We study a game-theoretic variant of the maximum circulation problem. In a flow allocation game, we are given a directed flow network. Each node is a rational agent and can strategically allocate any incoming flow to the outgoing edges. Given the strategy choices of all agents, a maximal circulation that adheres to the chosen allocation strategies evolves in the network. Each agent wants to maximize the amount of flow through her node. Flow allocation games can be used to express strategic incentives of clearing in financial networks. We provide a cumulative set of results on the existence and computational complexity of pure Nash and strong equilibria, as well as tight bounds on the (strong) prices of anarchy and stability. Our results show an interesting dichotomy: Ranking strategies over individual flow units allow to obtain optimal strong equilibria for many objective functions. In contrast, more intuitive ranking strategies over edges can give rise to unfavorable incentive properties.
In the game theory literature, there appears to be little research on equilibrium selection for normal-form games with an infinite strategy space and discontinuous utility functions. Moreover, many existing selection methods are not applicable to games involving both cooperative and noncooperative scenarios (e.g., "games on signed graphs"). With the purpose of equilibrium selection, the power allocation game developed in \cite{allocation}, which is a static, resource allocation game on signed graphs, will be reformulated into an extensive form. Results about the subgame perfect Nash equilibria…
We characterize the assignment games which admit a population monotonic allocation scheme (PMAS) in terms of efficiently verifiable structural properties of the nonnegative matrix that induces the game. We prove that an assignment game is PMAS-admissible if and only if the positive elements of the underlying nonnegative matrix form orthogonal submatrices of three special types. In game theoretic terms it means that an assignment game is PMAS-admissible if and only if it contains a veto player or a dominant veto mixed pair or is composed of from these two types of special assignment games. We a…
The well-known Braess paradox in congestion games states that adding an additional road to a transportation network may increase the total travel time, and consequently decrease the overall efficiency. Motivated by this, this paper presents a paradox in a similar spirit emerging from another distributed resource allocation game on networks, namely the power allocation game between countries developed in \cite{allocation}. The paradox is that by having additional friends may actually decrease a country's total welfare in equilibrium. Conditions for this paradox to occur as well as some price of…
For vertex cover games (introduced by Deng et al., Math. Oper. Res., 24:751-766, 1999), we investigate population monotonic allocation schemes (introduced by Sprumont, Games Econ. Behav., 2: 378-394, 1990). We show that the existence of a population monotonic allocation scheme (PMAS for short) for vertex cover games can be determined efficiently and that a PMAS, if exists, can be constructed accordingly. We also show that integral PMAS-es for vertex cover games can be characterized with stable matchings and be enumerated by employing Gale-Shapley algorithm (introduced by Gale and Shapley, Amer…
The concept of Owen point, introduced in Guardiola et al. (2009), is an appealing solution concept that for Production-Inventory games (PI-games) always belongs to their core. The Owen point allows all the players in the game to operate at minimum cost but it does not take into account the cost reduction induced by essential players over their followers (fans). Thus, it may be seen as an altruistic allocation for essential players what can be criticized. The aim this paper is two-fold: to study the structure and complexity of the core of PI-games and to introduce new core allocations for PI-ga…
For multiple emergencies caused by natural disasters, it is crucial to allocate resources equitably to each emergency location, especially when the availability of resources is limited in quantity. This paper has developed a multi-event crisis management system using a non-cooperative, complete information, strategic form game model. In the proposed system, each emergency event is assumed to occur in different locations simultaneously. These locations are represented as the players in the game, competing with the other players for an optimal allocation of scarce resources available at differen…
Richman games are zero-sum games, where in each turn players bid in order to determine who will play next [Lazarus et al.'99]. We extend the theory to impartial general-sum two player games called \emph{bidding games}, showing the existence of pure subgame-perfect equilibria (PSPE). In particular, we show that PSPEs form a semilattice, with a unique and natural \emph{Bottom Equilibrium}. Our main result shows that if only two actions available to the players in each node, then the Bottom Equilibrium has additional properties: (a) utilities are monotone in budget; (b) every outcome is Pareto-ef…
This paper studies a special kind of equilibrium termed as "balanced equilibrium" which arises in the power allocation game defined in \cite{allocation}. In equilibrium, each country in antagonism has to use all of its own power to counteract received threats, and the "threats" made to each adversary just balance out the threats received from that adversary. This paper establishes conditions on different types of networked international environments in order for this equilibrium to exist. The paper also links the existence of this type of equilibrium on structurally balanced graphs to the Hall…
We present a partial operator-theoretic characterization of approachability principle and based on this characterization, we interpret a particular distributed payoff allocation algorithm to be a sequence of time-varying paracontractions. Further, we also propose a distributed algorithm, under the context of coalitional game, on time-varying communication networks. The state in the proposed algorithm converges to a consensus within, the predefined, desired set. For convergence analysis, we rely on the operator-theoretic property of paracontraction.
How is efficiency affected when demand excesses over supply are signalled through waiting in queues? We consider a class of congestion games with a nonatomic set of players of a constant mass, based on a formulation of generic linear programs as sequential resource allocation games. Players continuously select activities such that they maximize linear objectives interpreted as time-average of activity rewards, while active resource constraints cause queueing. In turn, the resulting waiting delays enter in the optimization problem of each player. The existence of Wardrop-type equilibria and the…
This paper generalizes L.S. Shapley's celebrated value allocation theory on coalition games by discovering and applying a fundamental connection between stochastic path integration driven by canonical time-reversible Markov chains and Hodge-theoretic discrete Poisson's equations on general weighted graphs. More precisely, we begin by defining cooperative games on general graphs and generalize Shapley's value allocation formula for those games in terms of stochastic path integral driven by the associated canonical Markov chain. We then show the value allocation operator, one for each player def…
In this paper two algorithms with the goal of generating the equilibrium set of the power allocation game first developed in \cite{allocation} are proposed. Based on the first algorithm, the geometric property of the pure strategy Nash equilibrium set will be proven to be a collection of convex polytopes. The second, simulation-based, algorithm is developed to overcome the shortcoming of the first algorithm in terms of generating the equilibrium set efficiently and then making policy-relevant predictions based on the set. The second algorithm will be usefully applied to a real-world case study…
The decisions that human beings make to allocate time has significant bearing on economic output and to the sustenance of social networks. The time allocation problem motivates our formal analysis of the resource allocation game, where agents on a social network, who have asymmetric, private interaction preferences, make decisions on how to allocate time, a bounded endowment, over their neighbors. Unlike the well-known opinion formation game on a social network, our game appears not to be a potential game, and the Best-Response dynamics is non-differentiable making the analysis of Best-Respons…
A matching game is a cooperative profit game defined on an edge-weighted graph, where the players are the vertices and the profit of a coalition is the maximum weight of matchings in the subgraph induced by the coalition. A population monotonic allocation scheme is a collection of rules defining how to share the profit among players in each coalition such that every player is better off when the coalition expands. In this paper, we study matching games and provide a necessary and sufficient characterization for the existence of population monotonic allocation schemes. Our characterization also…
We introduce the Colonel Blotto game with favoritism, an extension of the famous Colonel Blotto game where the winner-determination rule is generalized to include pre-allocations and asymmetry of the players' resources effectiveness on each battlefield. Such favoritism is found in many classical applications of the Colonel Blotto game. We focus on the Nash equilibrium. First, we consider the closely related model of all-pay auctions with favoritism and completely characterize its equilibrium. Based on this result, we prove the existence of a set of optimal univariate distributions -- which ser…
In this paper, we introduce a game-theoretical formulation for a specific form of collaborative industrial relations called "Industrial Symbiotic Relation (ISR) games" and provide a formal framework to model, verify, and support collaboration decisions in this new class of two-person operational games. ISR games are formalized as cooperative cost-allocation games with the aim to allocate the total ISR-related operational cost to involved industrial firms in a fair and stable manner by taking into account their contribution to the total traditional ISR-related cost. We tailor two types of alloc…
Computational advertising has been studied to design efficient marketing strategies that maximize the number of acquired customers. In an increased competitive market, however, a market leader (a leader) requires the acquisition of new customers as well as the retention of her loyal customers because there often exists a competitor (a follower) who tries to attract customers away from the market leader. In this paper, we formalize a new model called the Stackelberg budget allocation game with a bipartite influence model by extending a budget allocation problem over a bipartite graph to a Stack…
In multi-rate IEEE 802.11 WLANs, the traditional user association based on the strongest received signal and the well known anomaly of the MAC protocol can lead to overloaded Access Points (APs), and poor or heterogeneous performance. Our goal is to propose an alternative game-theoretic approach for association. We model the joint resource allocation and user association as a matching game with complementarities and peer effects consisting of selfish players solely interested in their individual throughputs. Using recent game-theoretic results we first show that various resource sharing protoc…
Asymmetric-Information Resource Allocation Games: An LP Approach to Purposeful Deception
School of Aerospace Engineering, Georgia Institute of Technology（佐治亚理工学院航空航天工程学院）；College of Engineering and Computing, George Mason University（乔治梅森大学工程与计算学院）
In this article, we study the repeated routing game problem on a parallel network with affine latency functions on each edge. We cast the game setup in a LQR control theoretic framework, leveraging the Rosenthal potential formulation. We use control techniques to analyze the convergence of the game dynamics with specific cases that lend themselves to optimal control. We design proper dynamics parameters so that the conservation of flow is guaranteed. We provide an algorithmic solution for the general optimal control setup using a multiparametric quadratic programming approach (explicit MPC). F…
The matching game is a cooperative game where the value of every coalition is the maximum revenue of players in the coalition can make by forming pairwise disjoint partners. The multiple partners matching game generalizes the matching game by allowing each player to have more than one possibly repeated partner. In this paper, we study profit-sharing in multiple partners matching games. A central concept for profit-sharing is the core which consists of all possible ways of distributing the profit among individual players such that the grand coalition remains intact. The core of multiple partner…
Network Allocation Games with Anonymous Preferences
Royal Holloway, University of London（伦敦大学皇家霍洛威学院）；AGH University of Krakow（克拉科夫AGH科技大学）；Czech Technical University in Prague（布拉格捷克理工大学）；University of Southern Denmark（南丹麦大学）
We present a new type of coordination mechanism among multiple agents for the allocation of a finite resource, such as the allocation of time slots for passing an intersection. We consider the setting where we associate one counter to each agent, which we call karma value, and where there is an established mechanism to decide resource allocation based on agents exchanging karma. The idea is that agents might be inclined to pass on using resources today, in exchange for karma, which will make it easier for them to claim the resource use in the future. To understand whether such a system might w…
In networking and computing, resource allocation is typically addressed using classical sharing protocols as, for instance, the proportional division rule, the max-min fair allocation , or other solutions inspired by cooperative game theory. In this paper, we argue that, describing the resource allocation problem as a cooperative game, such classical resource allocation approaches, as well as associated notions of fairness, show important limitations. We identify in the individual satisfaction rate the key aspect of the challenge of defining a new notion of fairness and, consequently, a resour…
We study the equilibrium computation problem for two classical resource allocation games: atomic splittable congestion games and multimarket Cournot oligopolies. For atomic splittable congestion games with singleton strategies and player-specific affine cost functions, we devise the first polynomial time algorithm computing a pure Nash equilibrium. Our algorithm is combinatorial and computes the exact equilibrium assuming rational input. The idea is to compute an equilibrium for an associated integrally-splittable singleton congestion game in which the players can only split their demands in i…
Today's intelligent computing environments, including Internet of Things, cloud computing and fog computing, allow many organizations around the world to optimize their resource allocation regarding time and energy consumption. Due to the sensitive conditions of utilizing resources by users and the real-time nature of the data, a comprehensive and integrated computing environment has not yet been able to provide a robust and reliable capability for proper resource allocation. Although, traditional methods of resource allocation in a low-capacity hardware resource system are efficient for small…
Flemish Institute for Technological Research（弗拉芒技术研究院）
In this paper, a transmission-distribution systems flexibility market is introduced, in which system operators (SOs) jointly procure flexibility from different systems to meet their needs (balancing and congestion management) using a common market. This common market is, then, formulated as a cooperative game aiming at identifying a stable and efficient split of costs of the jointly procured flexibility among the participating SOs to incentivize their cooperation. The non-emptiness of the core of this game is then mathematically proven, implying the stability of the game and the naturally-aris…
Mobile edge computing seeks to provide resources to different delay-sensitive applications. However, allocating the limited edge resources to a number of applications is a challenging problem. To alleviate the resource scarcity problem, we propose sharing of resources among multiple edge computing service providers where each service provider has a particular utility to optimize. We model the resource allocation and sharing problem as a multi-objective optimization problem and present a \emph{Cooperative Game Theory} (CGT) based framework, where each edge service provider first satisfies its n…
This paper considers the setting where a cloud server services a static set or a dynamic sequence of tasks submitted by multiple clients. Every client wishes to assure honest execution of tasks by additionally employing a trusted third party (TTP) to re-compute the tasks with a certain probability. The cloud server makes a deposit for each task it takes, each client allocates a budget (including the wage for the server and the cost for possibly hiring TTP) for each task submitted, and every party has its limited fund for either deposits or task budgets. We study how to allocate the funds optim…
