Payment networks were introduced to address the limitation on the transaction throughput of popular blockchains. To open a payment channel one has to publish a transaction on-chain and pay the appropriate transaction fee. A transaction can be routed in the network, as long as there is a path of channels with the necessary capital. The intermediate nodes on this path can ask for a fee to forward the transaction. Hence, opening channels, although costly, can benefit a party, both by reducing the cost of the party for sending a transaction and by collecting the fees from forwarding transactions of other parties.
This trade-off spawns a network creation game between the channel parties. In this work, we introduce the first game theoretic model for analyzing the network creation game on blockchain payment channels. Further, we examine various network structures (path, star, complete bipartite graph and clique) and determine for each one of them the constraints (fee value) under which they constitute a Nash equilibrium, given a fixed fee policy. Last, we show that the star is a Nash equilibrium when each channel party can freely decide the channel fee. On the other hand, we prove the complete bipartite graph can never be a Nash equilibrium, given a free fee policy.
We consider transformations of normal form games by binding preplay offers of players for payments of utility to other players conditional on them playing designated in the offers strategies. The game-theoretic effect of such preplay offers is transformation of the payoff matrix of the game by transferring payoffs between players. Here we analyze and completely characterize the possible transformations of the payoff matrix of a normal form game by sets of preplay offers.
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 propose a game-theoretic framework to study the outcomes of packetized payments, a cross-ledger transaction protocol, with strategic and possibly malicious agents. We derive the transaction failure rate and demonstrate that without disciplinary mechanisms, packetized payments are likely to be incomplete. Our analysis suggests that collateral deposits can prevent malicious agents from taking advantage of the protocol. We further infer that the deposit amount should depend on the underlying asset price volatility or that it should be dynamically adjusted as the price changes.
In this paper, we study the egalitarian solution for games with discrete side payment, where the characteristic function is integer-valued and payoffs of players are integral vectors. The egalitarian solution, introduced by Dutta and Ray in 1989, is a solution concept for transferable utility cooperative games in characteristic form, which combines commitment for egalitarianism and promotion of indivisual interests in a consistent manner. We first point out that the nice properties of the egalitarian solution (in the continuous case) do not extend to games with discrete side payment. Then we s…
Artificial agents are typically oriented to the realization of an externally assigned task and try to optimize over secondary aspects of plan execution such time lapse or power consumption, technically displaying a quasi-dichotomous preference relation. Boolean games have been developed as a paradigm for modelling societies of agents with this type of preference. In boolean games agents exercise control over propositional variables and strive to achieve a goal formula whose realization might require the opponents' cooperation. Recently, a theory of incentive engineering for such games has been…
In many applications, we want to influence the decisions of independent agents by designing incentives for their actions. We revisit a fundamental problem in this area, called GAME IMPLEMENTATION: Given a game in standard form and a set of desired strategies, can we design a set of payment promises such that if the players take the payment promises into account, then all undominated strategies are desired? Furthermore, we aim to minimize the cost, that is, the worst-case amount of payments. We study the tractability of computing such payment promises and determine more closely what obstruction…
Policy makers focus on stable strategies as the ones adopted by rational players. If there are many such solutions an important question is how to select amongst them. We study this question for the Multicommodity Flow Coalition Game, used to model cooperation between autonomous systems (AS) in the Internet. In short, strategies are flows in a capacitated network. The payoff to a node is the total flow which it terminates. Markakis-Saberi show this game is balanced and hence has a non-empty core by Scarf's Theorem. In the transferable utility (TU) version this gives a polynomial-time algorithm…
We study financial systems from a game-theoretic standpoint. A financial system is represented by a network, where nodes correspond to firms, and directed labeled edges correspond to debt contracts between them. The existence of cycles in the network indicates that a payment of a firm to one of its lenders might result to some incoming payment. So, if a firm cannot fully repay its debt, then the exact (partial) payments it makes to each of its creditors can affect the cash inflow back to itself. We naturally assume that the firms are interested in their financial well-being (utility) which is …
The Egalitarian Allocation (EA) is a well-known profit sharing method for cooperative games which attempts to distribute profit among participants in a most equal way while respecting the individual contributions to the obtained profit. Despite having desirable properties from the viewpoint of game theory like being contained in the core, the EA is in general hard to compute. Another well-known method is given by Vickrey Payments (VP). Again, the VP have desirable properties like coalitional rationality, the VP do not fulfill budget balance in general and, thus, are not contained in the core i…
The problem of analyzing the effect of privacy concerns on the behavior of selfish utility-maximizing agents has received much attention lately. Privacy concerns are often modeled by altering the utility functions of agents to consider also their privacy loss. Such privacy aware agents prefer to take a randomized strategy even in very simple games in which non-privacy aware agents play pure strategies. In some cases, the behavior of privacy aware agents follows the framework of Randomized Response, a well-known mechanism that preserves differential privacy. Our work is aimed at better understa…
Learning Strategic Value and Cooperation in Multi-Player Stochastic Games through Side Payments
Department of Computer Science & Engineering, Texas A&M University（德克萨斯A&M大学计算机科学与工程系）；Naval Information Warfare Center Atlantic（海军信息战中心大西洋分部）；Department of Mechanical and Aerospace Engineering, University of California, Irvine（加州大学 Irvine 分校机械与航空航天工程系）
We consider a model of priced resource sharing that combines both queueing behavior and strategic behavior. We study a priority service model where a single server allocates its capacity to agents in proportion to their payment to the system, and users from different classes act to minimize the sum of their cost for processing delay and payment. As the exact processing time of this system is hard to compute, we introduce the notion of heavy traffic equilibrium as an approximation of the Nash equilibrium, derived by considering the asymptotic regime where the system load approaches capacity. We…
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…
Financial network games model payment incentives in the context of networked liabilities. In this paper, we advance the understanding of incentives in financial networks in two important directions: minimal clearing (arising, e.g., as a result of sequential execution of payments) and seniorities (i.e., priorities over debt contracts). We distinguish between priorities that are chosen endogenously or exogenously. For endogenous priorities and standard (maximal) clearing, the games exhibit a coalitional form of weak acyclicity. A strong equilibrium exists and can be reached after a polynomial nu…
Microsoft Research（微软研究院）；University of Southampton（南安普顿大学）；Nanyang Technological University（南洋理工大学）；Hebrew University（希伯来大学）；Heinrich-Heine-Universität Düsseldorf（杜塞尔多夫海因里希·海涅大学）
A key question in cooperative game theory is that of coalitional stability, usually captured by the notion of the \emph{core}--the set of outcomes such that no subgroup of players has an incentive to deviate. However, some coalitional games have empty cores, and any outcome in such a game is unstable. In this paper, we investigate the possibility of stabilizing a coalitional game by using external payments. We consider a scenario where an external party, which is interested in having the players work together, offers a supplemental payment to the grand coalition (or, more generally, a particul…
We study a coordination game motivated by the formation of Internet Exchange Points (IXPs), in which agents choose which facilities to join. Joining the same facility as other agents you communicate with has benefits, but different facilities have different costs for each agent. Thus, the players wish to join the same facilities as their "friends", but this is balanced by them not wanting to pay the cost of joining a facility. We first show that the Price of Stability ($PoS$) of this game is at most 2, and more generally there always exists an $α$-approximate equilibrium with cost at most $\fr…
We study Nash equilibria in the network creation game of Fabrikant et al.[10]. In this game a vertex can buy an edge to another vertex for a cost of $α$, and the objective of each vertex is to minimize the sum of the costs of the edges it purchases plus the sum of the distances to every other vertex in the resultant network. A long-standing conjecture states that if $α\ge n$ then every Nash equilibrium in the game is a spanning tree. We prove the conjecture holds for any $α>3n-3$.
Celebrity games, a new model of network creation games is introduced. The specific features of this model are that players have different celebrity weights and that a critical distance is taken into consideration. The aim of any player is to be close (at distance less than critical) to the others, mainly to those with high celebrity weights. The cost of each player depends on the cost of establishing direct links to other players and on the sum of the weights of those players at a distance greater than the critical distance. We show that celebrity games always have pure Nash equilibria and we …
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 t…
Each participant in peer-to-peer network prefers to free-ride on the contribution of other participants. Reputation based resource sharing is a way to control the free riding. Instead of classical game theory we use evolutionary game theory to analyse the reputation based resource sharing in peer to peer system. Classical game-theoretical approach requires global information of the population. However, the evolutionary games only assumes light cognitive capabilities of users, that is, each user imitates the behavior of other user with better payoff. We find that without any extra benefit reput…
This paper discusses an interested party who wishes to influence the behavior of agents in a game (multi-agent interaction), which is not under his control. The interested party cannot design a new game, cannot enforce agents' behavior, cannot enforce payments by the agents, and cannot prohibit strategies available to the agents. However, he can influence the outcome of the game by committing to non-negative monetary transfers for the different strategy profiles that may be selected by the agents. The interested party assumes that agents are rational in the commonly agreed sense that they do n…
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…
Network creation games model the creation and usage costs of networks formed by n selfish nodes. Each node v can buy a set of edges, each for a fixed price α> 0. Its goal is to minimize its private costs, i.e., the sum (SUM-game, Fabrikant et al., PODC 2003) or maximum (MAX-game, Demaine et al., PODC 2007) of distances from $v$ to all other nodes plus the prices of the bought edges. The above papers show the existence of Nash equilibria as well as upper and lower bounds for the prices of anarchy and stability. In several subsequent papers, these bounds were improved for a wide range of prices …
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 generalize two well-known game-theoretic models by introducing multiple partners matching games, defined by a graph $G=(N,E)$, with an integer vertex capacity function $b$ and an edge weighting $w$. The set $N$ consists of a number of players that are to form a set $M\subseteq E$ of 2-player coalitions $ij$ with value $w(ij)$, such that each player $i$ is in at most $b(i)$ coalitions. A payoff vector is a mapping $p: N \times N \rightarrow {\mathbb R}$ with $p(i,j)+p(j,i)=w(ij)$ if $ij\in M$ and $p(i,j)=p(j,i)=0$ if $ij\notin M$. The pair $(M,p)$ is called a solution. A pair of players $i,j…
Network creation games have been extensively studied, both from economists and computer scientists, due to their versatility in modeling individual-based community formation processes, which in turn are the theoretical counterpart of several economics, social, and computational applications on the Internet. In their several variants, these games model the tension of a player between her two antagonistic goals: to be as close as possible to the other players, and to activate a cheapest possible set of links. However, the generally adopted assumption is that players have a \emph{common and compl…
Off-chain transaction channels represent one of the leading techniques to scale the transaction throughput in cryptocurrencies such as Bitcoin. They allow multiple agents to route payments through one another. So far, the topology and construction of payment networks has not been explored much. Participants are expected to minimize costs that are due to the allocation of liquidity as well as blockchain record fees. In this paper we study the optimization of maintenance costs of such networks. We present for the first time, a closed model for symmetric off-chain channels, and provide efficient …
Network Creation Games are an important framework for understanding the formation of real-world networks. These games usually assume a set of indistinguishable agents strategically buying edges at a uniform price leading to a network among them. However, in real life, agents are heterogeneous and their relationships often display a bias towards similar agents, say of the same ethnic group. This homophilic behavior on the agent level can then lead to the emergent global phenomenon of social segregation. We initiate the study of Network Creation Games with multiple types of homophilic agents and…
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…
We investigate a non-cooperative game-theoretic model for the formation of communication networks by selfish agents. Each agent aims for a central position at minimum cost for creating edges. In particular, the general model (Fabrikant et al., PODC'03) became popular for studying the structure of the Internet or social networks. Despite its significance, locality in this game was first studied only recently (Bilò et al., SPAA'14), where a worst case locality model was presented, which came with a high efficiency loss in terms of quality of equilibria. Our main contribution is a new and more op…
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…
A network creation game simulates a decentralized and non-cooperative building of a communication network. Informally, there are $n$ players sitting on the network nodes, which attempt to establish a reciprocal communication by activating, incurring a certain cost, any of their incident links. The goal of each player is to have all the other nodes as close as possible in the resulting network, while buying as few links as possible. According to this intuition, any model of the game must then appropriately address a balance between these two conflicting objectives. Motivated by the fact that a …
Network creation games model the creation and usage costs of networks formed by a set of selfish peers. Each peer has the ability to change the network in a limited way, e.g., by creating or deleting incident links. In doing so, a peer can reduce its individual communication cost. Typically, these costs are modeled by the maximum or average distance in the network. We introduce a generalized version of the basic network creation game (BNCG). In the BNCG (by Alon et al., SPAA 2010), each peer may replace one of its incident links by a link to an arbitrary peer. This is done in a selfish way in …
We study Nash equilibria and the price of anarchy in the classical 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. Since it was shown that the price of anarchy for trees is constant, if the tree conjecture were true, then the price of anarchy would be constant for $α>n$. Moreover, Demaine et al. conjectured that the price of a…
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…
Selfish behaviors are common in self-organized Mobile Ad hoc Networks (MANETs) where nodes belong to different authorities. Since cooperation of nodes is essential for routing protocols, various methods have been proposed to stimulate cooperation among selfish nodes. In order to provide sufficient incentives, most of these methods pay nodes a premium over their actual costs of participation. However, they lead to considerably large overpayments. Moreover, existing methods ignore mobility of nodes, for simplicity. However, owing to the mobile nature of MANETs, this assumption seems unrealistic.…
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…
User-generated content can be distributed at a low cost using peer-to-peer (P2P) networks, but the free-rider problem hinders the utilization of P2P networks. In order to achieve an efficient use of P2P networks, we investigate fundamental issues on incentives in content production and sharing using game theory. We build a basic model to analyze non-cooperative outcomes without an incentive scheme and then use different game formulations derived from the basic model to examine five incentive schemes: cooperative, payment, repeated interaction, intervention, and enforced full sharing. The resul…
In this paper we study a generalization of the classic \emph{network creation game} in the scenario in which the $n$ players sit on a given arbitrary \emph{host graph}, which constrains the set of edges a player can activate at a cost of $α\geq 0$ each. This finds its motivations in the physical limitations one can have in constructing links in practice, and it has been studied in the past only when the routing cost component of a player is given by the sum of distances to all the other nodes. Here, we focus on another popular routing cost, namely that which takes into account for each player …
Network creation games investigate complex networks from a game-theoretic point of view. Based on the original model by Fabrikant et al. [PODC'03] many variants have been introduced. However, almost all versions have the drawback that edges are treated uniformly, i.e. every edge has the same cost and that this common parameter heavily influences the outcomes and the analysis of these games. We propose and analyze simple and natural parameter-free network creation games with non-uniform edge cost. Our models are inspired by social networks where the cost of forming a link is proportional to the…
We consider a network creation game in which each player (vertex) has a fixed budget to establish links to other players. In our model, each link has unit price and each agent tries to minimize its cost, which is either its local diameter or its total distance to other players in the (undirected) underlying graph of the created network. Two versions of the game are studied: in the MAX version, the cost incurred to a vertex is the maximum distance between the vertex and other vertices, and in the SUM version, the cost incurred to a vertex is the sum of distances between the vertex and other ver…
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…
