Abstract
Mechanism design arises in environments where a set of strategic agents should achieve a common goal, but this goal may be affected by the selfish behavior of the agents. A popular tool to mitigate this impact is incentive compatibility, the design of mechanisms in such a way that strategic agents are motivated to act honestly. Many times this can be done using payments: monetary transactions can be implemented by the mechanism, which provide the agents with the right incentives to reveal their true colors. However, there are cases where such payments are not applicable for various reasons, moral, legal, or practical. In this thesis, we focus on problems where payments are prohibited, and we propose incentive compatible solutions, respecting this constraint. We concentrate on two main problems: the problem of impartial selection and the problem of truthful budget aggregation. In both problems, strategic agents need to come up with a joint decision, but their selfish behavior may lead t ...
Mechanism design arises in environments where a set of strategic agents should achieve a common goal, but this goal may be affected by the selfish behavior of the agents. A popular tool to mitigate this impact is incentive compatibility, the design of mechanisms in such a way that strategic agents are motivated to act honestly. Many times this can be done using payments: monetary transactions can be implemented by the mechanism, which provide the agents with the right incentives to reveal their true colors. However, there are cases where such payments are not applicable for various reasons, moral, legal, or practical. In this thesis, we focus on problems where payments are prohibited, and we propose incentive compatible solutions, respecting this constraint. We concentrate on two main problems: the problem of impartial selection and the problem of truthful budget aggregation. In both problems, strategic agents need to come up with a joint decision, but their selfish behavior may lead them to highly sub-optimal solutions. Our goal is to design mechanisms providing the agents with proper incentives to act sincerely. Unfortunately, we are only able to achieve this by sacrificing the quality of the solution, in the sense that the solutions we get are not as good as the solutions we could get in an environment where the agents would not be strategic. Therefore, we compare our mechanisms with ideal, non-strategic outcomes, providing worst-case approximation guarantees. The first problem we confront, impartial selection, involves the selection of an influential member of a community of individuals. This community can be described by a directed graph, where the nodes represent the individuals and the directed edges represent nominations. The task is given this graph to select the node with the highest number of nominations. However, the community members are selfish agents; hence, their reported nominations are not trusted, and this seemingly trivial task is now challenging. Impartiality, a property requiring no single node to influence her selection probability, provides proper incentives to the agents to act honestly. Recent progress in the literature has identified impartial selection rules with optimal approximation ratios, i.e., the ratio between the maximum in-degree and the in-degree of the selected node. However, it was noted that worst-case instances are graphs with small in-degrees. Motivated by this fact, we deviate from the trend and propose the study of additive approximation: the difference between the highest number of nominations and the number of nominations of the selected member, as an alternative measure of the quality of impartial selection mechanisms. The first part of this thesis is concerned with the design of impartial selection mechanisms with small additive approximation guarantees. On the positive side, we were able to design two randomized impartial selection mechanisms with sub-linear, on the community size, additive approximation guarantees for two well-studied models in the literature. We complement our positive results by providing negative results for various cases. We continue our investigation of the impartial selection problem from another direction. Getting our inspiration from the design of auction and posted pricing mechanisms with good approximation guarantees for welfare and profit maximization, we follow up our work with an enhanced model, where we study the extent to which prior information on voters' preferences could be helpful in the design of efficient deterministic impartial selection mechanisms with good additive approximation guarantees. First, we define a hierarchy of three models of prior information, which we call the opinion poll, the a priori popularity, and the uniform models. Then, we analyze the performance of a natural mechanism that we call Approval Voting with Default and show that it achieves a sub-linear additive guarantee for opinion poll and a polylogarithmic for a priori popularity inputs. We consider the polylogarithmic bound as the leading technical contribution of this part. Finally, we complement this last result by showing that our analysis is close to tight. We then turn our attention to the truthful budget aggregation problem. In this problem, strategic voters wish to split a divisible budget among different projects by aggregating their proposals into a single budget division. Unfortunately, it is well-known that the straightforward rule that divides the budget proportionally is susceptible to manipulation. While sophisticated incentive compatible mechanisms have been proposed in the literature, their outcomes are often far from fair. To capture this loss of fairness imposed by the need for truthfulness, we propose a quantitative framework that evaluates a budget aggregation mechanism according to its worst-case distance from the proportional allocation. We study this measure in the recently proposed class of incentive compatible mechanisms, called the moving phantom}mechanisms, and we provide approximation guarantees. For two projects, we show that the well-known Uniform Phantom mechanism is optimal among all truthful mechanisms. For three projects, we propose the proportional, Piecewise Uniform mechanism that is optimal among all moving phantom mechanisms. Finally, we provide impossibility results regarding the approximability of moving phantom mechanisms, and budget aggregation mechanisms, in general.
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