Taiki Todo

Characterization of Strategy-Proof, Revenue Monotone Combinatorial Auction Mechanisms and Connection with False-Name-Proofness

A combinatorial auction mechanism consists of an allocation rule and a payment rule. There have been several studies on characterizing strategy-proof allocation rules. In particular, conditions called weak-monotonicity has been identified as a full characterization of them. On the other hand, revenue monotonicity is recognized as one of the desirable properties. A combinatorial auction mechanism is revenue monotone if a sellers revenue is guaranteed to weakly increase as the number of bidders grows. Though the property is quite reasonable, there exists virtually no work on the characterization. In this paper, we identified a simple condition called summation-monotonicity. We then proved that we can construct a strategy-proof, revenue monotone mechanism if and only if the allocation rule satisfies weak-monotonicity and summation-monotonicity. To the best of our knowledge, this is the first attempt to characterize revenue monotone allocation rules. In addition, we shed light on a connection between revenue monotonicity and false-name-proofness. In fact, we proved that, assuming a natural condition, revenue monotonicity is equivalent to false-name-proofness for single-item auctions.

Characteristics of sustainable OSS projects: a theoretical and empirical study

How can we attract developers? What can we do to incentivize developers to write code? We started the study by introducing the population pyramid visualization to software development communities, called software population pyramids, and found a typical pattern in shapes. This pattern comes from the differences in attracting coding contributors and discussion contributors. To understand the causes of the differences, we then build game-theoretical models of the contribution situation. Based on these results, we again analyzed the projects empirically to support the outcome of the models, and found empirical evidence. The answers to the initial questions are clear. To incentivize developers to code, the projects should prepare documents, or the projects or third parties should hire developers, and these are what sustainable projects in Git Hub did in reality. In addition, making innovations to reduce the writing costs can also have an impact in attracting coding contributors.

Strategy-Proof Cake Cutting Mechanisms for All-or-Nothing Utility

The cake cutting problem must fairly allocate a divisible good among agents who have varying preferences over it. Recently, designing strategy-proof cake cutting mechanisms has caught considerable attention from AI and MAS researchers. Previous works assumed that an agent’s utility function is additive so that theoretical analysis becomes tractable. However, in practice, agents have non-additive utility functions over a resource. In this paper, we consider the all-or-nothing utility function as a representative example of non-additive utility because it can widely cover agents’ preferences for real-world resources, such as the usage of meeting rooms, time slots for computational resources, bandwidth usage, and so on. We first show the incompatibility between envy-freeness and Pareto efficiency when each agent has all-or-nothing utility. We next propose two strategy-proofmechanisms that satisfy Pareto efficiency, which are based on a serial dictatorship mechanism, at the sacrifice of envy-freeness. To address computational feasibility, we propose an approximation algorithm to find a near-optimal allocation in time polynomial in the number of agents, since the problem of finding a Pareto efficient allocation is NP-hard. As another approach that abandon Pareto efficiency, we develop anenvy-free mechanism and show that one of our serial dictatorship based mechanisms satisfies proportionality in expectation, which is a weaker definition of proportionality. Finally, we evaluate the efficiency obtained by our proposed mechanisms by computational experiments.

Generalizing envy-freeness toward group of agents

Envy-freeness is a well-known fairness concept for analyzing mechanisms. Its traditional definition requires that no individual envies another individual. However, an individual (or a group of agents) may envy another group, even if she (or they) does not envy another individual. In mechanisms with monetary transfer, such as combinatorial auctions, considering such fairness requirements, which are refinements of traditional envy-freeness, is meaningful and brings up a new interesting research direction in mechanism design. In this paper, we introduce two new concepts of fairness called envy-freeness of an individual toward a group, and envy-freeness of a group toward a group. They are natural extensions of traditional envy-freeness. We discuss combinatorial auction mechanisms that satisfy these concepts. First, we characterize such mechanisms by focusing on their allocation rules. Then we clarify the connections between these concepts and three other properties: the core, strategy-proofness, and false-name-proofness.

False-name-proofness in facility location problem on the real line

Recently, mechanism design without monetary transfers is attracting much attention, since in many application domains on Internet, introducing monetary transfers is impossible or undesirable. Mechanism design studies how to design mechanisms that result in good outcomes even when agents strategically report their preferences. However, in highly anonymous settings such as the Internet, declaring preferences dishonestly is not the only way to manipulate the mechanism. Often, it is possible for an agent to pretend to be multiple agents, and submit multiple reports using different identifiers, e.g., different e-mail addresses. Such false-name manipulations are more likely to occur in a mechanism without monetary transfers, since submitting multiple reports would be less risky in such a mechanism. In this paper, we formalize false-name manipulations in facility location problems on the real line and discuss the effect of such manipulations.

Service Exchange Problem

In this paper, we study the service exchange problem where each agent is willing to provide her service in order to receive in exchange the service of someone else. We assume that agent’s preference depends both on the service that she receives and the person who receives her service. This framework is an extension of the housing market problem to preferences including a degree of externalities. We investigate the complexity of computing an individually rational and Pareto efficient allocation of services to agents for ordinal preferences, and the complexity of computing an allocation which maximizes either the utility sum or the utility of the least served agent for cardinal preferences.

Strategy-proof Cake Cutting Mechanisms for All-or-nothing Utility

The cake cutting problem must fairly allocate a divisible good among agents who have varying preferences over it. Recently, designing strategy-proof cake cutting mechanisms has caught considerable attention from AI and MAS researchers. Previous works assumed that an agent’s utility function is additive so that theoretical analysis becomes tractable. However, in practice, agents have non-additive utility functions over a resource. In this paper, we consider the all-or-nothing utility function as a representative example of non-additive utility because it can widely cover agents’ preferences for real-world resources, such as the usage of meeting rooms, time slots for computational resources, bandwidth usage, and so on. We first show the incompatibility between envy-freeness and Pareto efficiency when each agent has all-or-nothing utility. We next propose two strategy-proofmechanisms that satisfy Pareto efficiency, which are based on a serial dictatorship mechanism, at the sacrifice of envy-freeness. To address computational feasibility, we propose an approximation algorithm to find a near-optimal allocation in time polynomial in the number of agents, since the problem of finding a Pareto efficient allocation is NP-hard. As another approach that abandon Pareto efficiency, we develop anenvy-free mechanism and show that one of our serial dictatorship based mechanisms satisfies proportionality in expectation, which is a weaker definition of proportionality. Finally, we evaluate the efficiency obtained by our proposed mechanisms by computational experiments.

Rename and False-Name Manipulations in Discrete Facility Location with Optional Preferences

We consider the problem of locating facilities on a discrete acyclic graph, where agents’ locations are publicly known and the agents are requested to report their demands, i.e., which facilities they want to access. In this paper, we study the effect of manipulations by agents that utilize vacant vertices. Such manipulations are called rename or false-name manipulations in game theory and mechanism design literature. For locating one facility on a path, we carefully compare our model with traditional ones and clarify their differences by pointing out that some existing results in the traditional model do not carry over to our model. For locating two facilities, we analyze the existing and new mechanisms from a perspective of approximation ratio and provide non-trivial lower bounds. Finally, we introduce a new mechanism design model where richer information is available to the mechanism designer and show that under the new model false-name-proofness does not always imply population monotonicity.

Individually Rational Strategy-Proof Social Choice with Exogenous Indifference Sets

We consider a social choice problem where individual rationality is required. The status quo belongs to the outcome space, and the selected alternative must be weakly better than the status quo for everybody. If the mechanism designer has no knowledge of the alternatives, we obtain a negative result: any individually rational (IR) and strategy-proof (SP) mechanism can choose at most one alternative (besides the status quo), regardless of the preferences. To overcome this negative result, we consider a domain where the alternatives have a known structure, i.e., an agent is indifferent between the status quo and a subset of the outcomes. This set is exogenously given and public information. This assumption is natural if the social choice involves the participation of agents. For example, consider a group of people organizing a trip where participation is voluntary. We can assume each agent is indifferent between the trip plans in which she does not participate and the status quo (i.e., no trip). In this setting, we obtain more positive results: we develop a class of mechanisms called Approve and Choose mechanisms, which are IR and SP, and can choose multiple alternatives as well as the status quo.

False-name-proof combinatorial auction design via single-minded decomposition

This paper proposes a new approach to building false-name-proof (FNP) combinatorial auctions from those that are FNP only with single-minded bidders, each of whom requires only one particular bundle. Under this approach, a general bidder is decomposed into a set of single-minded bidders, and after the decomposition the price and the allocation are determined by the FNP auctions for single-minded bidders. We first show that the auctions we get with the single-minded decomposition are FNP if those for single-minded bidders satisfy a condition called PIA. We then show that another condition, weaker than PIA, is necessary for the decomposition to build FNP auctions. To close the gap between the two conditions, we have found another sufficient condition weaker than PIA for the decomposition to produce strategy-proof mechanisms. Furthermore, we demonstrate that once we have PIA, the mechanisms created by the decomposition actually satisfy a stronger version of false-name-proofness, called false-name-proofness with withdrawal.