On Existence and Properties of Approximate Pure Nash Equilibria in Bandwidth Allocation Games

In \emph{bandwidth allocation games} (BAGs), the strategy of a player consists of various demands on different resources. The player's utility is at most the sum of these demands, provided they are fully satisfied. Every resource has a limited capacity and if it is exceeded by the total demand, it has to be split between the players. Since these games generally do not have pure Nash equilibria, we consider approximate pure Nash equilibria, in which no player can improve her utility by more than some fixed factor $\alpha$ through unilateral strategy changes. There is a threshold $\alpha_\delta$ (where $\delta$ is a parameter that limits the demand of each player on a specific resource) such that $\alpha$-approximate pure Nash equilibria always exist for $\alpha \geq \alpha_\delta$, but not for $\alpha < \alpha_\delta$. We give both upper and lower bounds on this threshold $\alpha_\delta$ and show that the corresponding decision problem is ${\sf NP}$-hard. We also show that the $\alpha$-approximate price of anarchy for BAGs is $\alpha+1$. For a restricted version of the game, where demands of players only differ slightly from each other (e.g. symmetric games), we show that approximate Nash equilibria can be reached (and thus also be computed) in polynomial time using the best-response dynamic. Finally, we show that a broader class of utility-maximization games (which includes BAGs) converges quickly towards states whose social welfare is close to the optimum

Approximate Equilibrium and Incentivizing Social Coordination

We study techniques to incentivize self-interested agents to form socially desirable solutions in scenarios where they benefit from mutual coordination. Towards this end, we consider coordination games where agents have different intrinsic preferences but they stand to gain if others choose the same strategy as them. For non-trivial versions of our game, stable solutions like Nash Equilibrium may not exist, or may be socially inefficient even when they do exist. This motivates us to focus on designing efficient algorithms to compute (almost) stable solutions like Approximate Equilibrium that can be realized if agents are provided some additional incentives. Our results apply in many settings like adoption of new products, project selection, and group formation, where a central authority can direct agents towards a strategy but agents may defect if they have better alternatives. We show that for any given instance, we can either compute a high quality approximate equilibrium or a near-optimal solution that can be stabilized by providing small payments to some players. We then generalize our model to encompass situations where player relationships may exhibit complementarities and present an algorithm to compute an Approximate Equilibrium whose stability factor is linear in the degree of complementarity. Our results imply that a little influence is necessary in order to ensure that selfish players coordinate and form socially efficient solutions.Comment: A preliminary version of this work will appear in AAAI-14: Twenty-Eighth Conference on Artificial Intelligenc

Project Games

International audienceWe consider a strategic game called project game where each agent has to choose a project among his own list of available projects. The model includes positive weights expressing the capacity of a given agent to contribute to a given project The realization of a project produces some reward that has to be allocated to the agents. The reward of a realized project is fully allocated to its contributors, according to a simple proportional rule. Existence and computational complexity of pure Nash equilibria is addressed and their efficiency is investigated according to both the utilitarian and the egalitarian social function

Computing Stable Coalitions: Approximation Algorithms for Reward Sharing

Consider a setting where selfish agents are to be assigned to coalitions or projects from a fixed set P. Each project k is characterized by a valuation function; v_k(S) is the value generated by a set S of agents working on project k. We study the following classic problem in this setting: "how should the agents divide the value that they collectively create?". One traditional approach in cooperative game theory is to study core stability with the implicit assumption that there are infinite copies of one project, and agents can partition themselves into any number of coalitions. In contrast, we consider a model with a finite number of non-identical projects; this makes computing both high-welfare solutions and core payments highly non-trivial. The main contribution of this paper is a black-box mechanism that reduces the problem of computing a near-optimal core stable solution to the purely algorithmic problem of welfare maximization; we apply this to compute an approximately core stable solution that extracts one-fourth of the optimal social welfare for the class of subadditive valuations. We also show much stronger results for several popular sub-classes: anonymous, fractionally subadditive, and submodular valuations, as well as provide new approximation algorithms for welfare maximization with anonymous functions. Finally, we establish a connection between our setting and the well-studied simultaneous auctions with item bidding; we adapt our results to compute approximate pure Nash equilibria for these auctions.Comment: Under Revie

Large-scale coalition formation: application in power distribution systems

Doctor of PhilosophyDepartment of Computing and Information SciencesScott A. DeLoachCoalition formation is a key cooperative behavior of a system of multiple autonomous agents. When the capabilities of individual agents are not su fficient for the improvement of well-being of the individual agents or of the entire system, the agents can bene t by joining forces together in coalitions. Coalition formation is a technique for finding coalitions that are best fi tted to achieve individual or group goals. This is a computationally expensive task because often all combinations of agents have to be considered in order to find the best assignments of agents to coalitions. Previous research has therefore focused mainly on small-scale or otherwise restricted systems. In this thesis we study coalition formation in large-scale multi-agent systems. We propose an approach for coalition formation based on multi-agent simulation. This approach allows us to find coalitions in systems with thousands of agents. It also lets us modify behaviors of individual agents in order to better match a specific coalition formation application. Finally, our approach can consider both social welfare of the multi-agent system and well-being of individual self-interested agents. Power distribution systems are used to deliver electric energy from the transmission system to households. Because of the increased availability of distributed generation using renewable resources, push towards higher use of renewable energy, and increasing use of electric vehicles, the power distribution systems are undergoing significant changes towards active consumers who participate in both supply and demand sides of the electricity market and the underlying power grid. In this thesis we address the ongoing change in power distribution systems by studying how the use of renewable energy can be increased with the help of coalition formation. We propose an approach that lets renewable generators, which face uncertainty in generation prediction, to form coalitions with energy stores, which on the other hand are always able to deliver the committed power. These coalitions help decrease the uncertainty of the power generation of renewable generators, consequently allowing the generators to increase their use of renewable energy while at the same time increasing their pro fits. Energy stores also bene t from participating in coalitions with renewable generators, because they receive payments from the generators for the availability of their power at specific time slots. We first study this problem assuming no physical constraints of the underlying power grid. Then we analyze how coalition formation of renewable generators and energy stores in a power grid with physical constraints impacts the state of the grid, and we propose agent behavior that leads to increase in use of renewable energy as well as maintains stability of the grid

Scalable Task Schedulers for Many-Core Architectures

This thesis develops schedulers for many-cores with different optimization objectives. The proposed schedulers are designed to be scale up as the number of cores in many-cores increase while continuing to provide guarantees on the quality of the schedule