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Register a new userMechanisms for Fair Allocation Problems: No-Punishment Payment Rules in Fully Verifiable Settings
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Added by
Francesco Scarcello
Publication date
2012
fields
Informatics Engineering
and research's language is
English
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Mechanism design is addressed in the context of fair allocations of indivisible goods with monetary compensation. Motivated by a real-world social choice problem, mechanisms with verification are considered in a setting where (i) agents declarations on allocated goods can be fully verified before payments are performed, and where (ii) verification is not used to punish agents whose declarations resulted in incorrect ones. Within this setting, a mechanism is designed that is shown to be truthful, efficient, and budget-balanced, and where agents utilities are fairly determined by the Shapley value of suitable coalitional games. The proposed mechanism is however shown to be #P-complete. Thus, to deal with applications with many agents involved, two polynomial-time randomized variants are also proposed: one that is still truthful and efficient, and which is approximately budget-balanced with high probability, and another one that is truthful in expectation, while still budget-balanced and efficient.
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We introduce the problem of assigning resources to improve their utilization. The motivation comes from settings where agents have uncertainty about their own values for using a resource, and where it is in the interest of a group that resources be used and not wasted. Done in the right way, improved utilization maximizes social welfare--- balancing the utility of a high value but unreliable agent with the groups preference that resources be used. We introduce the family of contingent payment mechanisms (CP), which may charge an agent contingent on use (a penalty). A CP mechanism is parameterized by a maximum penalty, and has a dominant-strategy equilibrium. Under a set of axiomatic properties, we establish welfare-optimality for the special case CP(W), with CP instantiated for a maximum penalty equal to societal value W for utilization. CP(W) is not dominated for expected welfare by any other mechanism, and second, amongst mechanisms that always allocate the resource and have a simple indirect structure, CP(W) strictly dominates every other mechanism. The special case with no upper bound on penalty, the contingent second-price mechanism, maximizes utilization. We extend the mechanisms to assign multiple, heterogeneous resources, and present a simulation study of the welfare properties of these mechanisms.
This paper considers the setting where a cloud server services a static set or a dynamic sequence of tasks submitted by multiple clients. Every client wishes to assure honest execution of tasks by additionally employing a trusted third party (TTP) to re-compute the tasks with a certain probability. The cloud server makes a deposit for each task it takes, each client allocates a budget (including the wage for the server and the cost for possibly hiring TTP) for each task submitted, and every party has its limited fund for either deposits or task budgets. We study how to allocate the funds optimally to achieve the three-fold goals: a rational cloud server honestly computes each task; the servers wage is maximized; the overall delay for task verification is minimized. We apply game theory to formulate the optimization problems, and develop the optimal or heuristic solutions for three application scenarios. For each of the solutions, we analyze it through either rigorous proofs or extensive simulations. To the best of our knowledge, this is the first work on optimizing fund allocation for verifiable outsourcing of computation in the setting of one server and multiple clients, based on game theory.
Settings such as lending and policing can be modeled by a centralized agent allocating a resource (loans or police officers) amongst several groups, in order to maximize some objective (loans given that are repaid or criminals that are apprehended). Often in such problems fairness is also a concern. A natural notion of fairness, based on general principles of equality of opportunity, asks that conditional on an individual being a candidate for the resource, the probability of actually receiving it is approximately independent of the individuals group. In lending this means that equally creditworthy individuals in different racial groups have roughly equal chances of receiving a loan. In policing it means that two individuals committing the same crime in different districts would have roughly equal chances of being arrested. We formalize this fairness notion for allocation problems and investigate its algorithmic consequences. Our main technical results include an efficient learning algorithm that converges to an optimal fair allocation even when the frequency of candidates (creditworthy individuals or criminals) in each group is unknown. The algorithm operates in a censored feedback model in which only the number of candidates who received the resource in a given allocation can be observed, rather than the true number of candidates. This models the fact that we do not learn the creditworthiness of individuals we do not give loans to nor learn about crimes committed if the police presence in a district is low. As an application of our framework, we consider the predictive policing problem. The learning algorithm is trained on arrest data gathered from its own deployments on previous days, resulting in a potential feedback loop that our algorithm provably overcomes. We empirically investigate the performance of our algorithm on the Philadelphia Crime Incidents dataset.
We consider the problem of allocating a set on indivisible items to players with private preferences in an efficient and fair way. We focus on valuations that have dichotomous marginals, in which the added value of any item to a set is either 0 or 1, and aim to design truthful allocation mechanisms (without money) that maximize welfare and are fair. For the case that players have submodular valuations with dichotomous marginals, we design such a deterministic truthful allocation mechanism. The allocation output by our mechanism is Lorenz dominating, and consequently satisfies many desired fairness properties, such as being envy-free up to any item (EFX), and maximizing the Nash Social Welfare (NSW). We then show that our mechanism with random priorities is envy-free ex-ante, while having all the above properties ex-post. Furthermore, we present several impossibility results precluding similar results for the larger class of XOS valuations. To gauge the robustness of our positive results, we also study $epsilon$-dichotomous valuations, in which the added value of any item to a set is either non-positive, or in the range $[1, 1 + epsilon]$. We show several impossibility results in this setting, and also a positive result: for players that have additive $epsilon$-dichotomous valuations with sufficiently small $epsilon$, we design a randomized truthful mechanism with strong ex-post guarantees. For $rho = frac{1}{1 + epsilon}$, the allocations that it produces generate at least a $rho$-fraction of the maximum welfare, and enjoy $rho$-approximations for various fairness properties, such as being envy-free up to one item (EF1), and giving each player at least her maximin share.
This paper combines two key ingredients for online algorithms - competitive analysis (e.g. the competitive ratio) and advice complexity (e.g. the number of advice bits needed to improve online decisions) - in the context of a simple online fair division model where items arrive one by one and are allocated to agents via some mechanism. We consider four such online mechanisms: the popular Ranking matching mechanism adapted from online bipartite matching and the Like, Balanced Like and Maximum Like allocation mechanisms firstly introduced for online fair division problems. Our first contribution is that we perform a competitive analysis of these mechanisms with respect to the expected size of the matching, the utilitarian welfare, and the egalitarian welfare. We also suppose that an oracle can give a number of advice bits to the mechanisms. Our second contribution is to give several impossibility results; e.g. no mechanism can achieve the egalitarian outcome of the optimal offline mechanism supposing they receive partial advice from the oracle. Our third contribution is that we quantify the competitive performance of these four mechanisms w.r.t. the number of oracle requests they can make. We thus present a most-competitive mechanism for each objective.
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