The impact of timing on linearizability in counting networks

{\em Counting networks} form a new class of distributed, low-contention data structures, made up of {\em balancers} and {\em wires,} which are suitable for solving a variety of multiprocessor synchronization problems that can be expressed as counting problems. A {\em linearizable} counting network guarantees that the order of the values it returns respects the real-time order they were requested. Linearizability significantly raises the capabilities of the network, but at a possible price in network size or synchronization support. In this work, we further pursue the systematic study of the impact of {\em timing} assumptions on linearizability for counting networks, along the line of research recently initiated by Lynch~{\em et~al.} in [18]. We consider two basic {\em timing} models, the {instantaneous balancer} model, in which the transition of a token from an input to an output port of a balancer is modeled as an instantaneous event, and the {\em periodic balancer} model, where balancers send out tokens at a fixed rate. In both models, we assume lower and upper bounds on the delays incurred by wires connecting the balancers. We present necessary and sufficient conditions for linearizability in these models, in the form of precise inequalities that involve not only parameters of the timing models, but also certain structural parameters of the counting network, which may be of more general interest. Our results extend and strengthen previous impossibility and possibility results on linearizability in counting networks

Multi-Player Diffusion Games on Graph Classes

We study competitive diffusion games on graphs introduced by Alon et al. [1] to model the spread of influence in social networks. Extending results of Roshanbin [8] for two players, we investigate the existence of pure Nash equilibria for at least three players on different classes of graphs including paths, cycles, grid graphs and hypercubes; as a main contribution, we answer an open question proving that there is no Nash equilibrium for three players on (m x n) grids with min(m, n) >= 5. Further, extending results of Etesami and Basar [3] for two players, we prove the existence of pure Nash equilibria for four players on every d-dimensional hypercube.Comment: Extended version of the TAMC 2015 conference version now discussing hypercube results (added details for the proof of Proposition 1

Budget-restricted utility games with ordered strategic decisions

We introduce the concept of budget games. Players choose a set of tasks and each task has a certain demand on every resource in the game. Each resource has a budget. If the budget is not enough to satisfy the sum of all demands, it has to be shared between the tasks. We study strategic budget games, where the budget is shared proportionally. We also consider a variant in which the order of the strategic decisions influences the distribution of the budgets. The complexity of the optimal solution as well as existence, complexity and quality of equilibria are analyzed. Finally, we show that the time an ordered budget game needs to convergence towards an equilibrium may be exponential

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

Facets of the Fully Mixed Nash Equilibrium Conjecture

In this work, we continue the study of the many facets of the Fully Mixed Nash Equilibrium Conjecture, henceforth abbreviated as the FMNE Conjecture, in selfish routing for the special case of n identical users over two (identical) parallel links. We introduce a new measure of Social Cost, defined to be the expectation of the square of the maximum congestion on a link; we call it Quadratic Maximum Social Cost. A Nash equilibrium is a stable state where no user can improve her (expected) latency by switching her mixed strategy; a worst-case Nash equilibrium is one that maximizes Quadratic Maximum Social Cost. In the fully mixed Nash equilibrium, allmixed strategies achieve full support. Formulated within this framework is yet another facet of the FMNE Conjecture, which states that the fully mixed Nash equilibrium is the worst-case Nash equilibrium. We present an extensive proof of the FMNE Conjecture; the proof employs a mixture of combinatorial arguments and ana-lytical estimations. Some of these analytical estimations are derived through some new bounds on generalized medians of the binomial distribution [22] we obtain, which are of independent interest.

Congestion Games with Complementarities

We study a model of selfish resource allocation that seeks to incorporate dependencies among resources as they exist in modern networked environments. Our model is inspired by utility functions with constant elasticity of substitution (CES) which is a well-studied model in economics. We consider congestion games with different aggregation functions. In particular, we study $L_p$ norms and analyze the existence and complexity of (approximate) pure Nash equilibria. Additionally, we give an almost tight characterization based on monotonicity properties to describe the set of aggregation functions that guarantee the existence of pure Nash equilibria.Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-57586-5_1

Boolean Game with Prioritized Norms

In this paper we study boolean game with prioritized norms. Norms distinguish illegal strategies from legal strategies. Notions like legal strategy and legal Nash equilibrium are introduced. Our formal model is a combination of (weighted) boolean game and so called (prioritized) input/output logic. After formally presenting the model, we use examples to show that non-optimal Nash equilibrium can be avoided by making use of norms.We study various complexity issues related to legal strategy and legal Nash equilibrium

Network-Formation Games with Regular Objectives

Abstract. Classical network-formation games are played on a directed graph. Players have reachability objectives, and each player has to select a path satisfy-ing his objective. Edges are associated with costs, and when several players use the same edge, they evenly share its cost. The theoretical and practical aspects of network-formation games have been extensively studied and are well understood. We introduce and study network-formation games with regular objectives. In our setting, the edges are labeled by alphabet letters and the objective of each player is a regular language over the alphabet of labels, given by means of an automaton or a temporal-logic formula. Thus, beyond reachability properties, a player may restrict attention to paths that satisfy certain properties, referring, for example, to the providers of the traversed edges, the actions associated with them, their quality of service, security, etc. Unlike the case of network-formation games with reachability objectives, here the paths selected by the players need not be simple, thus a player may traverse some transitions several times. Edge costs are shared by the players with the share being proportional to the number of times the transition is traversed. We study the exis-tence of a pure Nash equilibrium (NE), convergence of best-response-dynamics, the complexity of finding the social optimum, and the inefficiency of a NE com-pared to a social-optimum solution. We examine several classes of networks (for example, networks with uniform edge costs, or alphabet of size 1) and several classes of regular objectives. We show that many properties of classical network-formation games are no longer valid in our game. In particular, a pure NE might not exist and the Price of Stability equals the number of players (as opposed to logarithmic in the number of players in the classic setting, where a pure NE al-ways exists). In light of these results, we also present special cases for which the resulting game is more stable.

Efficient, Strongly Consistent Implementations of Shared Memory (Extended Abstract)

) Marios Mavronicolas ? Dan Roth ?? Aiken Computation Laboratory, Harvard University, Cambridge, MA 02138, USA Abstract. We present linearizable implementations for two distributed organizations of multiprocessor shared memory. For the full caching organization, where each process keeps a local copy of the whole memory, we present a linearizable implementations of read/write memory objects that achieves essentially optimal efficiency and allows quantitative degradation of the less frequently employed operation. For the single ownership organization, where each memory object is &quot;owned&quot; by a single process which is most likely to access it frequently, our linearizable implementation allows local operations to be performed much faster (almost instantaneously) than remote ones. We suggest to combine these organizations in a &quot;hybrid&quot; memory structure that allows processes to access local and remote information in a transparent manner, while at a lower level of the memory consistency sys..