Multiagent Maximum Coverage Problems: The Trade-off Between Anarchy and Stability

The price of anarchy and price of stability are three well-studied performance metrics that seek to characterize the inefficiency of equilibria in distributed systems. The distinction between these two performance metrics centers on the equilibria that they focus on: the price of anarchy characterizes the quality of the worst-performing equilibria, while the price of stability characterizes the quality of the best-performing equilibria. While much of the literature focuses on these metrics from an analysis perspective, in this work we consider these performance metrics from a design perspective. Specifically, we focus on the setting where a system operator is tasked with designing local utility functions to optimize these performance metrics in a class of games termed covering games. Our main result characterizes a fundamental trade-off between the price of anarchy and price of stability in the form of a fully explicit Pareto frontier. Within this setup, optimizing the price of anarchy comes directly at the expense of the price of stability (and vice versa). Our second results demonstrates how a system-operator could incorporate an additional piece of system-level information into the design of the agents' utility functions to breach these limitations and improve the system's performance. This valuable piece of system-level information pertains to the performance of worst performing agent in the system.Comment: 14 pages, 4 figure

Social Data Offloading in D2D-Enhanced Cellular Networks by Network Formation Games

Recently, cellular networks are severely overloaded by social-based services, such as YouTube, Facebook and Twitter, in which thousands of clients subscribe a common content provider (e.g., a popular singer) and download his/her content updates all the time. Offloading such traffic through complementary networks, such as a delay tolerant network formed by device-to-device (D2D) communications between mobile subscribers, is a promising solution to reduce the cellular burdens. In the existing solutions, mobile users are assumed to be volunteers who selfishlessly deliver the content to every other user in proximity while moving. However, practical users are selfish and they will evaluate their individual payoffs in the D2D sharing process, which may highly influence the network performance compared to the case of selfishless users. In this paper, we take user selfishness into consideration and propose a network formation game to capture the dynamic characteristics of selfish behaviors. In the proposed game, we provide the utility function of each user and specify the conditions under which the subscribers are guaranteed to converge to a stable network. Then, we propose a practical network formation algorithm in which the users can decide their D2D sharing strategies based on their historical records. Simulation results show that user selfishness can highly degrade the efficiency of data offloading, compared with ideal volunteer users. Also, the decrease caused by user selfishness can be highly affected by the cost ratio between the cellular transmission and D2D transmission, the access delays, and mobility patterns

Informative Voting and the Samuelson Rule

We study the classical free-rider problem in public goods provision in a large economy with uncertainty about the average valuation of the public good. Individual preferences over public goods are shaped by a skill and a taste parameter. We use a mechanism design approach to solve for the optimal utilitarian provision rule. The relevant incentive constraints for information aggregation ensure that individuals behave as if they were engaging in informative voting over the level of public good provision. It is shown that the use of information by an optimal provision rule is inversely related to the polarization of preferences which results from the properties of the skill distribution

Endowment additivity and the weighted proportional rules for adjudicating conflicting claims

We propose and study a new axiom, restricted endowment additivity, for the problem of adjudicating conflicting claims. This axiom requires that awards be additively decomposable with respect to the endowment whenever no agent’s claim is filled. For two-claimant problems, restricted endowment additivity essentially characterizes weighted extensions of the proportional rule. With additional agents, however, the axiom is satisfied by a great variety of rules. Further imposing versions of continuity and consistency, we characterize a new family of rules which generalize the proportional rule. Defined by a priority relation and a weighting function, each rule aims, as nearly as possible, to assign awards within each priority class in proportion to these weights. We also identify important subfamilies and obtain new characterizations of the constrained equal awards and proportional rules based on restricted endowment additivity

Quantum Probabilities as Behavioral Probabilities

We demonstrate that behavioral probabilities of human decision makers share many common features with quantum probabilities. This does not imply that humans are some quantum objects, but just shows that the mathematics of quantum theory is applicable to the description of human decision making. The applicability of quantum rules for describing decision making is connected with the nontrivial process of making decisions in the case of composite prospects under uncertainty. Such a process involves deliberations of a decision maker when making a choice. In addition to the evaluation of the utilities of considered prospects, real decision makers also appreciate their respective attractiveness. Therefore, human choice is not based solely on the utility of prospects, but includes the necessity of resolving the utility-attraction duality. In order to justify that human consciousness really functions similarly to the rules of quantum theory, we develop an approach defining human behavioral probabilities as the probabilities determined by quantum rules. We show that quantum behavioral probabilities of humans not merely explain qualitatively how human decisions are made, but they predict quantitative values of the behavioral probabilities. Analyzing a large set of empirical data, we find good quantitative agreement between theoretical predictions and observed experimental data.Comment: Latex file, 32 page

The self-organization of combinatoriality and phonotactics in vocalization systems

This paper shows how a society of agents can self-organize a shared vocalization system that is discrete, combinatorial and has a form of primitive phonotactics, starting from holistic inarticulate vocalizations. The originality of the system is that: (1) it does not include any explicit pressure for communication; (2) agents do not possess capabilities of coordinated interactions, in particular they do not play language games; (3) agents possess no specific linguistic capacities; and (4) initially there exists no convention that agents can use. As a consequence, the system shows how a primitive speech code may bootstrap in the absence of a communication system between agents, i.e. before the appearance of language