arXiv subjects

Christopher Griffin

Publications and source records attributed to Christopher Griffin.

53 records · Page 3Linked to original sources

arXiv2017

Increasing Peer Pressure on any Connected Graph Leads to Consensus

In this paper, we study a model of opinion dynamics in a social network in the presence increasing interpersonal influence, i.e., increasing peer pressure. Each agent in the social network has a distinct social stress function given by a weighted sum of internal and external behavioral pressures. We assume a weighted average update rule and prove conditions under which a connected group of agents converge to a fixed opinion distribution, and under which conditions the group reaches consensus. We show that the update rule is a gradient descent and explain its transient and asymptotic convergence properties. Through simulation, we study the rate of convergence on a scale-free network and then validate the assumption of increasing peer pressure in a simple empirical model.

cs.SI↗

arXiv2017

Optimal Digital Product Maintenance with a Continuous Revenue Stream

We use a control framework to analyze the digital vendor's profit maximization problem. The vendor captures market share by focusing costly effort on post-launch product maintenance, which influences user perception of the product and drives a revenue stream associated with product use. Our theoretical results show necessary and sufficient conditions for product maintenance to decline over a product's life-cycle, thus showing conditions when Lehman's 7th law of software evolution holds. We also numerically illustrate control paths under different market conditions.

q-fin.GN↗

arXiv2017

Minimum Probabilistic Finite State Learning Problem on Finite Data Sets: Complexity, Solution and Approximations

In this paper, we study the problem of determining a minimum state probabilistic finite state machine capable of generating statistically identical symbol sequences to samples provided. This problem is qualitatively similar to the classical Hidden Markov Model problem and has been studied from a practical point of view in several works beginning with the work presented in: Shalizi, C.R., Shalizi, K.L., Crutchfield, J.P. (2002) \textit{An algorithm for pattern discovery in time series.} Technical Report 02-10-060, Santa Fe Institute. arxiv.org/abs/cs.LG/0210025. We show that the underlying problem is $\mathrm{NP}$-hard and thus all existing polynomial time algorithms must be approximations on finite data sets. Using our $\mathrm{NP}$-hardness proof, we show how to construct a provably correct algorithm for constructing a minimum state probabilistic finite state machine given data and empirically study its running time.

cs.FL↗

arXiv2014

Roaming charges for customers of cellular-wireless entrant and incumbent providers

We consider a simple two-player game involving a large incumbent and small entrant into a cellular wireless access provider marketplace. The entrant's customers must pay roaming charges. We assume that the roaming charges are regulated, because if they are dictated by the incumbent then they could be set so high so as to be a barrier to entry in the marketplace. The game is studied at its Nash equilibrium. A roaming charge is identified that is arguably fair in the sense that revenues for the access providers are proportionate to their infrastructure costs.

cs.NI↗

arXiv2014

Generation bidding game with flexible demand

For a simple model of price-responsive demand, we consider a deregulated electricity marketplace wherein the grid (ISO, retailer-distributor) accepts bids per-unit supply from generators (simplified herein neither to consider start-up/ramp-up expenses nor day-ahead or shorter-term load following) which are then averaged (by supply allocations via an economic dispatch) to a common "clearing" price borne by customers (irrespective of variations in transmission/distribution or generation prices), i.e., the ISO does not compensate generators based on their marginal costs. Rather, the ISO provides sufficient information for generators to sensibly adjust their bids. Notwithstanding our idealizations, the dispatch dynamics are complex. For a simple benchmark power system, we find a price-symmetric Nash equilibrium through numerical experiments.

cs.GT↗

arXiv2014

A cooperate-defect model for the spread of deviant behavior in social networks

We present a game-theoretic model for the spread of deviant behavior in online social networks. We utilize a two-strategy framework wherein each player's behavior is classified as normal or deviant and evolves according to the cooperate-defect payoff scheme of the classic prisoner's dilemma game. We demonstrate convergence of individual behavior over time to a final strategy vector and indicate counterexamples to this convergence outside the context of prisoner's dilemma. Theoretical results are validated on a real-world dataset collected from a popular online forum.

cs.GT↗

arXiv2013

Behavior in a Shared Resource Game with Cooperative, Greedy, and Vigilante Players

We study a problem of trust in a distributed system in which a common resource is shared by multiple parties. In such naturally information-limited settings, parties abide by a behavioral protocol that leads to fair sharing of the resource. However, greedy players may defect from a cooperative protocol and achieve a greater than fair share of resources, often without significant adverse consequences to themselves. In this paper, we study the role of a few vigilante players who also defect from a cooperative resource-sharing protocol but only in response to perceived greedy behavior. For a simple model of engagement, we demonstrate surprisingly complex dynamics among greedy and vigilante players. We show that the best response function for the greedy-player under our formulation has a jump discontinuity, which leads to conditions under which there is no Nash equilibrium. To study this property, we formulate an exact representation for the greedy player best response function in the case when there is one greedy player, one vigilante player and $N-2$ cooperative players. We use this formulation to show conditions under which a Nash equilibrium exists. We also illustrate that in the case when there is no Nash equilibrium, then the discrete dynamic system generated from fictitious play will not converge, but will oscillate indefinitely as a result of the jump discontinuity. The case of multiple vigilante and greedy players is studied numerically. Finally, we explore the relationship between fictitious play and the better response dynamics (gradient descent) and illustrate that this dynamical system can have a fixed point even when the discrete dynamical system arising from fictitious play does not.

cs.GT↗

arXiv2013

Modeling and Control of Rare Segments in BitTorrent with Epidemic Dynamics

Despite its existing incentives for leecher cooperation, BitTorrent file sharing fundamentally relies on the presence of seeder peers. Seeder peers essentially operate outside the BitTorrent incentives, with two caveats: slow downlinks lead to increased numbers of "temporary" seeders (who left their console, but will terminate their seeder role when they return), and the copyright liability boon that file segmentation offers for permanent seeders. Using a simple epidemic model for a two-segment BitTorrent swarm, we focus on the BitTorrent rule to disseminate the (locally) rarest segments first. With our model, we show that the rarest-segment first rule minimizes transition time to seeder (complete file acquisition) and equalizes the segment populations in steady-state. We discuss how alternative dissemination rules may {\em beneficially increase} file acquisition times causing leechers to remain in the system longer (particularly as temporary seeders). The result is that leechers are further enticed to cooperate. This eliminates the threat of extinction of rare segments which is prevented by the needed presence of permanent seeders. Our model allows us to study the corresponding trade-offs between performance improvement, load on permanent seeders, and content availability, which we leave for future work. Finally, interpreting the two-segment model as one involving a rare segment and a "lumped" segment representing the rest, we study a model that jointly considers control of rare segments and different uplinks causing "choking," where high-uplink peers will not engage in certain transactions with low-uplink peers.

cs.NI↗

arXiv2012

Game Theoretic Iterative Partitioning for Dynamic Load Balancing in Distributed Network Simulation

High fidelity simulation of large-sized complex networks can be realized on a distributed computing platform that leverages the combined resources of multiple processors or machines. In a discrete event driven simulation, the assignment of logical processes (LPs) to machines is a critical step that affects the computational and communication burden on the machines, which in turn affects the simulation execution time of the experiment. We study a network partitioning game wherein each node (LP) acts as a selfish player. We derive two local node-level cost frameworks which are feasible in the sense that the aggregate state information required to be exchanged between the machines is independent of the size of the simulated network model. For both cost frameworks, we prove the existence of stable Nash equilibria in pure strategies. Using iterative partition improvements, we propose game theoretic partitioning algorithms based on the two cost criteria and show that each descends in a global cost. To exploit the distributed nature of the system, the algorithm is distributed, with each node's decision based on its local information and on a few global quantities which can be communicated machine-to-machine. We demonstrate the performance of our partitioning algorithm on an optimistic discrete event driven simulation platform that models an actual parallel simulator.

cs.DC↗

arXiv2012

Two Species Evolutionary Game Model of User and Moderator Dynamics

We construct a two species evolutionary game model of an online society consisting of ordinary users and behavior enforcers (moderators). Among themselves, moderators play a coordination game choosing between being "positive" or "negative" (or harsh) while ordinary users play prisoner's dilemma. When interacting, moderators motivate good behavior (cooperation) among the users through punitive actions while the moderators themselves are encouraged or discouraged in their strategic choice by these interactions. We show the following results: (i) We show that the $ω$-limit set of the proposed system is sensitive both to the degree of punishment and the proportion of moderators in closed form. (ii) We demonstrate that the basin of attraction for the Pareto optimal strategy $(\text{Cooperate},\text{Positive})$ can be computed exactly. (iii) We demonstrate that for certain initial conditions the system is self-regulating. These results partially explain the stability of many online users communities such as Reddit. We illustrate our results with examples from this online system.

cs.GT↗

arXiv2012

Game Theoretic Formation of a Centrality Based Network

We model the formation of networks as a game where players aspire to maximize their own centrality by increasing the number of other players to which they are path-wise connected, while simultaneously incurring a cost for each added adjacent edge. We simulate the interactions between players using an algorithm that factors in rational strategic behavior based on a common objective function. The resulting networks exhibit pairwise stability, from which we derive necessary stable conditions for specific graph topologies. We then expand the model to simulate non-trivial games with large numbers of players. We show that using conditions necessary for the stability of star topologies we can induce the formation of hub players that positively impact the total welfare of the network.

cs.GT↗

arXiv2012

An Informed Model of Personal Information Release in Social Networking Sites

The emergence of online social networks and the growing popularity of digital communication has resulted in an increasingly amount of information about individuals available on the Internet. Social network users are given the freedom to create complex digital identities, and enrich them with truthful or even fake personal information. However, this freedom has led to serious security and privacy incidents, due to the role users' identities play in establishing social and privacy settings. In this paper, we take a step toward a better understanding of online information exposure. Based on the detailed analysis of a sample of real-world data, we develop a deception model for online users. The model uses a game theoretic approach to characterizing a user's willingness to release, withhold or lie about information depending on the behavior of individuals within the user's circle of friends. In the model, we take into account both the heterogeneous nature of users and their different attitudes, as well as the different types of information they may expose online.

cs.SI↗

arXiv2012

CSMA Local Area Networking under Dynamic Altruism

In this paper, we consider medium access control of local area networks (LANs) under limited-information conditions as befits a distributed system. Rather than assuming "by rule" conformance to a protocol designed to regulate packet-flow rates (e.g., CSMA windowing), we begin with a non-cooperative game framework and build a dynamic altruism term into the net utility. The effects of altruism are analyzed at Nash equilibrium for both the ALOHA and CSMA frameworks in the quasistationary (fictitious play) regime. We consider either power or throughput based costs of networking, and the cases of identical or heterogeneous (independent) users/players. In a numerical study we consider diverse players, and we see that the effects of altruism for similar players can be beneficial in the presence of significant congestion, but excessive altruism may lead to underuse of the channel when demand is low.

cs.NI↗

arXiv2012

A Game Theoretic Perspective on Network Topologies

As an alternative view to the graph formation models in the statistical physics community, we introduce graph formation models using \textit{network formation} through selfish competition as an approach to modeling graphs with particular topologies. We further investigate a specific application of our results to collaborative oligopolies. We extend the results of Goyal and Joshi (S. Goyal and S. Joshi. Networks of collaboration in oligopoly. Games and Economic behavior, 43(1):57-85, 2003), who first considered the problem of collaboration networks of oligopolies and showed that under certain linear assumptions network collaboration produced a stable complete graph through selfish competition. We show with nonlinear cost functions and player payoff alteration that stable collaboration graphs with an arbitrary degree sequence can result.

math.OC↗

arXiv2012

The Calculation and Simulation of the Price of Anarchy for Network Formation Games

We model the formation of networks as the result of a game where by players act selfishly to get the portfolio of links they desire most. The integration of player strategies into the network formation model is appropriate for organizational networks because in these smaller networks, dynamics are not random, but the result of intentional actions carried through by players maximizing their own objectives. This model is a better framework for the analysis of influences upon a network because it integrates the strategies of the players involved. We present an Integer Program that calculates the price of anarchy of this game by finding the worst stable graph and the best coordinated graph for this game. We simulate the formation of the network and calculated the simulated price of anarchy, which we find tends to be rather low.

math.OC↗

arXiv2011

Collaborative Network Formation in Spatial Oligopolies

Recently, it has been shown that networks with an arbitrary degree sequence may be a stable solution to a network formation game. Further, in recent years there has been a rise in the number of firms participating in collaborative efforts. In this paper, we show conditions under which a graph with an arbitrary degree sequence is admitted as a stable firm collaboration graph.

math.OC↗

arXiv2011

Link Biased Strategies in Network Formation Games

We show a simple method for constructing an infinite family of graph formation games with link bias so that the resulting games admits, as a \textit{pairwise stable} solution, a graph with an arbitrarily specified degree distribution. Pairwise stability is used as the equilibrium condition over the more commonly used Nash equilibrium to prevent the occurrence of ill-behaved equilibrium strategies that do not occur in ordinary play. We construct this family of games by solving an integer programming problem whose constraints enforce the terminal pairwise stability property we desire.

math.OC↗