Bounding the price of anarchy, which quantifies the damage to social welfare due to selfish behavior of the participants, has been an important area of research. In this paper, we study this phenomenon in the context of a game modeling queuing systems: routers compete for servers, where packets that do not get service will be resent at future rounds, resulting in a system where the number of packets at each round depends on the success of the routers in the previous rounds. We model this as an (infinitely) repeated game, where the system holds a state (number of packets held by each queue) that arises from the results of the previous round. We assume that routers satisfy the no-regret condition, e.g. they use learning strategies to identify the server where their packets get the best service.
Classical work on repeated games makes the strong assumption that the subsequent rounds of the repeated games are independent (beyond the influence on learning from past history). The carryover effect caused by packets remaining in this system makes learning in our context result in a highly dependent random process. We analyze this random process and find that if the capacity of the servers is high enough to allow a centralized and knowledgeable scheduler to get all packets served even with double the packet arrival rate, and queues use no-regret learning algorithms, then the expected number of packets in the queues will remain bounded throughout time, assuming older packets have priority. This paper is the first to study the effect of selfish learning in a queuing system, where the learners compete for resources, but rounds are not all independent: the number of packets to be routed at each round depends on the success of the routers in the previous rounds.
We consider the problem of selfish agents in discrete-time queuing systems, where competitive queues try to get their packets served. In this model, a queue gets to send a packet each step to one of the servers, which will attempt to serve the oldest arriving packet, and unprocessed packets are returned to each queue. We model this as a repeated game where queues compete for the capacity of the servers, but where the state of the game evolves as the length of each queue varies, resulting in a highly dependent random process. Earlier work by the authors [EC'20] shows that with no-regret learner…
Singapore University of Technology and Design（新加坡科技设计大学）；Forth AI（Forth人工智能公司）；University of Colorado Denver（科罗拉多大学丹佛分校）
There is a rapidly growing demand for itinerary planning in tourism but this task remains complex and difficult, especially when considering the need to optimize for queuing time and crowd levels for multiple users. This difficulty is further complicated by the large amount of parameters involved, i.e., attraction popularity, queuing time, walking time, operating hours, etc. Many recent works propose solutions based on the single-person perspective, but otherwise do not address real-world problems resulting from natural crowd behavior, such as the Selfish Routing problem, which describes the c…
CREST, ENSAE Paris（国立统计与经济行政学校经济研究与应用中心）；Centre Borelli, ENS Paris-Saclay（巴黎萨克雷高等师范学校博雷利中心）；CRITEO AI Lab（Criteo人工智能实验室）
Motivated by packet routing in computer networks, online queuing systems are composed of queues receiving packets at different rates. Repeatedly, they send packets to servers, each of them treating only at most one packet at a time. In the centralized case, the number of accumulated packets remains bounded (i.e., the system is \textit{stable}) as long as the ratio between service rates and arrival rates is larger than $1$. In the decentralized case, individual no-regret strategies ensures stability when this ratio is larger than $2$. Yet, myopically minimizing regret disregards the long term e…
This paper considers a class of reinforcement-learning that belongs to the family of Learning Automata and provides a stochastic-stability analysis in strategic-form games. For this class of dynamics, convergence to pure Nash equilibria has been demonstrated only for the fine class of potential games. Prior work primarily provides convergence properties of the dynamics through stochastic approximations, where the asymptotic behavior can be associated with the limit points of an ordinary-differential equation (ODE). However, analyzing global convergence through the ODE-approximation requires th…
We consider the stability of matchings when individuals strategically submit preference information to a publicly known algorithm. Most pure Nash equilibria of the ensuing game yield a matching that is unstable with respect to the individuals' sincere preferences. We introduce a well-supported minimal dishonesty constraint, and obtain conditions under which every pure Nash equilibrium yields a matching that is stable with respect to the sincere preferences. The conditions on the matching algorithm are to be either fully-randomized, or monotonic and independent of non-spouses (INS), an IIA-like…
Communication Enhances LLMs' Stability in Strategic Thinking
Network Science Institute Northeastern University（东北大学网络科学研究所）；Department of Mechanical and Industrial Engineering, Institute of Experiential AI（机械与工业工程系，体验式人工智能研究所）
We introduce a game-theoretic approach to the study of recommendation systems with strategic content providers. Such systems should be fair and stable. Showing that traditional approaches fail to satisfy these requirements, we propose the Shapley mediator. We show that the Shapley mediator fulfills the fairness and stability requirements, runs in linear time, and is the only economically efficient mechanism satisfying these properties.
Beyond Right to be Forgotten: Managing Heterogeneity Side Effects Through Strategic Incentives
Duke Kunshan University（杜克昆山大学）；Westlake University（西交大学）；Huazhong University of Science and Technology（华中科技大学）；Hong Kong University of Science and Technology（香港科技大学）
Evolutionary game theory is used to model the evolution of competing strategies in a population of players. Evolutionary stability of a strategy is a dynamic equilibrium, in which any competing mutated strategy would be wiped out from a population. If a strategy is weak evolutionarily stable, the competing strategy may manage to survive within the network. Understanding the network-related factors that affect the evolutionary stability of a strategy would be critical in making accurate predictions about the behaviour of a strategy in a real-world strategic decision making environment. In this …
In this paper, we employ a hypergame framework to analyze the single-leader-multiple-followers (SLMF) Stackelberg security game with two typical misinformed situations: misperception and deception. We provide a stability criterion with the help of hyper Nash equilibrium (HNE) to investigate both strategic stability and cognitive stability of equilibria in SLMF games with misinformation. In fact, we find mild stable conditions such that the equilibria with misperception and deception can become HNE. Moreover, we discuss the robustness of the equilibria to reveal whether players have the ability…
We study a recently introduced class of strategic games that is motivated by and generalizes Schelling's well-known residential segregation model. These games are played on undirected graphs, with the set of agents partitioned into multiple types; each agent either occupies a node of the graph and never moves away or aims to maximize the fraction of her neighbors who are of her own type. We consider a variant of this model that we call swap Schelling games, where the number of agents is equal to the number of nodes of the graph, and agents may {\em swap} positions with other agents to increase…
This paper considers a class of reinforcement-based learning (namely, perturbed learning automata) and provides a stochastic-stability analysis in repeatedly-played, positive-utility, finite strategic-form games. Prior work in this class of learning dynamics primarily analyzes asymptotic convergence through stochastic approximations, where convergence can be associated with the limit points of an ordinary-differential equation (ODE). However, analyzing global convergence through an ODE-approximation requires the existence of a Lyapunov or a potential function, which naturally restricts the ana…
A critical aspect in strategic modeling of transportation systems is user heterogeneity. In many real-world scenarios, e.g., when tolls are charged and drivers have different trade-offs between time and money, or when they get informed about current congestion by different routing apps, modeling users as rational decision makers with homogeneous utility functions becomes too restrictive. While global asymptotic stability of user equilibria in homogeneous routing games is known to hold for a broad class of evolutionary dynamics, the stability analysis of user equilibria in heterogeneous routing…
We introduce a new measure of the discrepancy in strategic games between the social welfare in a Nash equilibrium and in a social optimum, that we call selfishness level. It is the smallest fraction of the social welfare that needs to be offered to each player to achieve that a social optimum is realized in a pure Nash equilibrium. The selfishness level is unrelated to the price of stability and the price of anarchy and is invariant under positive linear transformations of the payoff functions. Also, it naturally applies to other solution concepts and other forms of games. We study the selfish…
This paper introduces a novel payoff-based learning scheme for distributed optimization in repeatedly-played strategic-form games. Standard reinforcement-based learning exhibits several limitations with respect to their asymptotic stability. For example, in two-player coordination games, payoff-dominant (or efficient) Nash equilibria may not be stochastically stable. In this work, we present an extension of perturbed learning automata, namely aspiration-based perturbed learning automata (APLA) that overcomes these limitations. We provide a stochastic stability analysis of APLA in multi-player …
We consider strategic games that are inspired by Schelling's model of residential segregation. In our model, the agents are partitioned into k types and need to select locations on an undirected graph. Agents can be either stubborn, in which case they will always choose their preferred location, or strategic, in which case they aim to maximize the fraction of agents of their own type in their neighborhood. We investigate the existence of equilibria in these games, study the complexity of finding an equilibrium outcome or an outcome with high social welfare, and also provide upper and lower bou…
Analysis of Equilibria and Strategic Interaction in Complex Networks
GRASP Laboratory, School of Engineering and Applied Science, University of Pennsylvania（宾夕法尼亚大学工程与应用科学学院）；Department of Operations and Information Management, Wharton School, University of Pennsylvania（宾夕法尼亚大学沃顿商学院运营管理系）
Residential segregation in metropolitan areas is a phenomenon that can be observed all over the world. Recently, this was investigated via game-theoretic models. There, selfish agents of two types are equipped with a monotone utility function that ensures higher utility if an agent has more same-type neighbors. The agents strategically choose their location on a given graph that serves as residential area to maximize their utility. However, sociological polls suggest that real-world agents are actually favoring mixed-type neighborhoods, and hence should be modeled via non-monotone utility func…
We study strategic network formation games in which agents attempt to form (costly) links in order to maximize their network centrality. Our model derives from Jackson and Wolinsky's symmetric connection model, but allows for heterogeneity in agent utilities by replacing decay centrality (implicit in the Jackson-Wolinsky model) by a variety of classical centrality and game-theoretic measures of centrality. We are primarily interested in characterizing the asymptotically pairwise stable networks, i.e. those networks that are pairwise stable for all sufficiently small, positive edge costs. We un…
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 o…
Coalition Formation in LLM Agent Networks: Stability Analysis and Convergence Guarantees
Department of Compute Science, The University of Hong Kong（香港大学计算机科学系）；Brain Investing Limited（Brain Investing有限公司）；Stellaris AI Limited（Stellaris AI有限公司）
