In general, the games are played on a host graph, where each node is a selfish independent agent (player) and each edge has a fixed link creation cost α. Together the agents create a network (a subgraph of the host graph) while selfishly minimizing the link creation costs plus the sum of the distances to all other players (usage cost). In this paper, we pursue two important facets of the network creation game. First, we study extensively a natural version of the game, called the cooperative model, where nodes can collaborate and share the cost of creating any edge in the host graph. We prove the first nontrivial bounds in this model, establishing that the price of anarchy is polylogarithmic in n for all values of α in complete host graphs. This bound is the first result of this type for any version of the network creation game; most previous general upper bounds are polynomial in n. Interestingly, we also show that equilibrium graphs have polylogarithmic diameter for the most natural range of α(at most n polylg n). Second, we study the impact of the natural assumption that the host graph is a general graph, not necessarily complete. This model is a simple example of nonuniform creation costs among the edges (effectively allowing weights of αand \infty). We prove the first assemblage of upper and lower bounds for this context, stablishing nontrivial tight bounds for many ranges of α, for both the unilateral and cooperative versions of network creation. In particular, we establish polynomial lower bounds for both versions and many ranges of α, even for this simple nonuniform cost model, which sharply contrasts the conjectured constant bounds for these games in complete (uniform) graphs.
We study Nash equilibria and the price of anarchy in the classic model of Network Creation Games introduced by Fabrikant, Luthra, Maneva, Papadimitriou and Shenker in 2003. This is a selfish network creation model where players correspond to nodes in a network and each of them can create links to the other $n-1$ players at a prefixed price $α> 0$. The player's goal is to minimise the sum of her cost buying edges and her cost for using the resulting network. One of the main conjectures for this model states that the price of anarchy, i.e. the relative cost of the lack of coordination, is consta…
We study Nash equilibria and the price of anarchy in the classic model of Network Creation Games introduced by Fabrikant et al. In this model every agent (node) buys links at a prefixed price $α> 0$ in order to get connected to the network formed by all the $n$ agents. In this setting, the reformulated tree conjecture states that for $α> n$, every Nash equilibrium network is a tree. Moreover, Demaine et al. conjectured that the price of anarchy for this model is constant. Since it was shown that the price of anarchy for trees is constant, if the tree conjecture were true, then the price of ana…
We study the Nash equilibrium and the price of anarchy in the max-distance network creation game. Network creation game, first introduced and studied by Fabrikant et al., is a classic model for real-world networks from a game-theoretic point of view. In a network creation game with n selfish vertex agents, each vertex can build undirected edges incident to a subset of the other vertices. The goal of every agent is to minimize its creation cost plus its usage cost, where the creation cost is the unit edge cost $α$ times the number of edges it builds, and the usage cost is the sum of distances t…
Selfish Network Creation focuses on modeling real world networks from a game-theoretic point of view. One of the classic models by Fabrikant et al. [PODC'03] is the network creation game, where agents correspond to nodes in a network which buy incident edges for the price of $α$ per edge to minimize their total distance to all other nodes. The model is well-studied but still has intriguing open problems. The most famous conjectures state that the price of anarchy is constant for all $α$ and that for $α\geq n$ all equilibrium networks are trees. We introduce a novel technique for analyzing stab…
Pool block withholding attack is performed among mining pools in digital cryptocurrencies, such as Bitcoin. Instead of mining honestly, pools can be incentivized to infiltrate their own miners into other pools. These infiltrators report partial solutions but withhold full solutions, share block rewards but make no contribution to block mining. The block withholding attack among mining pools can be modeled as a non-cooperative game called "the miner's dilemm", which reduces effective mining power in the system and leads to potential systemic instability in the blockchain. However, existing lite…
Network Creation Games are a well-known approach for explaining and analyzing the structure, quality and dynamics of real-world networks like the Internet and other infrastructure networks which evolved via the interaction of selfish agents without a central authority. In these games selfish agents which correspond to nodes in a network strategically buy incident edges to improve their centrality. However, past research on these games has only considered the creation of networks with unit-weight edges. In practice, e.g. when constructing a fiber-optic network, the choice of which nodes to conn…
University of South Carolina（南卡罗来纳大学）；Virginia Tech（弗吉尼亚理工大学）
We study the performance of policy gradient methods for the subclass of Markov games known as Markov potential games (MPGs), which extends the notion of normal-form potential games to the stateful setting and includes the important special case of the fully cooperative setting where the agents share an identical reward function. Our focus in this paper is to study the convergence of the policy gradient method for solving MPGs under softmax policy parameterization, both tabular and parameterized with general function approximators such as neural networks. We first show the asymptotic convergenc…
During a pandemic people have to find a trade-off between meeting others and staying safely at home. While meeting others is pleasant, it also increases the risk of infection. We consider this dilemma by introducing a game-theoretic network creation model in which selfish agents can form bilateral connections. They benefit from network neighbors, but at the same time, they want to maximize their distance to all other agents. This models the inherent conflict that social distancing rules impose on the behavior of selfish agents in a social network. Besides addressing this familiar issue, our mo…
Cooperative game theory deals with systems where players want to cooperate to improve their payoffs. But players may choose coalitions in a non-cooperative manner, leading to a coalition-formation game. We consider such a game with several players (willing to cooperate) and an adamant player (unwilling to cooperate) involved in resource-sharing. Here, the strategy of a player is the set of players with whom it wants to form a coalition. Given a strategy profile, an appropriate partition of coalitions is formed; players in each coalition maximize their collective utilities leading to a non-coop…
Private blockchain is driving the creation of business networks, resulting in the creation of new value or new business models to the enterprises participating in the network. Such business networks form when enterprises come together to derive value through a network which is greater than the value that can be derived solely by any single company. This results in a setting that combines both competitive and cooperative behavior, and which we call strategic coopetition. Traditionally, cooperative and competitive behavior have been analyzed separately in game theory. In this article, we provide…
Network Creation Games(NCGs) model the creation of decentralized communication networks like the Internet. In such games strategic agents corresponding to network nodes selfishly decide with whom to connect to optimize some objective function. Past research intensively analyzed models where the agents strive for a central position in the network. This models agents optimizing the network for low-latency applications like VoIP. However, with today's abundance of streaming services it is important to ensure that the created network can satisfy the increased bandwidth demand. To the best of our k…
We study the sum classic network creation game introduced by Fabrikant et al. in which $n$ players conform a network buying links at individual price $α$. When studying this model we are mostly interested in \emph{Nash equilibria} (\NE) and the \emph{Price of Anarchy} (\PoA). It is conjectured that the \PoA is constant for any $α$. Up until now, it has been proved constant \PoA for the range $α= O(n^{1-δ_1})$ with $δ_1>0$ a positive constant and it has been proved constant \PoA for the range $α>n(1+δ_2)$ with $δ_2>0$ a positive constant. Our contribution consists in proving that \NE graphs sat…
Payment channels were introduced to solve various eminent cryptocurrency scalability issues. Multiple payment channels build a network on top of a blockchain, the so-called layer 2. In this work, we analyze payment networks through the lens of network creation games. We identify betweenness and closeness centrality as central concepts regarding payment networks. We study the topologies that emerge when players act selfishly and determine the parameter space in which they constitute a Nash equilibrium. Moreover, we determine the social optima depending on the correlation of betweenness and clos…
We study strong equilibria in network creation games. These form a classical and well-studied class of games where a set of players form a network by buying edges to their neighbors at a cost of a fixed parameter $α$. The cost of a player is defined to be the cost of the bought edges plus the sum of distances to all the players in the resulting graph. We identify and characterize various structural properties of strong equilibria, which lead to a characterization of the set of strong equilibria for all $α$ in the range $(0,2)$. For $α> 2$, Andelman et al. (2009) prove that a star graph in whic…
This is the first paper to address the topology structure of Job Edge-Fog interconnection network in the perspective of network creation game. A two level network creation game model is given, in which the first level is similar to the traditional network creation game with total length objective to other nodes. The second level adopts two types of cost functions, one is created based on the Jackson-Wolinsky type of distance based utility, another is created based on the Network-Only Cost in the IoT literature. We show the performance of this two level game (Price of Anarchy). This work disclo…
网络创建游戏已经被广泛研究，无论是经济学家和计算机科学家，由于其在建模基于个人的社区形成过程中的多功能性，这反过来又是一些经济学，社会和计算应用在互联网上的理论对应。在它们的几个变体中，这些游戏模拟了一个玩家在两个对立目标之间的紧张关系：尽可能接近其他玩家，并激活一组尽可能便宜的链接。然而，普遍采用的假设是，玩家具有关于正在进行的网络的\emph{common and complete}信息，这在实践中是相当不现实的。在本文中，我们考虑了一个更引人注目的场景，其中玩家只有有限的信息，他们嵌入的网络。更确切地说，我们探讨的博弈论和计算的影响，假设玩家有一个完整的知识的网络结构只有一个给定的半径$k$，这是一个最合格的\emph{local-knowledge models}用于分布式计算。在这方面，我们定义了一个合适的均衡概念，并为$k$的整个价值范围提供了一套全面的无政府代价的上限和下限，并为游戏的两个经典变体，也就是说，玩家的成本--除了拥有的链接的激活成本--取决于最大/分别到网络中其他节点的所有距离之和。这些界限最后通过一组广泛的实验进行评估。
In the swap game (SG) selfish players, each of which is associated to a vertex, form a graph by edge swaps, i.e., a player changes its strategy by simultaneously removing an adjacent edge and forming a new edge (Alon et al., 2013). The cost of a player considers the average distance to all other players or the maximum distance to other players. Any SG by $n$ players starting from a tree converges to an equilibrium with a constant Price of Anarchy (PoA) within $O(n^3)$ edge swaps (Lenzner, 2011). We focus on SGs where each player knows the subgraph induced by players within distance $k$. Theref…
Understanding real-world networks has been a core research endeavor throughout the last two decades. Network Creation Games are a promising approach for this from a game-theoretic perspective. In these games, selfish agents corresponding to nodes in a network strategically decide which links to form to optimize their centrality. Many versions have been introduced and analyzed, but none of them fits to modeling the evolution of social networks. In real-world social networks, connections are often established by recommendations from common acquaintances or by a chain of such recommendations. Thu…
As a momentous enabling of the Internet of things (IoT), mobile edge computing (MEC) provides IoT mobile devices (MD) with powerful external computing and storage resources. However, a mechanism addressing distributed task offloading and price competition for the open exchange marketplace has not been established properly, which has become a huge obstacle to MEC's application in the IoT market. In this paper, we formulate a distributed mechanism to analyze the interaction between OSPs and IoT MDs in the MEC enabled edge-cloud system by appling multi-leader multi-follower two-tier Stackelberg g…
Assume that a treasure is placed in one of $M$ boxes according to a known distribution and that $k$ searchers are searching for it in parallel during $T$ rounds. We study the question of how to incentivize selfish players so that the success probability, namely, the probability that at least one player finds the treasure, would be maximized. We focus on congestion policies $C(s)$ that specify the reward that a player receives if it is one of $s$ players that (simultaneously) find the treasure for the first time. Our main technical contribution is proving that the exclusive policy, in which $C(…
The application of Internet of Things (IoT) and Machine Learning (ML) to the agricultural industry has enabled the development and creation of smart farms and precision agriculture. The growth in the number of smart farms and potential cooperation between these farms has given rise to the Cooperative Smart Farming (CSF) where different connected farms collaborate with each other and share data for their mutual benefit. This data sharing through CSF has various advantages where individual data from separate farms can be aggregated by ML models and be used to produce actionable outputs which the…
Maximal (also miner) extractable value, or MEV, usually refers to the value that privileged players can extract by strategically ordering, censoring, and placing transactions in a blockchain. Each blockchain network, which we refer to as a domain, has its own consensus, ordering, and block-creation mechanisms, which gives rise to different optimal strategies to extract MEV. The strategic behaviour of rational players, known as searchers, lead to MEV games that have different impacts and externalities in each domain. Several ordering mechanisms, which determine the inclusion and position of tra…
Online content platforms are concerned about the freshness of their content updates to their end customers, and increasingly more platforms now invite and pay the crowd to sample real-time information (e.g., traffic observations and sensor data) to help reduce their ages of information (AoI). How much crowdsourced data to sample and buy over time is a critical question for a platform's AoI management, requiring a good balance between its AoI and the incurred sampling cost. This question becomes more interesting by considering the stage after sampling, where multiple platforms coexist in sharin…
Network Design problems typically ask for a minimum cost sub-network from a given host network. This classical point-of-view assumes a central authority enforcing the optimum solution. But how should networks be designed to cope with selfish agents that own parts of the network? In this setting, agents will deviate from a minimum cost network if this decreases their individual cost. Hence, designed networks should be both efficient in terms of total cost and stable in terms of the agents' willingness to accept the network. We study this novel type of Network Design problem by investigating the…
