial orders, which we call the individually undominated mechanisms and the collectively undominated mechanisms, respectively.

The assignment of tasks to multiple resources becomes an interesting game theoretic problem, when both the task owner and the resources are strategic. In the classical, nonstrategic setting, where the states of the tasks and resources are observable by the controller, this problem is that of finding an optimal policy for a Markov decision process (MDP). When the states are held by strategic agents, the problem of an efficient task allocation extends beyond that of solving an MDP and becomes that of designing a mechanism. Motivated by this fact, we propose a general mechanism which decides on an allocation rule for the tasks and resources and a payment rule to incentivize agents' participation and truthful reports. In contrast to related dynamic strategic control problems studied in recent literature, the problem studied here has interdependent values: the benefit of an allocation to the task owner is not simply a function of the characteristics of the task itself and the allocation, but also of the state of the resources. We introduce a dynamic extension of Mezzetti's two phase mechanism for interdependent valuations. In this changed setting, the proposed dynamic mechanism is efficient, within period ex-post incentive compatible, and within period ex-post individually rational.

There are p heterogeneous objects to be assigned to n competing agents (n > p) each with unit demand. It is required to design a Groves mechanism for this assignment problem satisfying weak budget balance, individual rationality, and minimizing the budget imbalance. This calls for designing an appropriate rebate function. When the objects are identical, this problem has been solved which we refer as WCO mechanism. We measure the performance of such mechanisms by the redistribution index. We first prove an impossibility theorem which rules out linear rebate functions with non-zero redistribution index in heterogeneous object assignment. Motivated by this theorem, we explore two approaches to get around this impossibility. In the first approach, we show that linear rebate functions with non-zero redistribution index are possible when the valuations for the objects have a certain type of relationship and we design a mechanism with linear rebate function that is worst case optimal. In the second approach, we show that rebate functions with non-zero efficiency are possible if linearity is relaxed. We extend the rebate functions of the WCO mechanism to heterogeneous objects assignment and conjecture them to be worst case optimal.