In this work we study the problem of {\em Stochastic Budgeted Multi-round Submodular Maximization} (SBMSm), in which we would like to adaptively maximize the sum over multiple rounds of the value of a monotone and submodular objective function defined on a subset of items, subject to the fact that the values of this function depend on the realization of stochastic events and the number of items that we can select over all rounds is limited by a given budget. This problem extends, and generalizes to multiple round settings, well-studied problems such as (adaptive) influence maximization and stochastic probing. We first show that, if the number of items and stochastic events is somehow bounded, there is a polynomial time dynamic programming algorithm for SBMSm. Then, we provide a simple greedy approximation algorithm for SBMSm, that first non-adaptively allocates the budget to be spent at each round, and then greedily and adaptively maximizes the objective function by using the budget assigned at each round. Such algorithm guarantees a $(1-1/e-\epsilon)$-approximation to the optimal adaptive value. Finally, by introducing a metric called {\em budget-adaptivity gap}, we measure how much an optimal policy for SBMSm, that is adaptive in both the budget allocation and item selection, is better than an optimal partially adaptive policy that, as in our greedy algorithm, determined the budget allocation in advance. We show a tight bound of $e/(e-1)$ on the budget-adaptivity gap, and this result implies that our greedy algorithm guarantees the best approximation among all partially adaptive policies.

A growing body of work in economics and computation focuses on the trade-off between implementability and simplicity in mechanism design. The goal is to develop a theory that not only allows to design an incentive structure easy to grasp for imperfectly rational agents, but also understand the ensuing limitations on the class of mechanisms that enforce it. In this context, the concept of OSP mechanisms has assumed a prominent role since they provably account for the absence of contingent reasoning skills, a specific cognitive limitation. For single-dimensional agents, it is known that OSP mechanisms need to use certain greedy algorithms. In this work, we introduce a notion that interpolates between OSP and SOSP, a more stringent notion where agents only plan a subset of their own future moves. We provide an algorithmic characterization of this novel class of mechanisms for single-dimensional domains and binary allocation problems, that precisely measures the interplay between simplicity and implementability. We build on this to show how mechanisms based on reverse greedy algorithms (a.k.a., deferred acceptance auctions) are algorithmically more robust to imperfectly rationality than those adopting greedy algorithms.

The design of algorithms or protocols that are able to align the goals of the planner with the selfish interests of the agents involved in these protocols is of paramount importance in almost every decentralized setting (such as, computer networks, markets, etc.) as shown by the rich literature in Mechanism Design. Recently, huge interest has been devoted to the design of mechanisms for imperfectly rational agents, i.e., mechanisms for which agents are able to easily grasp that there is no action different from following the protocol that would satisfy their interests better. This work has culminated in the definition of Obviously Strategyproof (OSP) Mechanisms, that have been shown to capture the incentives of agents without contingent reasoning skills. Without an understanding of the algorithmic nature of OSP mechanisms, it is hard to assess how well these mechanisms can satisfy the goals of the planner. For the case of binary allocation problems and agents whose private type is a single number, recent work has shown that a generalization of greedy completely characterizes OSP. In this work, we strengthen the connection between greedy and OSP by providing a characterization of OSP mechanisms for all optimization problems involving these single-parameter agents. Specifically, we prove that OSP mechanisms must essentially work as follows: they either greedily look for agents with ``better'' types and allocate them larger outcomes; or reverse greedily look for agents with ``worse'' types and allocate them smaller outcomes; or, finally, split the domain of agents in ``good'' and ``bad'' types, and subsequently proceed in a reverse greedy fashion for the former and greedily for the latter. We further demonstrate how to use this characterization to give bounds on the approximation guarantee of OSP mechanisms for the well known scheduling related machines problem.

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).

In this paper, we study protocols that allow to discern conscious and unconscious decisions of human beings; i.e., protocols that measure awareness. Consciousness is a central research theme in Neuroscience and AI, which remains, to date, an obscure phenomenon of human brains. Our starting point is a recent experiment, called Post Decision Wagering (PDW) (Persaud, McLeod, and Cowey 2007), that attempts to align experimenters' and subjects' objectives by leveraging financial incentives. We note a similarity with mechanism design, a research area which aims at the design of protocols that reconcile often divergent objectives through incentive-compatibility. We look at the issue of measuring awareness from this perspective. We abstract the setting underlying the PDW experiment and identify three factors that could make it ineffective: rationality, risk attitude and bias of subjects. Using mechanism design tools, we study the barrier between possibility and impossibility of incentive compatibility with respect to the aforementioned characteristics of subjects. We complete this study by showing how to use our mechanisms to potentially get a better understanding of consciousness.