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We study a stochastic game framework with dynamic set of players, for modeling and analyzing their computational investment strategies in distributed computing. Players obtain a certain reward for solving the problem or for providing their computational resources, while incur a certain cost based on the invested time and computational power. We first study a scenario where the reward is offered for solving the problem, such as in blockchain mining. We show that, in Markov perfect equilibrium, players with cost parameters exceeding a certain threshold, do not invest; while those with cost parameters less than this threshold, invest maximal power. Here, players need not know the system state. We then consider a scenario where the reward is offered for contributing to the computational power of a common central entity, such as in volunteer computing. Here, in Markov perfect equilibrium, only players with cost parameters in a relatively low range in a given state, invest. For the case where players are homogeneous, they invest proportionally to the reward to cost ratio. For both the scenarios, we study the effects of players arrival and departure rates on their utilities using simulations and provide additional insights.
Runtime verification is a computing analysis paradigm based on observing a system at runtime (to check its expected behaviour) by means of monitors generated from formal specifications. Distributed runtime verification is runtime verification in connection with distributed systems: it comprises both monitoring of distributed systems and using distributed systems for monitoring. Aggregate computing is a programming paradigm based on a reference computing machine that is the aggregate collection of devices that cooperatively carry out a computational process: the details of behaviour, position and number of devices are largely abstracted away, to be replaced with a space-filling computational environment. In this position paper we argue, by means of simple examples, that aggregate computing is particularly well suited for implementing distributed monitors. Our aim is to foster further research on how to generate aggregate computing monitors from suitable formal specifications.
Fog computing is a promising architecture to provide economic and low latency data services for future Internet of things (IoT)-based network systems. It relies on a set of low-power fog nodes that are close to the end users to offload the services originally targeting at cloud data centers. In this paper, we consider a specific fog computing network consisting of a set of data service operators (DSOs) each of which controls a set of fog nodes to provide the required data service to a set of data service subscribers (DSSs). How to allocate the limited computing resources of fog nodes (FNs) to all the DSSs to achieve an optimal and stable performance is an important problem. In this paper, we propose a joint optimization framework for all FNs, DSOs and DSSs to achieve the optimal resource allocation schemes in a distributed fashion. In the framework, we first formulate a Stackelberg game to analyze the pricing problem for the DSOs as well as the resource allocation problem for the DSSs. Under the scenarios that the DSOs can know the expected amount of resource purchased by the DSSs, a many-to-many matching game is applied to investigate the pairing problem between DSOs and FNs. Finally, within the same DSO, we apply another layer of many-to-many matching between each of the paired FNs and serving DSSs to solve the FN-DSS pairing problem. Simulation results show that our proposed framework can significantly improve the performance of the IoT-based network systems.
Graphical games are a useful framework for modeling the interactions of (selfish) agents who are connected via an underlying topology and whose behaviors influence each other. They have wide applications ranging from computer science to economics and biology. Yet, even though a players payoff only depends on the actions of their direct neighbors in graphical games, computing the Nash equilibria and making statements about the convergence time of natural local dynamics in particular can be highly challenging. In this work, we present a novel approach for classifying complexity of Nash equilibria in graphical games by establishing a connection to local graph algorithms, a subfield of distributed computing. In particular, we make the observation that the equilibria of graphical games are equivalent to locally verifiable labelings (LVL) in graphs; vertex labelings which are verifiable with a constant-round local algorithm. This connection allows us to derive novel lower bounds on the convergence time to equilibrium of best-response dynamics in graphical games. Since we establish that distributed convergence can sometimes be provably slow, we also introduce and give bounds on an intuitive notion of time-constrained inefficiency of best responses. We exemplify how our results can be used in the implementation of mechanisms that ensure convergence of best responses to a Nash equilibrium. Our results thus also give insight into the convergence of strategy-proof algorithms for graphical games, which is still not well understood.
We describe a structured system for distributed mechanism design. It consists of a sequence of layers. The lower layers deal with the operations relevant for distributed computing only, while the upper layers are concerned only with communication among players, including broadcasting and multicasting, and distributed decision making. This yields a highly flexible distributed system whose specific applications are realized as instances of its top layer. This design supports fault-tolerance, prevents manipulations and makes it possible to implement distributed policing. The system is implemented in Java. We illustrate it by discussing a number of implemented examples.
We study the problem of optimally investing in nodes of a social network in a competitive setting, wherein two camps aim to drive the average opinion of the population in their own favor. Using a well-established model of opinion dynamics, we formulate the problem as a zero-sum game with its players being the two camps. We derive optimal investment strategies for both camps, and show that a random investment strategy is optimal when the underlying network follows a popular class of weight distributions. We study a broad framework, where we consider various well-motivated settings of the problem, namely, when the influence of a camp on a node is a concave function of its investment on that node, when a camp aims at maximizing competitors investment or deviation from its desired investment, and when one of the camps has uncertain information about the values of the model parameters. We also study a Stackelberg variant of this game under common coupled constraints on the combined investments by the camps and derive their equilibrium strategies, and hence quantify the first-mover advantage. For a quantitative and illustrative study, we conduct simulations on real-world datasets and provide results and insights.