Lower-level Game Research Articles

A Game-Based Incentive-Driven Offloading Framework for Dispersed Computing

The popularization of smart Internet of Things (IoT) devices has facilitated the development of fog/edge computing. However, these infrastructure-based service paradigms may fail to complete tasks successfully due to computation and communication overload, or damage in challenging scenarios such as disasters or traffic jams. Noticing that a crowd of devices with considerable idle resources could be available, we investigate the problems of addressing the computation and communication unavailability with peer assistance in this work. To this end, we propose a dispersed service framework for resource-exhausted scenarios that adaptively offloads users’ data to available network computation points. However, the users may not be able to achieve the offloading due to geographical hindrances. Consequently, the relay is introduced as a bridge for data offloading between the users and the network computation points. Furthermore, a game-based incentive-driven offloading mechanism is designed by analyzing and balancing the cost and gain factors of three main entities (users, relays, and network computation points). Considering the interactions among the entities, a two-level Stackelberg game is established for efficiently allocating potential computation resource, as well as balancing the utility conflicts due to the data offloading. Given the hierarchical interaction structure, the upper level game involves network computation points as followers and the relay as a leader, while the lower level game includes the relay as a follower and users as leaders. Moreover, to facilitate applicability in large-scale scenarios with multiple relays, we decompose multiple relays into multiple single relay problems using a tripartite matching strategy that assigns appropriate relays to users and network computation points. The simulation results demonstrate the effectiveness of the proposed game-based incentive-driven mechanism and show that it outperforms the baselines in terms of the overall utilities of the involved entities and the average energy consumption of users.

An incentive mechanism to promote residential renewable energy consumption in China's electricity retail market: A two-level Stackelberg game approach

This paper proposes an incentive mechanism considering three different participants: the government, retailers and residents. To comprehensively understand the impact factors contributing to renewable energy consumption, the incentive mechanism is conducted in two forms, monetary incentive and price incentive, under the regulation of government and retailers. A two-level Stackelberg game is formulated to operate the proposed incentive mechanism. In the upper-level game, the government first sets the optimal monetary incentive to minimize its cost and then retailers determine the optimal incentives to maximize their profits. Similarly, in the lower-level game, the retailers send the incentive signals to residents, directing them choose the optimal renewable energy consumption ratios to maximize their welfare. The existence and uniqueness of Stackelberg Equilibrium are proved and the optimal strategies for each participant are given. To better describe the characteristics of residents, the seasonal variation of power demand and renewable energy, such as photovoltaic and wind power, is taken into consideration in the case study. The results indicate that, first, the cooperation of government and retailers raises the consumption ratio by 51.80% compared with 26.03% of individual participation of retailers in the winter typical day, which is the most effective seasonal day to operate the proposed incentive mechanism. Second, monetary incentive and price incentive can both promote renewable energy consumption, but the enhancement with price incentive is 77.04%, which is more than 51.80% with monetary incentive, in the winter typical day as well. The results also suggest that the proposed incentive mechanism should be applied to strengthen the electricity retail market position and achieve the carbon reduction goals.

A Dynamic Hierarchical Framework for IoT-Assisted Digital Twin Synchronization in the Metaverse

Metaverse, also known as the Internet of 3-D worlds, has recently attracted much attention from both academia and industry. Each virtual subworld, operated by a virtual service provider (VSP), provides a type of virtual service. Digital twins (DTs), namely, digital replicas of physical objects, are key enablers. Generally, a DT belongs to the party that develops it and establishes the communication link between the two worlds. However, in an interoperable metaverse, data-like DTs can be “shared” within the platform. Therefore, one set of DTs can be leveraged by multiple VSPs. As the quality of the shared DTs may not always be satisfying, in this article, we propose an agile solution, i.e., a dynamic hierarchical framework, in which a group of Internet of Things devices in the lower level are incentivized to collectively sense physical objects’ status information and VSPs in the upper level determine synchronization intensities to maximize their payoffs. We adopt an evolutionary game approach to model the devices VSP selections and a simultaneous differential game to model the optimal synchronization intensity control problem. We further extend it as a Stackelberg differential game by considering some VSPs to be first movers. We provide open-loop solutions based on the control theory for both formulations. We theoretically and experimentally show the existence, uniqueness, and stability of the equilibrium to the lower level game and further provide a sensitivity analysis for various system parameters. Experiments show that the proposed dynamic hierarchical game outperforms the baseline.

Countermeasures of Financial Internal Supervision Institutions of Administrative Institutions Based on the Double Game

The state audit in the new era focuses on strengthening the restriction and supervision of public power, and it will inevitably require strengthening the audit and supervision of administrative institutions, which leads to the discussion of the efficiency of the internal supervision institutions in administrative institutions. In order to effectively control the finance internal supervision risk, a moral hazard monitoring model with a two-tier game mechanism is proposed. In the model, it establishes an upper-level game and a lower-level game analysis framework for the "lazy" and "Free-riding" behaviors in moral hazard. Combining the equilibrium conditions to explain the game results, and put forward the overall risk monitoring countermeasures for the two behaviors.

A master–slave game optimal scheduling strategy for park-integrated energy systems based on adjustable robust optimization

As the bridge between power companies and users, the integrated energy system has become one of the carriers of energy reform, energy-saving, and emission reduction. Based on this, a master–slave game bilevel optimization model considering power company–park-integrated energy system (PIES)–user is established. In the upper game, the power company, as the leader, takes the maximization of its interests as the goal to consider and formulate the price of purchasing and selling electricity with the park. As a follower, combined with the fluctuation of electricity price and the electricity demand of its equipment, the park determines the relationship between purchasing and selling electricity with the power company. In the lower-level game, the park becomes the leader, taking into account the energy needs of users and formulating a reasonable price for selling energy. Users, as followers, intend to maximize consumer surplus and adjust their energy demand strategies to achieve the best energy consumption experience. Analyzing the properties of the game, it is verified that there is a unique Nash equilibrium solution in the game model. At the same time, the idea of solving the distribution of the model is adopted, and the equilibrium solution of the model is obtained by using limited information. In addition, the output uncertainty of renewable energy in the park is dealt with by adjustable robust optimization. Finally, aiming at achieving a win–win situation among all stakeholders, the proposed game model is verified to effectively solve the equilibrium strategy problem among the PIES, the power company, and users through simulation analysis of an example.

Dynamic Edge Association and Resource Allocation in Self-Organizing Hierarchical Federated Learning Networks

Federated Learning (FL) is a promising privacy-preserving distributed machine learning paradigm. However, communication inefficiency remains the key bottleneck that impedes its large-scale implementation. Recently, hierarchical FL (HFL) has been proposed in which data owners, i.e., workers, can first transmit their updated model parameters to edge servers for intermediate aggregation. This reduces the instances of global communication and straggling workers. To enable efficient HFL, it is important to address the issues of edge association and resource allocation in the context of non-cooperative players, i.e., workers, edge servers, and model owner. However, the existing studies merely focus on static approaches and do not consider the dynamic interactions and bounded rationalities of the players. In this paper, we propose a hierarchical game framework to study the dynamics of edge association and resource allocation in self-organizing HFL networks. In the lower-level game, the edge association strategies of the workers are modelled using an evolutionary game. In the upper-level game, a Stackelberg differential game is adopted in which the model owner decides an optimal reward scheme given the expected bandwidth allocation control strategy of the edge server. Finally, we provide numerical results to validate that our proposed framework captures the HFL system dynamics under varying sources of network heterogeneity.

Energy Management Optimization of Microgrid Cluster Based on Multi-Agent-System and Hierarchical Stackelberg Game Theory

To realize the win-win benefits and resource coordination of the multilevel operating entities of a “microgrid cluster (MGC), microgrid (MG) and user” and improve the self-consumption of new energy in the MGC, this paper proposes an energy trading model and solution algorithm of an “MGC, MG and user” based on a multi-agent-system, incentive demand response, and hierarchical Stackelberg game theory. By analyzing the game objectives and strategies of these participants, the unique Stackelberg equilibrium (SE) of the hierarchical Stackelberg game is proved theoretically. The game optimization process is divided into two levels. In the upper-level game, the MGC as a leader stimulates the MG to participate in intracluster dispatching by establishing an internal price incentive mechanism. As the follower, the MG determines the number of electricity transactions based on the realized internal price to maximize its own profits. In the lower-level game, the MG leads the game by deciding electricity selling prices based on the load demands of users, and the user as follower adjust electricity consumption using strategies to balance expenditure and experience of electricity usage. Simulation results verified the effectiveness and good convergence of the proposed method and demonstrated that the proposed hierarchical game strategy can improve the economic benefits of each participant, which is conducive to the establishment of friendly grid-connected MGC.

The Standard Pessimistic Bilevel Problem

Pessimistic bilevel optimization problems, as do optimistic ones, possess a structure involving three interrelated optimization problems. Moreover, their finite infima are only attained under strong conditions. We address these difficulties within a framework of moderate assumptions and a perturbation approach which allows us to approximate such finite infima arbitrarily well by minimal values of a sequence of solvable single-level problems. To this end, as has already been done for optimistic problems, for the first time in the literature we introduce the standard version of the pessimistic bilevel problem. For its algorithmic treatment, we reformulate it as a standard optimistic bilevel program with a two follower Nash game in the lower level. The latter lower-level game, in turn, is replaced by its Karush--Kuhn--Tucker conditions, resulting in a single-level mathematical program with complementarity constraints. We prove that the perturbed pessimistic bilevel problem, its standard version, the two follower game, as well as the mathematical program with complementarity constraints are equivalent with respect to their global minimal points. We study the more intricate connections between their local minimal points in detail. As an illustration, we numerically solve a regulator problem from economics for different values of the perturbation parameters.

OSNR game optimization with link capacity constraints in general topology WDM networks

This work studies games with coupled constraints in general topology optical wavelength-division multiplexed (WDM) networks towards optimizing channel optical signal-to-noise ratio (OSNR). We first develop a model to describe the network and an OSNR model for each link by investigating the interaction between the network and physical layers. The nonlinear threshold is considered as the link capacity constraint and we study the case in which channel powers are adjustable at optical switching nodes (e.g., optical cross-connects (OXCs)). An OSNR Nash game is formulated with coupled utilities and constraints, in which each player (channel) maximizes its own utility function related to minimizing its individual OSNR degradation. We exploit this OSNR Nash game in three types of network topologies: multi-link topology, quasi-ring topology and general topology. A hierarchical decomposition approach leads to a lower-level game for channels with no coupled constraints and a higher-level optimization problem for the network. Computation of equilibria based on this hierarchical algorithm is discussed and evaluated by simulation for each of the three network topologies.

DISCOUNTING AND AVERAGING IN GAMES ACROSS TIME SCALES

We introduce two-level discounted and mean-payoff games played by two players on a perfect-information stochastic game graph. The upper level game is a discounted or mean-payoff game and the lower level game is a (undiscounted) reachability game. Two-level games model hierarchical and sequential decision making under uncertainty across different time scales. For both discounted and mean-payoff two-level games, we show the existence of pure memoryless optimal strategies for both players and an ordered field property. We show that if there is only one player (Markov decision processes), then the values can be computed in polynomial time. It follows that whether the value of a player is equal to a given rational constant in two-level discounted or mean-payoff games can be decided in NP ∩ coNP . We also give an alternate strategy improvement algorithm to compute the value.

Discounting in Games across Time Scales

We introduce two-level discounted games played by two players on a perfect-information stochastic game graph. The upper level game is a discounted game and the lower level game is an undiscounted reachability game. Two-level games model hierarchical and sequential decision making under uncertainty across different time scales. We show the existence of pure memoryless optimal strategies for both players and an ordered field property for such games. We show that if there is only one player (Markov decision processes), then the values can be computed in polynomial time. It follows that whether the value of a player is equal to a given rational constant in two-level discounted games can be decided in NP intersected coNP. We also give an alternate strategy improvement algorithm to compute the value.

FORMULATION AND APPLICATIONS OF HIERARCHY GAMES

In this paper, I discuss the formulation and some applications of a framework called "hierarchy games". Hierarchy games are a game theoretical framework in which two or more games interact with one another. The interaction among games can be best described by the following two characteristics: (1) the outcome of a lower-level game could restrict the available actions of a player in higher-level. (2) the payoff of a higher-level player is shared by lower-level players. The above ideas were first proposed by Hausken in 1995. The paper attempts to develop further those ideas. First, some parts of the framework are defined more rigorously than Hausken's formulation. Secondly, some applications of the framework to the field of International Relations are discussed.