The Quality of Equilibria for Set Packing Games

We introduce set packing games as an abstraction of situations in which $n$ selfish players select subsets of a finite set of indivisible items, and analyze the quality of several equilibria for this class of games. Assuming that players are able to approximately play equilibrium strategies, we show that the total quality of the resulting equilibrium solutions is only moderately suboptimal. Our results are tight bounds on the price of anarchy for three equilibrium concepts, namely Nash equilibria, subgame perfect equilibria, and an equilibrium concept that we refer to as $k$-collusion Nash equilibrium

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

Collocation Games and Their Application to Distributed Resource Management

We introduce Collocation Games as the basis of a general framework for modeling, analyzing, and facilitating the interactions between the various stakeholders in distributed systems in general, and in cloud computing environments in particular. Cloud computing enables fixed-capacity (processing, communication, and storage) resources to be offered by infrastructure providers as commodities for sale at a fixed cost in an open marketplace to independent, rational parties (players) interested in setting up their own applications over the Internet. Virtualization technologies enable the partitioning of such fixed-capacity resources so as to allow each player to dynamically acquire appropriate fractions of the resources for unencumbered use. In such a paradigm, the resource management problem reduces to that of partitioning the entire set of applications (players) into subsets, each of which is assigned to fixed-capacity cloud resources. If the infrastructure and the various applications are under a single administrative domain, this partitioning reduces to an optimization problem whose objective is to minimize the overall deployment cost. In a marketplace, in which the infrastructure provider is interested in maximizing its own profit, and in which each player is interested in minimizing its own cost, it should be evident that a global optimization is precisely the wrong framework. Rather, in this paper we use a game-theoretic framework in which the assignment of players to fixed-capacity resources is the outcome of a strategic "Collocation Game". Although we show that determining the existence of an equilibrium for collocation games in general is NP-hard, we present a number of simplified, practically-motivated variants of the collocation game for which we establish convergence to a Nash Equilibrium, and for which we derive convergence and price of anarchy bounds. In addition to these analytical results, we present an experimental evaluation of implementations of some of these variants for cloud infrastructures consisting of a collection of multidimensional resources of homogeneous or heterogeneous capacities. Experimental results using trace-driven simulations and synthetically generated datasets corroborate our analytical results and also illustrate how collocation games offer a feasible distributed resource management alternative for autonomic/self-organizing systems, in which the adoption of a global optimization approach (centralized or distributed) would be neither practical nor justifiable.NSF (CCF-0820138, CSR-0720604, EFRI-0735974, CNS-0524477, CNS-052016, CCR-0635102); Universidad Pontificia Bolivariana; COLCIENCIAS–Instituto Colombiano para el Desarrollo de la Ciencia y la Tecnología "Francisco José de Caldas

Bottleneck Routing Games with Low Price of Anarchy

We study {\em bottleneck routing games} where the social cost is determined by the worst congestion on any edge in the network. In the literature, bottleneck games assume player utility costs determined by the worst congested edge in their paths. However, the Nash equilibria of such games are inefficient since the price of anarchy can be very high and proportional to the size of the network. In order to obtain smaller price of anarchy we introduce {\em exponential bottleneck games} where the utility costs of the players are exponential functions of their congestions. We find that exponential bottleneck games are very efficient and give a poly-log bound on the price of anarchy: $O(\log L \cdot \log |E|)$, where $L$ is the largest path length in the players' strategy sets and $E$ is the set of edges in the graph. By adjusting the exponential utility costs with a logarithm we obtain games whose player costs are almost identical to those in regular bottleneck games, and at the same time have the good price of anarchy of exponential games.Comment: 12 page

Trade & Cap: A Customer-Managed, Market-Based System for Trading Bandwidth Allowances at a Shared Link

We propose Trade & Cap (T&C), an economics-inspired mechanism that incentivizes users to voluntarily coordinate their consumption of the bandwidth of a shared resource (e.g., a DSLAM link) so as to converge on what they perceive to be an equitable allocation, while ensuring efficient resource utilization. Under T&C, rather than acting as an arbiter, an Internet Service Provider (ISP) acts as an enforcer of what the community of rational users sharing the resource decides is a fair allocation of that resource. Our T&C mechanism proceeds in two phases. In the first, software agents acting on behalf of users engage in a strategic trading game in which each user agent selfishly chooses bandwidth slots to reserve in support of primary, interactive network usage activities. In the second phase, each user is allowed to acquire additional bandwidth slots in support of presumed open-ended need for fluid bandwidth, catering to secondary applications. The acquisition of this fluid bandwidth is subject to the remaining "buying power" of each user and by prevalent "market prices" – both of which are determined by the results of the trading phase and a desirable aggregate cap on link utilization. We present analytical results that establish the underpinnings of our T&C mechanism, including game-theoretic results pertaining to the trading phase, and pricing of fluid bandwidth allocation pertaining to the capping phase. Using real network traces, we present extensive experimental results that demonstrate the benefits of our scheme, which we also show to be practical by highlighting the salient features of an efficient implementation architecture.National Science Foundation (CCF-0820138, CSR-0720604, EFRI-0735974, CNS-0524477, and CNS-0520166); Universidad Pontificia Bolivariana and COLCIENCIAS–Instituto Colombiano para el Desarrollo de la Ciencia y la Tecnología “Francisco Jose ́ de Caldas”

Resource Buying Games

In resource buying games a set of players jointly buys a subset of a finite resource set E (e.g., machines, edges, or nodes in a digraph). The cost of a resource e depends on the number (or load) of players using e, and has to be paid completely by the players before it becomes available. Each player i needs at least one set of a predefined family S_i in 2^E to be available. Thus, resource buying games can be seen as a variant of congestion games in which the load-dependent costs of the resources can be shared arbitrarily among the players. A strategy of player i in resource buying games is a tuple consisting of one of i's desired configurations S_i together with a payment vector p_i in R^E_+ indicating how much i is willing to contribute towards the purchase of the chosen resources. In this paper, we study the existence and computational complexity of pure Nash equilibria (PNE, for short) of resource buying games. In contrast to classical congestion games for which equilibria are guaranteed to exist, the existence of equilibria in resource buying games strongly depends on the underlying structure of the S_i's and the behavior of the cost functions. We show that for marginally non-increasing cost functions, matroids are exactly the right structure to consider, and that resource buying games with marginally non-decreasing cost functions always admit a PNE

ERA: A Framework for Economic Resource Allocation for the Cloud

Cloud computing has reached significant maturity from a systems perspective, but currently deployed solutions rely on rather basic economics mechanisms that yield suboptimal allocation of the costly hardware resources. In this paper we present Economic Resource Allocation (ERA), a complete framework for scheduling and pricing cloud resources, aimed at increasing the efficiency of cloud resources usage by allocating resources according to economic principles. The ERA architecture carefully abstracts the underlying cloud infrastructure, enabling the development of scheduling and pricing algorithms independently of the concrete lower-level cloud infrastructure and independently of its concerns. Specifically, ERA is designed as a flexible layer that can sit on top of any cloud system and interfaces with both the cloud resource manager and with the users who reserve resources to run their jobs. The jobs are scheduled based on prices that are dynamically calculated according to the predicted demand. Additionally, ERA provides a key internal API to pluggable algorithmic modules that include scheduling, pricing and demand prediction. We provide a proof-of-concept software and demonstrate the effectiveness of the architecture by testing ERA over both public and private cloud systems -- Azure Batch of Microsoft and Hadoop/YARN. A broader intent of our work is to foster collaborations between economics and system communities. To that end, we have developed a simulation platform via which economics and system experts can test their algorithmic implementations