Network games have been commonly used as a formalism to study the provisioning of public goods, and mechanism design as a tool to induce socially desirable effort from agents. When the type of public goods is non-excludable, i.e., an agent can opt out of the mechanism and yet continue to benefit from actions of those who remain in the mechanism, existing literature has shown the difficulty of designing transfer mechanisms that simultaneously achieve social optimality, weak budget balance, and voluntary participation. This challenge stems from the fact that the participation of some agents creates excessive positive externality, thereby reducing the incentive for others to voluntarily opt in. To get around this difficulty, we consider instead a sequential model whereby agents are invited in some order σ to commit to the mechanism, with each agent’s commitment contingent on the decisions of those preceding it and in anticipation of those following it. This gives rise to the notion of sequential participation referred to as σ -voluntary participation ( σ -VP), which is a full-participation outcome under the given order. We show that satisfying the conventional voluntary participation condition is equivalent to satisfying σ -VP for all orderings σ . Furthermore, we demonstrate via examples that it is possible to simultaneously achieve social optimality, weak budget balance, and full participation in the sense of σ -VP, especially in large systems.
Blockchain networks are exposed to several security attacks, including selfish mining attacks, which occur when a miner or a group of miners withhold their newly mined blocks and keep them in their private chain rather than immediately broadcasting them to the rest of the network. This strategy forces honest miners to waste their resources and degrades the efficiency of the network. This paper introduces a novel game-theoretic approach leveraging a war of attrition framework to mitigate selfish mining in PoW blockchains. We design reward and punishment mechanisms to incentivize miners to opt for honest strategies and discourage them from choosing selfish tactics. Additionally, a reputation function is utilized to ensure that miners are not indifferent to the presence of selfish miners in the network. Moreover, we examine whether the honest strategy remains stable within the system using the evolutionary game theory. Our findings indicate that the honest strategy is indeed stable under the proposed model. Our solution will help mitigate the threat of selfish mining in blockchain systems.
In real society, interactions between individuals are accompanied by emotional changes, which in turn affect their decisions. This paper proposes an emotion-strategy persistence mechanism that represents individuals’ value orientations through changes in emotions. Intelligent agents are classified into selfish, competitive individuals and mutually beneficial, non-competitive individuals. A positive-negative emotion threshold is introduced to define the emotional states of intelligent agents. A positive emotional state indicates that the intelligent agent is relatively satisfied with the current strategy, leading to persistence in maintaining it. Conversely, the agent is more inclined to change its current strategy. In addition, this paper introduces the concept of emotional sensitivity to measure the amplitude of emotional fluctuations in intelligent agents and introduces strategy duration sensitivity to measure the willingness of intelligent agents to change their current strategy. Extensive simulation experiments show that non-competitive individuals play a decisive role in promoting and emerging cooperative behavior within the group. When the positive-negative emotion threshold is higher and the emotional sensitivity is greater, the level of group cooperation is higher. However, the impact of strategy duration sensitivity on the group cooperation rate exhibits a non-monotonic trend, with an optimal strategy duration sensitivity that maximizes the level of group cooperation.
Various modeling approaches have been proposed in the literature to forecast the evolution of wildland fires over time and space and to control them. Here, a methodology based on cooperative game theory is proposed to optimize the use of limited resources to control a fire, such as firefighters, Canadair, drones, etc. In particular, the Shapley value, i.e., a solution concept of cooperative games, is exploited. It provides a measure of the value of each player in a so-called transferable-utility game, and recently it has been used to evaluate the importance of edges or nodes in a network. In the proposed approach, the wildland area is modeled as a network, in which nodes represent areas of particular interest. Some of them may become fire outbreaks, from which the fire can reach other nodes. The edges represent possible directions of fire evolution and can be weighted by taking into account several features, including elevation of the terrain, kind of vegetation, and estimated rate of spread. A temperature diffusion process is considered, where the global rate of diffusion is given by the second smallest eigenvalue of the weighted Laplacian matrix of the network. Then, a transferable-utility game is defined, where players form a subset of the edge set, and the utility function is related to the decrease of the global rate of diffusion of the fire when one or more edges are removed. This corresponds to control diffusion paths from a fire outbreak. The Shapley values are exploited to decide the order in which the edges should be removed, that is, how one should act with fire-extinguishing resources, in such a way as to effectively reduce the global fire diffusion rate.
In this paper, we develop a Cournot competition model to analyze a competitive wireless communications market where service providers (SPs) utilize both proprietary bandwidth—exclusively owned and consistently available—and intermittent bandwidth, which becomes available sporadically. Previous studies have considered such a setting where SPs offer a non-intermittent service, meaning that users must be served at all times. Here, we instead consider SPs that offer an intermittent service, where users can tolerate delays in service but at a cost. Our model captures how the availability of intermittent bandwidth affects the service latency experienced by users, the strategies adopted by SPs, and their resulting revenues. Through theoretical analysis, we find that intermittent bandwidth can significantly impact market dynamics, lowering barriers to entry and enabling new entrants to compete effectively against established incumbents. This increased competition can lead to favorable outcomes for consumers, such as lower prices and improved service quality. We support our findings with simulations that illustrate how intermittent bandwidth can be used and its effects on the market. Our study highlights the strategic importance of intermittent bandwidth in shaping competitive markets and offers insights into how it can be leveraged to enhance efficiency and innovation in the telecommunications industry.
We consider a game-theoretic variant of an interval scheduling problem. Every job is associated with a length, a weight, and a color. Each player controls all the jobs of a specific color, and needs to decide on a processing interval for each of its jobs. Jobs of the same color can be processed simultaneously by the machine. A job is covered if the machine is configured to its color during its whole processing interval. The goal of the machine is to maximize the sum of weights of all covered jobs, and the goal of each player is to place its jobs such that the sum of weights of covered jobs from its color is maximized. The study of this game is motivated by several applications like antenna scheduling for wireless networks. We first show that given a strategy profile of the players, the machine scheduling problem can be solved in polynomial time. We then study the game from the players' point of view. We analyze the existence of Nash equilibria, its computation, and inefficiency. We distinguish between instances of the classical interval scheduling problem, in which every player controls a single job, and instances in which color sets may include multiple jobs.
In the theory of multi-agent systems, deception refers to the strategic manipulation of information to influence the behavior of other agents, ultimately altering the long-term dynamics of the entire system. Recently, this concept has been examined in the context of model-free Nash equilibrium seeking (NES) algorithms for noncooperative games [16]. Specifically, it was demonstrated that players can exploit knowledge of other players’ exploration signals to drive the system toward a “deceptive” Nash equilibrium, while maintaining the stability of the closed-loop system. To extend this insight beyond the duopoly case, in this paper we conduct a comprehensive study of deception mechanisms in N-player oligopoly markets. By leveraging the structure of these games and employing stability techniques for nonlinear dynamical systems, we provide game-theoretic insights into deception and derive specialized results, including stability conditions. These results allow players to systematically adjust their NES dynamics by tuning gains and signal amplitudes, all while ensuring closed-loop stability. Additionally, we introduce novel sufficient conditions to demonstrate that the (practically) stable equilibrium point of the deceptive dynamics corresponds to a true Nash equilibrium of a different game, which we term the “deceptive game.” Our results show that, under the proposed adaptive dynamics with deception, a victim firm may develop a distorted perception of its competitors’ product appeal, which could lead to setting suboptimal prices.
In classical job-scheduling games, each job behaves as a selfish player, choosing a machine to minimize its own completion time. To reduce the equilibria inefficiency, coordination mechanisms [8] are employed, allowing each machine to follow its own scheduling policy. In this paper we study the effects of incorporating rank-based utilities within coordination mechanisms across environments with either identical or unrelated machines. With rank-based utilities, players aim to perform well relative to their competitors, rather than solely minimizing their completion time. We first demonstrate that even in basic setups, such as two identical machines with unit-length jobs, a pure Nash equilibrium (NE) assignment may not exist. This observation motivates our inquiry into the complexity of determining whether a given game instance admits a NE. We prove that this problem is NP-complete, even in highly restricted cases. In contrast, we identify specific classes of games where a NE is guaranteed to exist, or where the decision problem can be resolved in polynomial time. Additionally, we examine how competition impacts the efficiency of Nash equilibria, or sink equilibria if a NE does not exist. We derive tight bounds on the price of anarchy, and show that competition may either enhance or degrade overall performance.
We propose a novel hypergraph information structure for a Cournot network competition model and formulate it as a distributed optimization problem which we solve with continuous-time evolutionary game theoretic techniques that result in a dynamical system. The proposed hypergraph structure is more efficient and compact in terms of information transmission than a bipartite graph and exhibits faster convergence of the respective distributed evolutionary dynamical system. The equilibrium point of the distributed evolutionary dynamical system is unique and has the economic interpretation of the market clearing point. Thus, fast attainment is associated with economic benefits like price stability and efficient resource allocation.
In this work, we study a generalized Fisher market model that incorporates social influence. In this extended model, a buyer's utility depends not only on their own resource allocation but also on the allocations received by their competitors. We propose a novel competitive equilibrium formulation for this generalized Fisher market using a variational inequality approach. This framework effectively captures competitive equilibrium in markets that extend beyond the traditional assumption of homogeneous utility functions. We analyze key structural properties of the proposed variational inequality problem, including monotonicity, stability, and uniqueness. Additionally, we present two decentralized learning algorithms for buyers to achieve competitive equilibrium: a two-timescale stochastic approximation-based tâtonnement method and a trading-post mechanism-based learning method. Finally, we validate the proposed algorithms through numerical simulations.
The classical game theory considers rational players and proposes Nash equilibrium (NE) as the solution. However, real-world scenarios rarely feature rational players; instead, players make inconsistent and irrational decisions. Often, irrational players exhibit herding behaviour by simply following the majority. In this paper, we consider a mean-field game with α -fraction of rational players and the rest being herding-irrational players. For such a game, we introduce a novel concept of equilibrium named α -Rational NE (in short, α -RNE). We extensively analyze the α -RNEs and their implications in games with two actions. Due to herding-irrational players, new equilibria may arise, and some classical NEs may be deleted. We establish that the rational players are not harmed but benefit from the presence of irrational players. More interestingly, in some examples, the rational players attain higher utility (under α -RNE) than even the social optimal utility (in the classical setting), by leveraging upon the herding behaviour of irrational players. Surprisingly, the irrational players may also benefit by not being rational. We observe that irrational players do not lose compared to some classical NEs for participation and bandwidth-sharing games. Importantly, in bandwidth-sharing game, the irrational players also receive utility near social optimal utility. Such examples indicate that it may sometimes be ‘rational’ to be irrational.
The advent of cryptocurrency introduced by Bitcoin ignited an explosion of technological and entrepreneurial interest in payment processing. The user scale of Bitcoin is dynamic, and the participating identities are anonymous, which will lead to more hidden, sophisticated and intelligent money laundering crimes. Therefore, in order to realize intelligent anti-money laundering, it is necessary to accurately detect abnormal transactions. Recently, graph representation learning has shown strong advantages in the field of machine learning, and the current blockchain anomaly detection models based on graph representation learning are mainly designed for static graphs, however, real-world graphs evolve over time. Based on this, this paper proposes a block-chain abnormal transaction detection model DynAEGCN based on dynamic graph representation learning. This model uses the autoencoder as the framework. Firstly, the encoder uses the graph convolutional neural networks to gather neighborhood information to obtain low-dimensional feature vectors. Then, considering the dynamics of graphs, the GRU network is used to evolve the graph model itself over time. Finally, the decoder reconstructs the adjacency matrix and compares it with the real graph to construct the loss. Extensive experiments on the Bitcoin transaction dataset for edge classification tasks against financial crimes show that DynAEGCN model has better performance compared with related approaches.
We consider the problem of preserving a large amount of data generated inside base station-less sensor networks when sensor nodes are controlled by different authorities and behave selfishly. We modify the VCG mechanism to guarantee that each node, including the source nodes with overflow data packets, will voluntarily participate in data preservation. The mechanism ensures that each node truthfully reports its private type and network achieves efficiency for all the preserved data packets. Extensive simulations are conducted to further validate our results.
The increasing growth of maritime activities leads to the challenges for processing the maritime data. However, the resources-limited maritime devices cannot meet the requirements of transmission delay and energy consumption. In this paper, we investigate the resource allocation for computation offloading in maritime communication networks via game theory to improve the offloading efficiency and reduce the energy consumption of maritime devices. Specifically, we propose an optimization problem that jointly optimizes the offloading data, the computation resource allocation of unmanned surface vehicle (USV) and the allocation of acoustic channels, with the objective of minimizing the total energy consumption of underwater wireless sensor (UWS). Despite the nonconvexity of the joint optimization problem, we propose a layered structure and decompose it into a top-problem for optimizing the data offloading, a middleproblem for optimizing the computation resource allocation of USV, a bottom problem for optimizing the channel allocation. We conduct simulations to validate the effectiveness and efficiency of the proposed algorithms.
In this paper we consider a dilemma that arises in bandwidth scanning problems associated with the design of agents’ scanning strategies based on the principle of rationality and the principle of insufficient reasons. On one hand, engaging tools that estimate a network’s parameters allows an agent to act rationally to maximize its payoff. On the other hand, utilizing such engagement incurs extra costs associated with scanning. In particular, if the agent does not employ such tools, then the involved expenses can be reduced, although such a strategy might also cause a reduction in detection probability since in such cases the agent has to design strategy based on the principle of insufficient reasons (also called principle of indifference). In this paper we model this dilemma as a non-zero sum stochastic game between two players (Scanner and Invader). The equilibrium is found in closed form in stationary strategies via solving the corresponding Shapley-Bellman equations, and its dependence on network parameters is illustrated.
Deterministic Networking (DetNet) provides guaranteed packet transport services of ultra-low packet loss and bounded delay for the critical traffic in real-time applications such as the industrial control and the power grid. DetNet guarantees reliable packet transmissions by forwarding replicated packets on redundant paths in parallel. This service protection mechanism of DetNet is Packet Replication Elimination and Ordering Functions (PREOF). However, how to obtain the redundant paths and implement the packet replication and elimination functions of the PREOF remains to be a great challenge. This paper proposes an improved PREOF mechanism based on Segment Routing (SR-PREOF). It designs an edge-disjoint path-pair routing algorithm based on the improved Link Pruning method (LP-EDJPP). The proposed SR-PREOF implements the scheme with the SR technology. Network simulation results show that the proposed SRPREOF effectively improves the packet reception rate and reduces the end-to-end worst-case latency bound while achieving the comparable path reliability performance compared with the traditional PREOF. The packet reception rate of the SR-PREOF increases by 5.6% and the end-to-end worst-case latency bound decreases by 10.89% compared to the PREOF when the offered load is 0.7.
This paper studies budgeted adversarial resource utilization game, where one of the player’s (designer) strategy is the utilization of resources while the other player’s (adversary) role is to police the resources for misuse. In this context, we consider routing games where a designer plans routes on a computer network and the adversary intercepts the routes on the network. Another example is in determining adversarial strategies to block access to travel or resources that may be considered to pose a risk to society, e.g. during a pandemic where the population (designer) goal may not be coincide with the societal goal of minimizing accessing a banned resource. We model this as a zero-sum game with constraints on the adversary or designer budgets. While zero-sum games can be solved using linear programs, we illustrate faster combinatorial methods to solve the problem. We first consider the resource access problem game on a bipartite graph where both the designer and the adversary have independent budget constraints and distinct costs and show a fast algorithm to determine a Nash equilibrium. We also consider the situation where the designer would strategize on paths in a general graph. In this application of determining network paths, where the adversary would attack edges in order to block the paths, we also discuss the case of multiple designers and, in particular show faster algorithms when there are 2 designers. These results utilize properties of minimum cuts in 2-commodity flow routing.
In this paper, we consider the problem of determining how a joint (dual) radar and communication system should divide its effort between supporting its radar and communication tasks in the presence of a jammer that wants to obstruct the system's work by means of jamming. The system, besides the basic objective consisting of two tasks (a) to communicate with a receiver and (b) to track a radar target through the reflections witnessed at the system, also has the secondary objective to achieve the basic objective in a manner that is as unpredictable as possible to the jammer. The signal to interference and noise ratio (SINR) of the radar and communication's SINR are considered as the metrics that reflect the radar and communication tasks, respectively. The entropy associated with a system's strategy to switch between two tasks is considered as a metric that reflects unpredictability of its strategy for the jammer. We model this problem by a Bayesian game for a scenario where the system is at a disadvantage to access information about environmental parameters relative to the jammer. The established uniqueness of the equilibrium reflects stability of the designed anti-jamming strategy, even in such a disadvantageous situation for the system.
Service function chaining (SFC), consisting of a sequence of virtual network functions (VNFs) (i.e., firewalls and load balancers), is an effective service provision technique in modern data center networks. By requiring cloud user traffic to traverse the VNFs in order, SFC improves the security and performance of the cloud user applications. In this paper, we study how to place an SFC inside a data center to minimize the network traffic of the virtual machine (VM) communication. We take a cooperative multi-agent reinforcement learning approach, wherein multiple agents collaboratively figure out the traffic-efficient route for the VM communication. Underlying the SFC placement is a fundamental graph-theoretical problem called the k-stroll problem. Given a weighted graph G(V, E), two nodes s, t ∈ V , and an integer k, the k-stroll problem is to find the shortest path from s to t that visits at least k other nodes in the graph. Our work is the first to take a multi-agent learning approach to solve k-stroll problem. We compare our learning algorithm with an optimal and exhaustive algorithm and an existing dynamic programming(DP)-based heuristic algorithm. We show that our learning algorithm, although lacking the complete knowledge of the network assumed by existing research, delivers comparable or even better VM communication time while taking two orders of magnitude of less execution time.
We model in this paper the multipopulation vaccinatinon game over a fully connected graph. Each player decides whether to purchase a vaccine or not, and if they do, then they further decide which vaccine to purchase among a finite number of vaccine producers. The players need not be indistinguishable. A potential consumer belongs to a risk type that characterizes how important it is for them to be vaccinated. The cost of a vaccine may depend on the demand, on the cost of the production, and on the consumer’s class. We prove in the existence of an equilibrium within pure policies in the general multipopulation case. We further derive some properties of the equilibria in the case of a single risk-class.
