An internet of things edge cloud continuum idle user resource pricing method based on a three-stage evolutionary game

Abstract

The application discloses an idle user resource auxiliary pricing and distribution method for an Internet of Things edge cloud continuum. First, a multi-agent resource coordination architecture composed of idle users, edge / cloud server resource providers (ECSP) and sensor devices is constructed to cope with the challenges of limited computing resources and prominent supply-demand contradiction in the edge environment. Second, a three-stage evolutionary game model is established to simulate the strategy evolution process of the three types of participating agents in resource pricing and procurement decision-making, thereby realizing dynamic adjustment of pricing and reasonable allocation of resources. In order to improve the rationality of strategy evolution and system stability, the application introduces a reputation incentive mechanism to reward reasonable pricing or resource purchase behavior and punish irrational behavior, and promotes the system evolution to converge to a stable and efficient strategy configuration. By constructing a replicator dynamic equation and combining a stability analysis method, the evolutionary stable strategy (ESS) of the system is identified to ensure the utility optimization of each participant and the maximization of the overall social welfare of the system in a complex dynamic environment.

Description

Technical Field

[0001] This invention relates to the field of IoT edge computing technology, specifically a method for pricing and allocating idle user resources in an IoT edge-cloud continuum environment. In particular, it involves using three-stage evolutionary game theory for dynamic pricing strategy formulation, resource allocation scheduling, and efficient collaborative utilization of idle user resources. Background Technology

[0002] With the rapid development of Internet of Things (IoT) technology and edge computing, the number of smart devices worldwide is exploding, and the amount of data generated and the demand for processing are also rising rapidly. It is predicted that by 2030, the number of IoT devices worldwide will exceed 32 billion, with a significant increase in the proportion of data generated by edge computing devices. This presents both tremendous opportunities and severe challenges for Edge / Cloud Server Resource Providers (ECSPs), especially in high-demand scenarios such as natural disasters and traffic congestion, where the risk of computing resource overload and service interruption is particularly prominent. Furthermore, the inherent high latency of traditional cloud computing services further exacerbates the pressure on resource supply.

[0003] While existing edge computing technologies can significantly improve computing efficiency, current resource pricing and allocation strategies often struggle to meet increasingly complex market demands, particularly in handling complex issues such as multi-party competition and information asymmetry. Most current research employs static pricing models that fail to adequately consider market fluctuations, sudden surges in demand, and the randomness of participant behavior, leading to inefficient resource allocation and underutilization, thus threatening the stability of the overall system. Furthermore, because participants are typically driven by self-interest, they are often unwilling to disclose their resource status information, further exacerbating the market's information asymmetry problem. Simultaneously, service providers also incur significant costs to acquire resource demand information, resulting in decreased resource allocation efficiency and reduced overall social welfare. In summary, the resource allocation and pricing problems in the current edge cloud computing field are mainly reflected in the following aspects:

[0004] 1) Information asymmetry and conflict of interest among multiple parties: Participants often conceal their own resource situation due to self-interest, exacerbating information asymmetry. Furthermore, conflicts of interest among multiple parties increase the complexity of resource allocation and reduce the overall efficiency of the system.

[0005] 2) Bounded rationality in dynamic market environments: Traditional resource allocation models mostly assume that participants have perfect rationality and sufficient information. However, the high degree of uncertainty in the actual market environment and the bounded rationality of participants greatly reduce the effectiveness of traditional models in practical applications.

[0006] 3) Balancing the interests of multiple parties and dynamic pricing issues: In a dynamic and highly competitive market environment, resource prices often fail to accurately reflect real-time supply and demand, making it difficult to protect the interests of all parties involved, resulting in uneven resource allocation and ultimately affecting overall social benefits.

[0007] To address the aforementioned challenges, this invention utilizes the theoretical framework of Evolutionary Game Theory to solve resource pricing and allocation problems. Unlike traditional game theory, which assumes perfectly rational participants, Evolutionary Game Theory is better suited for analyzing the strategy evolution of individuals with bounded rationality, and can more effectively address market uncertainties and complex multi-party interactions. Based on this, this invention proposes a three-stage dynamic evolutionary game model. By constructing a resource interaction model involving idle users, edge / cloud server resource providers (ECSPs), and sensor devices, it aims to resolve issues of resource supply and demand fluctuations, information asymmetry, and conflicts of interest. The core method of this invention includes evolutionary analysis of pricing strategies based on replicating dynamic equations, and uses incentive mechanisms to mitigate information asymmetry, ultimately achieving efficient resource allocation and maximizing the overall social welfare of the system. Summary of the Invention

[0008] This invention relates to the field of IoT edge-cloud continuum technology, specifically to a pricing method for idle user resources in IoT edge-cloud continuum based on three-stage evolutionary game theory.

[0009] This invention is achieved using the following technical solution:

[0010] A method for collaborative computing of unmanned aerial vehicles (UAVs) assisted by idle vehicle resources is characterized by the following steps:

[0011] 1) A dynamic resource pricing logic framework based on three-stage evolutionary game was constructed.

[0012] 2) A three-stage evolutionary game model is proposed for resource allocation and pricing of budget-constrained sensor devices in edge environments.

[0013] 3) For scenarios with information asymmetry, introduce joint pricing mechanisms and reputation incentive mechanisms to optimize pricing decisions, reduce resource misallocation caused by information asymmetry, and improve collaboration and fairness.

[0014] 4) Establish benefit functions and benefit matrices for the three parties (Idle USER, Edge / Cloud Server Resource Provider (ECSP), and Sensor) under different strategy choices, construct the revenue model of each participant, and quantify their expected utility based on different strategy combinations to guide replication dynamics.

[0015] 5) Construct the replication dynamic equation and perform stability analysis to obtain the evolutionarily stable policy set (ESS) to determine the convergence policy.

[0016] In the above technical solution, the dynamic resource pricing logic framework of the three-stage evolutionary game described in step 1) further includes four parts:

[0017] (1) Information collection and status monitoring: used to collect resource demand information, budget constraints and satisfaction feedback from sensor devices in real time, while monitoring the load status of edge servers and the available computing and storage resources of idle users in the surrounding area, providing dynamic data support for game modeling.

[0018] (2) Resource strategy generation: Based on the three-stage evolutionary game model, the strategy space and interaction path between idle users, edge / cloud server resource providers and sensors are constructed. Their respective payoff functions and replication dynamic models are established to form a set of resource pricing and allocation strategies based on game feedback.

[0019] (3) Joint pricing and incentive mechanism: A joint pricing mechanism is introduced to enable idle users and ECSP to jointly set resource prices for sensors, and combined with a reputation incentive mechanism to promote multi-party cooperation, reduce the risk of information asymmetry, and improve resource allocation efficiency.

[0020] (4) Strategy feedback and evolution adjustment: Based on the behavioral choices of idle users, edge / cloud server resource providers, and sensors, the system continuously adjusts the strategy probabilities (x, y, z) according to the replication dynamic equation, identifies stable strategies (ESS) and guides the pricing behavior in the next round, and finally achieves the optimal utility of the game participants and the maximization of social welfare.

[0021] Furthermore, the three-stage evolutionary game model for resource allocation and pricing of budget-constrained sensors in edge environments, as described in step 2), is defined as follows:

[0022] The interaction process between idle users, edge / cloud server resource providers (ECSPs), and sensor devices is designed as a three-stage evolutionary game model as follows:

[0023] (1) Third stage: Sensor devices are followers of the SENSOR-ECSP stage. After understanding the unit resource price and total capacity of each member in the ECSP, they need to decide to transfer their computing needs to the ECSP. Their utility function is:

[0024]

[0025] Among them, Q i Q represents the satisfaction reward that sensor i receives by purchasing resources. i =ln[1+β]j (a i,j +b i,j To calculate β, we need to use []]. j It is a constant used to control the sensitivity to rewards. B represents the set of the number of sensors. i This indicates the sensor's own budget when purchasing resources.

[0026] Phase Two: The ECSP is a follower in the USER-ECSP phase and determines the amount of extended resources to purchase. Simultaneously, it is the leader in the ECSP-SENSOR phase and determines the pricing of resources sold to the SENSOR. The utility function of the j-th ECSP can be represented as:

[0027]

[0028] in, This represents the total number of cache resources sold by the j-th ECSP. p represents the total number of computing resources sold by the j-th ECSP; j,a p represents the unit price of ECSP's cache resources. j,b This represents the unit price for calculating resources when sold per unit. i,j and b i,j These represent the size of the cache and computing resources purchased by the i-th sensor from the j-th ECSP, respectively.

[0029] Phase 1: Idle users are the leaders in the USER-ECSP phase, determining the unit price of resources and providing computing services to the ECSP. Their utility function is defined as follows:

[0030]

[0031] in, This represents the total number of cached resources sold by the g-th idle user. p represents the total number of computing resources sold by the g-th idle user; g,a and p g,b These represent the selling price of a unit of cached resources and computing resources to an idle user, respectively. j,g and b j,g These represent the amounts of cache and computing resources purchased by the j-th ECSP from the g-th idle user, respectively.

[0032] Furthermore, the joint pricing and reputation mechanism described in step 3) is designed as follows:

[0033] 1) Joint pricing compensation: Idle users and edge / cloud server resource providers (ECSPs) can engage in joint pricing, with idle users paying joint compensation B_g to the edge / cloud server resource providers (ECSPs) to coordinate pricing strategies;

[0034] 2) Reputation Incentive Mechanism: Idle users, edge / cloud server resource providers (ECSPs), and sensors receive R respectively when implementing reasonable strategies. g ,R j ,R i Rewards, or conversely, receiving S g ,S j ,S i punish;

[0035] 3) Game feedback fusion: The difference between the returns of joint pricing and reputation incentives is embedded into the replication dynamic equation. The strategy evolution is driven by "reputation + game feedback" to improve collaborative efficiency.

[0036] Furthermore, the benefit functions and benefit matrices of the three parties under different strategy choices mentioned in step 4) are as follows:

[0037] Phase 1: In the three-stage evolutionary game model described above, the participating entities make different strategy choices due to conflicting objectives, information asymmetry, and the need to maximize their profits. The decision-making motivations and strategy choices of each entity are as follows:

[0038] (1) Strategy Selection for Idle Users: As resource providers, idle users aim to maximize the utility of their resource sales while avoiding excessively high resource pricing that would discourage buyers (ECSPs) from purchasing. Their strategy selection is as follows:

[0039] i. Reasonable pricing (x): By setting reasonable resource prices, resources remain attractive in a competitive market, thereby ensuring resource sales.

[0040] ii. Unreasonable pricing (1-x): Overpricing may prevent ECSP from purchasing, or due to information asymmetry, idle users may misjudge market demand, resulting in the inability to circulate resources and significant losses.

[0041] Where x represents the probability that an idle user chooses the "reasonable pricing" strategy; then 1-x represents the probability of choosing the "unreasonable pricing" strategy.

[0042] (2) Edge / Cloud Server Resource Providers (ECSPs): The goal of ECSPs is to maximize revenue from resource procurement and resale, while optimizing resource allocation and ensuring energy efficiency and cost control. Their strategy is as follows:

[0043] i. Reasonable pricing (y): ECSPs may set reasonable resource sales prices based on market demand and price sensitivity (especially the budget constraints of sensors), which can both guarantee their own profits and ensure that resources are sold smoothly.

[0044] ii. Unreasonable pricing (1-y): If the ECSP purchases idle users at excessively high prices or adopts unreasonable pricing strategies for its own benefit, it may lead to sensor selection not being purchased, resulting in unsold resources.

[0045] Similarly, 'y' represents the Edge / Cloud Server Resource Provider (ECSP) choosing "reasonable pricing".

[0046] The probability of the strategy, 1-y represents the probability of choosing the "unreasonable pricing" strategy.

[0047] (3) Sensor Device Strategy Selection: The goal of sensors is to maximize the utility of resources purchased from the ECSP within budget constraints. The strategy selection is as follows:

[0048] i. Purchase resources (z): If the ECSP provides resources at a reasonable price and within budget, the sensor will choose to purchase resources to complete its task.

[0049] ii. Refuse to purchase resources (1-z): If the price of resources is too high and exceeds the sensor's budget, the sensor will choose not to purchase the resources.

[0050] Similarly, z represents the probability that the sensor chooses the "buy resources" strategy, and 1-z represents the probability that it chooses the "refuse to buy resources" strategy.

[0051] Second: By analyzing their strategies, we can obtain the benefit matrix of each entity under different strategy choices. Assume E i,j It indicates the expected return, while This represents the average expected return for each participant in the game. In this model, i = 1, 2, 3 represent idle users, ECSPs, and sensors, respectively, while j = 1, 2 represent the different strategies chosen by each entity. The specific details are as follows:

[0052] (1) The expected returns for idle users choosing the "reasonable pricing" strategy and the "unreasonable pricing" strategy are E respectively. 1,1 and E 1,2 Its average expected return is

[0053]

[0054] Among them, E g This represents the energy consumed by the g-th idle user when selling resources, specifically expressed as... Where eg B represents the energy consumption coefficient of idle users; g This indicates that the idle user is co-priced with the ECSP and needs to pay compensation to the ECSP.

[0055] Combining equations (4), (5), and (6), we can obtain the replication dynamic equation for the idle user, as shown below:

[0056]

[0057] (2) The expected returns for ECSP when choosing the "reasonable pricing" strategy and the "unreasonable pricing" strategy are E, respectively. 2,1 and E 2,2 Its average expected return is

[0058]

[0059] Among them, E j This represents the energy consumption consumed by the j-th ECSP in selling resources, specifically expressed as... Where e j D represents the ECSP consumption coefficient. j This indicates the cost of the resources sold by the ECSP, specifically calculated as follows: c j,a and c j,b These represent the cost of a unit of cache resources and compute resources for that ECSP, respectively. j This indicates that the ECSP still purchased resources even when idle users chose the "unreasonable pricing" strategy, resulting in economic losses for the ECSP due to unreasonable pricing. j This represents the cost incurred by ECSP in purchasing idle resources, calculated as follows:

[0060] Combining equations (8), (9), and (10), the replication dynamic equations of ECSP can be obtained as follows:

[0061]

[0062] (3) Similarly, the expected returns for the sensor when choosing the "purchase resources" strategy and the "refuse to purchase resources" strategy are E respectively. 3,1 and E 3,2 Its average expected return is

[0063]

[0064] Among them, L iThis indicates that SENSOR still chose to purchase resources despite ECSP's "unreasonable pricing" strategy, resulting in economic losses for the sensor due to the unreasonable pricing.

[0065] Similarly, combining equations (12), (13), and (14), we obtain the sensor's replication dynamic equation:

[0066]

[0067] Furthermore, the construction of the replication dynamic function and the stability analysis described in step 5) are as follows:

[0068]

[0069] The inventive principle of this invention:

[0070] This invention primarily addresses the resource pricing and allocation problem in the IoT edge-cloud continuum environment, designing a resource pricing system based on a three-stage evolutionary game and a reputation incentive mechanism. Under the premise of satisfying the budget and supply-demand constraints of idle users, edge / cloud server resource providers (ECSPs), and sensors, the system aims to maximize the satisfaction of budget-constrained sensors and the profit of ECSPs. A three-stage evolutionary game model is constructed to describe the strategic interactions of idle pricing, ECSP pricing, and sensor resource procurement, clarifying the evolutionary paths among the three parties. An evolutionarily stable strategy (ESS) is solved through a replicating dynamic process. Furthermore, this invention extends to information asymmetry scenarios, introducing a joint pricing mechanism and a reputation incentive mechanism. This combines reputation feedback with strategy gains, incentivizing participants to make rational decisions and effectively mitigating resource misallocation. Finally, a multi-stage replicating dynamic search algorithm based on evolutionary paths is proposed to achieve stable evolution and convergence of the system's resource pricing and allocation scheme, ensuring optimal utility for all parties and overall social welfare of the system.

[0071] The beneficial effects of this invention are as follows:

[0072] This invention proposes for the first time a pricing method for idle user resources in an IoT edge-cloud continuum based on three-stage evolutionary game theory. By constructing a dynamic interaction model among idle users, ECSPs, and sensors, it systematically solves the problems of resource misallocation and decreased system stability caused by fluctuations in resource supply and demand, information asymmetry, and conflicts of interest among multiple parties in existing methods. Specifically, based on evolutionary game theory, this invention designs a three-stage replicative dynamic evolution mechanism, which can effectively capture the strategy adjustment process of entities with bounded rationality in a dynamic market environment. Through stability analysis, it determines the evolutionary stable strategy (ESS) to achieve resource supply and demand balance and maximize social welfare. Simultaneously, this invention innovatively introduces a joint pricing mechanism and a reputation incentive mechanism, which not only alleviates the information asymmetry problem among idle users, ECSPs, and sensor devices, but also promotes the spontaneous evolution of multi-party cooperative behavior, significantly improving the system's resource utilization efficiency and collaborative stability. Attached Figure Description

[0073] Figure 1 This is a diagram illustrating the interactive logic architecture of a three-stage evolutionary game.

[0074] Figure 2 Simulation results of the strategy convergence process of the three entities under different initial conditions;

[0075] Figure 3 A comparison of the dynamic evolution trends of the three entities with and without incentive mechanisms;

[0076] Figure 4 The impact of idle users on evolutionary strategies under different joint pricing compensation and reputation mechanism settings;

[0077] Figure 5 The impact of ESCP on evolutionary trends under a reputation mechanism setting;

[0078] Figure 6 The impact of sensor devices on evolutionary trends under a reputation mechanism setting.

[0079] Figure 7 The impact of different numbers of idle users, ECSPs, and sensors on social benefits under different pricing mechanisms;

[0080] Figure 8 The impact of different initial values ​​of idle users, ECSPs, and sensor devices on the evolution trend of the three-stage game. Detailed Implementation

[0081] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0082] A pricing method for idle user resources in an IoT edge-cloud continuum based on a three-stage evolutionary game theory approach, characterized by the following steps:

[0083] 1) A dynamic resource pricing logic framework based on three-stage evolutionary game theory was constructed;

[0084] 2) Establish a three-stage evolutionary game model for resource allocation and pricing of budget-constrained sensors in edge environments, and clarify the roles of leaders and followers and their decision-making order;

[0085] 3) For scenarios with information asymmetry, introduce joint pricing mechanisms and reputation incentive mechanisms to optimize pricing decisions, reduce resource misallocation caused by information asymmetry, and improve collaboration and fairness;

[0086] 4) Establish benefit functions and benefit matrices for idle users, edge / cloud server resource providers (ECSPs), and sensors under different strategy choices, construct benefit models for each participant, and quantify their expected utility based on different strategy combinations to guide replication dynamics.

[0087] 5) Construct the replication dynamic equation and perform stability analysis to obtain the evolutionarily stable policy set (ESS) to determine the convergence policy.

[0088] The logical framework of the three-stage evolutionary game dynamic resource pricing strategy proposed in this invention is as follows: Figure 1 As shown, it includes 4 parts:

[0089] (1) Information collection and status monitoring: Real-time collection of resource requirements, budget constraints and satisfaction feedback of sensor devices, monitoring of edge / cloud server load and available computing and storage resources of idle users in the surrounding area, providing dynamic data for game model.

[0090] (2) Resource strategy generation: Based on the three-stage evolutionary game model, the strategy space and interaction path between idle users, edge / cloud server resource providers and sensors are constructed. Their respective payoff functions and replication dynamic models are established to form a set of resource pricing and allocation strategies based on game feedback.

[0091] (3) Joint pricing and incentive mechanism: A joint pricing mechanism is introduced to enable idle users and ECSP to jointly set resource prices for sensors, and combined with a reputation incentive mechanism to promote multi-party cooperation, reduce the risk of information asymmetry, and improve resource allocation efficiency.

[0092] (4) Strategy feedback and evolution adjustment: Based on the behavioral choices of idle users, edge / cloud server resource providers, and sensors, the system continuously adjusts the strategy probabilities (x, y, z) according to the replication dynamic equation, identifies stable strategies (ESS) and guides the pricing behavior in the next round, and finally achieves the optimal utility of the game participants and the maximization of social welfare.

[0093] Figure 2This paper demonstrates how, through analysis of the replication dynamics equations of the three entities, we derive an Evolutionarily Stable Strategy Set (ESS) and verify its authenticity through simulation experiments. The model uses idle users, Edge / Cloud Server Resource Providers (ECSPs), and sensor devices as the main participating entities, designing a bottom-up, hierarchical resource pricing and evolution strategy framework. In the first stage of the game, idle users, as the initial price setters, autonomously set their resource selling prices to ECSPs based on resource availability, cost, and market expectations. This stage reflects the dominant role of individual idle resource providers in the supply of edge-cloud resources. In the second stage, ECSPs, as intermediaries, determine the unit resource price sold to downstream sensors based on the purchase price offered by idle users and their own resource consumption costs. At this point, ECSPs are both followers in the first stage and leaders in the third stage, playing a crucial role in bridging the gap between the two. In the third stage, sensor devices, as end-users, decide whether to purchase resources and the quantity to purchase based on the resource pricing strategy set by ECSPs, within their own budget constraints. The strategic interactions among the three parties rely on the continuous evolution of the replication dynamic equation to form a feedback loop, which ultimately drives the system strategy to converge toward the evolutionarily stable strategy (ESS), thereby achieving dynamic optimization of resource allocation and overall improvement of social utility.

[0094] (1) Third stage: Sensor devices are followers of the SENSOR-ECSP stage. After understanding the unit resource price and total capacity of each member in the ECSP, they need to decide to transfer their computing needs to the ECSP. Their utility function is:

[0095]

[0096] Among them, Q i Q represents the satisfaction reward that sensor i receives by purchasing resources. i =ln[1+β] j (a i,j +b i,j To calculate β, we need to use []]. j It is a constant used to control the sensitivity to rewards. B represents the set of the number of sensors. i This indicates the sensor's own budget when purchasing resources.

[0097] Phase Two: The ECSP is a follower in the USER-ECSP phase and determines the amount of extended resources to purchase. Simultaneously, it is the leader in the ECSP-SENSOR phase and determines the pricing of resources sold to the SENSOR. The utility function of the j-th ECSP can be represented as:

[0098]

[0099] in, This represents the total number of cache resources sold by the j-th ECSP. p represents the total number of computing resources sold by the j-th ECSP; j,a p represents the unit price of ECSP's cache resources. j,b This represents the unit price for calculating resources when sold per unit. i,j and b i,j These represent the size of the cache and computing resources purchased by the i-th sensor from the j-th ECSP, respectively.

[0100] Phase 1: Idle users are the leaders in the USER-ECSP phase, determining the unit price of resources and providing computing services to the ECSP. Their utility function is defined as follows:

[0101]

[0102] in, This represents the total number of cached resources sold by the g-th idle user. p represents the total number of computing resources sold by the g-th idle user; g,a and p g,b These represent the selling price of a unit of cached resources and computing resources to an idle user, respectively. j,g and b j,g These represent the amounts of cache and computing resources purchased by the j-th ECSP from the g-th idle user, respectively.

[0103] Furthermore, the joint pricing and reputation mechanism is designed as follows:

[0104] 1) Joint pricing compensation: Idle users and edge / cloud server resource providers (ECSPs) can engage in joint pricing, with idle users paying joint compensation B_g to the edge / cloud server resource providers (ECSPs) to coordinate pricing strategies;

[0105] 2) Reputation Incentive Mechanism: Idle users, edge / cloud server resource providers (ECSPs), and sensors receive R respectively when implementing reasonable strategies. g ,R j ,R i Rewards, or conversely, receiving S g ,S j ,S i punish;

[0106] 3) Game feedback fusion: The difference between the returns of joint pricing and reputation incentives is embedded into the replication dynamic equation. The strategy evolution is driven by "reputation + game feedback" to improve collaborative efficiency.

[0107] Furthermore, the benefit functions and specific strategy choices for the three parties under different strategy selections are as follows:

[0108] Phase 1: In the three-stage evolutionary game model described above, the participating entities make different strategy choices due to conflicting objectives, information asymmetry, and the need to maximize their profits. The decision-making motivations and strategy choices of each entity are as follows:

[0109] (1) Strategy Selection for Idle Users: As resource providers, idle users aim to maximize the utility of their resource sales while avoiding excessively high resource pricing that would discourage buyers (ECSPs) from purchasing. Their strategy selection is as follows:

[0110] iii. Reasonable pricing (x): By setting reasonable resource prices, resources remain attractive in a competitive market, thereby ensuring resource sales.

[0111] iv. Unreasonable pricing (1-x): Overpricing may prevent ECSP from purchasing, or due to information asymmetry, idle users may misjudge market demand, resulting in the inability to circulate resources and significant losses.

[0112] Where x represents the probability that an idle user chooses the "reasonable pricing" strategy; then 1-x represents the probability of choosing the "unreasonable pricing" strategy.

[0113] (2) Edge / Cloud Server Resource Providers (ECSPs): The goal of ECSPs is to maximize revenue from resource procurement and resale, while optimizing resource allocation and ensuring energy efficiency and cost control. Their strategy is as follows:

[0114] iii. Reasonable pricing (y): ECSP may set reasonable resource sales prices based on market demand and price sensitivity (especially the budget constraints of sensors) to ensure both its own profit and the smooth sale of resources.

[0115] iv. Unreasonable pricing (1-y): If the ECSP purchases idle users at excessively high prices or adopts unreasonable pricing strategies for its own benefit, it may lead to sensor selection not being purchased, resulting in unsold resources.

[0116] Similarly, 'y' represents the Edge / Cloud Server Resource Provider (ECSP) choosing "reasonable pricing".

[0117] The probability of the strategy, 1-y represents the probability of choosing the "unreasonable pricing" strategy.

[0118] (3) Sensor Device Strategy Selection: The goal of sensors is to maximize the utility of resources purchased from the ECSP within budget constraints. The strategy selection is as follows:

[0119] iii. Purchasing Resources (z): If the ECSP provides resources at a reasonable price and within budget, the sensor will choose to purchase resources to complete its task.

[0120] iv. Refuse to purchase resources (1-z): If the price of resources is too high and exceeds the sensor's budget, the sensor will choose not to purchase the resources.

[0121] Similarly, z represents the probability that the sensor chooses the "buy resources" strategy, and 1-z represents the probability that it chooses the "refuse to buy resources" strategy.

[0122] Second: By analyzing their strategies, we can obtain the benefit matrix of each entity under different strategy choices. Assume E i,j E represents the expected return, while E i This represents the average expected return for each participant in the game. In this model, i = 1, 2, 3 represent idle users, ECSPs, and sensors, respectively, while j = 1, 2 represent the different strategies chosen by each entity. The specific details are as follows:

[0123] (4) The expected returns for idle users choosing the "reasonable pricing" strategy and the "unreasonable pricing" strategy are E respectively. 1,1 and E 1,2 Its average expected return is

[0124]

[0125] Among them, E g This represents the energy consumed by the g-th idle user when selling resources, specifically expressed as... Where e g B represents the consumption coefficient of idle users; g This indicates that the idle user is co-priced with the ECSP and needs to pay compensation to the ECSP.

[0126] Combining equations (4), (5), and (6), we can obtain the replication dynamic equation for the idle user, as shown below:

[0127]

[0128] (5) The expected returns for ECSP when choosing the "reasonable pricing" strategy and the "unreasonable pricing" strategy are E respectively. 2,1 and E 2,2 Its average expected return is

[0129]

[0130] Among them, E jThis represents the energy consumption consumed by the j-th ECSP in selling resources, specifically expressed as... Where e j D represents the ECSP consumption coefficient. j This indicates the cost of the resources sold by the ECSP, specifically calculated as follows: c j,a and c j,b These represent the cost of a unit of cache resources and compute resources for that ECSP, respectively. j This indicates that the ECSP still purchased resources even when idle users chose the "unreasonable pricing" strategy, resulting in economic losses for the ECSP due to unreasonable pricing. j This represents the cost incurred by ECSP in purchasing idle resources, calculated as follows:

[0131] Combining equations (8), (9), and (10), the replication dynamic equations of ECSP can be obtained as follows:

[0132]

[0133] (6) Similarly, the expected returns for the sensor when choosing the "purchase resources" strategy and the "refuse to purchase resources" strategy are E respectively. 3,1 and E 3,2 Its average expected return is

[0134]

[0135] Among them, L i This indicates that SENSOR still chose to purchase resources despite ECSP's "unreasonable pricing" strategy, resulting in economic losses for the sensor due to the unreasonable pricing.

[0136] Similarly, combining equations (12), (13), and (14), we obtain the sensor's replication dynamic equation:

[0137]

[0138] Finally, based on the obtained copy dynamic function and the stability analysis performed, the following is shown:

[0139]

[0140]

[0141] Figures 3 to 8 This invention demonstrates the dynamic evolution performance and system response capability of the proposed three-stage evolutionary game model under various mechanism configurations and parameter conditions. Figure 3The study compared the strategy evolution processes of the three participating entities (idle users, ECSP, and sensor devices) with and without incentive mechanisms. The results showed that after introducing joint pricing and reputation incentive mechanisms, the system converged to a cooperative strategy combination more quickly, exhibiting better stability and social benefits. However, without incentive mechanisms, the strategy fluctuated significantly, and the overall utility was low. Figure 4 Further analysis revealed the behavioral trends of idle users when setting joint pricing compensation parameters and reputation reward / penalty factors, indicating that a reasonable incentive mechanism can effectively promote their evolution towards reasonable pricing, thereby improving resource circulation efficiency. Figure 5 and Figure 6 The study explored the strategy adjustment process of ECSP and sensor devices under the influence of reputation mechanisms. The results showed that reputation rewards can significantly enhance the willingness and responsiveness of both supply and demand sides, and promote the overall strategy coordination and resource matching optimization of the system. Figure 7 The social welfare performance of the proposed model was compared with other pricing models under different conditions of varying numbers of idle users, ECSP participation, and sensor involvement. Experimental results show that the proposed model outperforms the comparative models under multiple conditions, verifying its stability and practicality. Figure 8 The evolution paths of the three-party policies under different initial policy settings are shown. Regardless of the initial values, the system can eventually converge to the stable evolutionary policy (ESS), further proving that the model of the present invention has good robustness and convergence.

Claims

1. A pricing method for idle user resources in an IoT edge-cloud continuum based on a three-stage evolutionary game, characterized in that, Includes the following steps: 1) A dynamic resource pricing logic framework based on three-stage evolutionary game was constructed. 2) A three-stage evolutionary game model is proposed for resource allocation and pricing of budget-constrained sensor devices in edge environments, clarifying the roles of leaders and followers and their decision-making order. 3) For scenarios with information asymmetry, introduce joint pricing mechanisms and reputation incentive mechanisms to optimize pricing decisions, reduce resource misallocation caused by information asymmetry, and improve collaboration and fairness. 4) Establish benefit functions and benefit matrices for the three parties—Idle Users, Edge / Cloud Server Resource Providers (ECSPs), and Sensors—under different strategy choices, construct benefit models for each participant, and quantify their expected utility based on different strategy combinations to guide replication dynamics. 5) Construct the replication dynamic equation and perform stability analysis to obtain the evolutionarily stable policy set (ESS) to determine the convergence policy.

2. The method for pricing idle user resources in the IoT edge-cloud continuum based on three-stage evolutionary game theory as described in claim 1, characterized in that, The dynamic resource pricing logic framework of the three-stage evolutionary game described in step 1) consists of four parts, as shown below: (1) Information collection and status monitoring: Real-time collection of resource requirements, budget constraints and satisfaction feedback of sensor devices, monitoring of edge / cloud server load and available computing and storage resources of idle users in the surrounding area, providing dynamic data for game model. (2) Resource strategy generation: Based on the three-stage evolutionary game model, the strategy space and interaction path between idle users, edge / cloud server resource providers and sensors are constructed. Their respective payoff functions and replication dynamic models are established to form a set of resource pricing and allocation strategies based on game feedback. (3) Joint pricing and incentive mechanism: A joint pricing mechanism is introduced to enable idle users and ECSP to jointly set resource prices for sensors, and combined with a reputation incentive mechanism to promote multi-party cooperation, reduce the risk of information asymmetry, and improve resource allocation efficiency. (4) Strategy feedback and evolution adjustment: Based on the behavioral choices of idle users, edge / cloud server resource providers, and sensors, the system continuously adjusts the strategy probabilities (x, y, z) according to the replication dynamic equation, identifies stable strategies (ESS) and guides the pricing behavior in the next round, and finally achieves the optimal utility of the game participants and the maximization of social welfare.

3. The method for resource allocation and pricing of idle user resources supplementing edge / cloud server resources for the IoT edge-cloud continuum based on three-stage evolutionary game theory, as described in claim 2, is characterized in that... The three-stage evolutionary game model for resource allocation and pricing of budget-constrained sensor devices in edge environments, as described in step 2), is defined as follows: The interaction process between idle users, edge / cloud server resource providers (ECSPs), and sensor devices is designed as a three-stage evolutionary game model as follows: (1) Third stage: Sensor devices are followers of the SENSOR-ECSP stage. After understanding the unit resource price and total capacity of each member in the ECSP, they need to decide to transfer their computing needs to the ECSP. Their utility function is: Among them, Q i Q represents the satisfaction reward that sensor i receives by purchasing resources. i =ln[1+β] j (a i,j +b i,j To calculate, β is used here. j It is a constant used to control the sensitivity to rewards. B represents the set of the number of sensors. i This indicates the sensor's own budget when purchasing resources. (2) Second stage: The ECSP is a follower in the USER-ECSP stage and determines the amount of extended resources to be purchased. At the same time, it is the leader in the ECSP-SENSOR stage and determines the pricing of resources sold to the SENSOR. The utility function of the j-th ECSP can be expressed as: in, This represents the total number of cache resources sold by the j-th ECSP. p represents the total number of computing resources sold by the j-th ECSP; j,a p represents the unit price of ECSP's cache resources. j,b This represents the unit price for calculating resources when sold per unit. i,j and b i,j These represent the size of the cache and computing resources purchased by the i-th sensor from the j-th ECSP, respectively. (3) First stage: Idle users are the leaders in the USER-ECSP stage, determining the unit price of resources and providing computing services to the ECSP. Their utility function is defined as follows: in, This represents the total number of cached resources sold by the g-th idle user. p represents the total number of computing resources sold by the g-th idle user; g,a and p g,b These represent the selling price of a unit of cached resources and computing resources to an idle user, respectively. j,g and b j,g These represent the amounts of cache and computing resources purchased by the j-th ECSP from the g-th idle user, respectively.

4. The case of extended information asymmetry as described in claim 3, characterized in that, The information asymmetric optimization mechanism described in step 3) includes the following: (1) Joint pricing compensation: Idle users and edge / cloud server resource providers (ECSPs) can engage in joint pricing, with idle users paying joint compensation B_g to edge / cloud server resource providers (ECSPs) to coordinate pricing strategies; (2) Design a reputation incentive mechanism: Idle users, edge / cloud server resource providers (ECSPs), and sensors will receive R respectively when implementing reasonable strategies. g ,R j ,R i Rewards, or conversely, receiving S g ,S j ,S i punish; (3) Game feedback integration: The difference between the returns of joint pricing and reputation incentives is embedded into the replication dynamic equation. The strategy evolution is driven by "reputation + game feedback" to improve collaborative efficiency.

5. The benefit matrix for establishing idle users, edge / cloud server resource providers (ECSPs), and sensors under different strategy choices, as described in claim 4, is characterized in that... The benefit matrix described in step 4) is constructed and its stability analyzed in two stages: (1) First Stage: In the three-stage evolutionary game model described above, the participating entities have different strategy choices due to goal conflicts, information asymmetry, and the need to maximize their interests. The decision-making motivations and strategy choices of each entity are as follows: 1) Strategy Choice for Idle Users: As resource providers, idle users aim to maximize the utility of their resource sales while avoiding excessively high resource pricing that would discourage buyers (ECSPs) from purchasing. Their strategy choice is as follows: Reasonable pricing (x): By setting reasonable resource prices, resources remain attractive in a competitive market, thereby ensuring resource sales. Unreasonable pricing (1-x): Overpricing may prevent ECSP from purchasing, or due to information asymmetry, idle users may misjudge market demand, resulting in the inability to circulate resources and significant losses. Where x represents the probability that an idle user chooses the "reasonable pricing" strategy; then 1-x represents the probability of choosing the "unreasonable pricing" strategy. 2) Edge / Cloud Server Resource Providers (ECSPs): ECSPs aim to maximize revenue from resource procurement and resale while optimizing resource allocation and ensuring energy efficiency and cost control. Their strategy is as follows: Reasonable pricing (y): ECSPs may set reasonable resource sales prices based on market demand and price sensitivity (especially the budget constraints of sensors) to ensure both their own profits and the smooth sale of resources. Unreasonable pricing (1-y): If the ECSP purchases too much from idle users or adopts unreasonable pricing strategies for its own benefit, it may lead to the decision not to purchase sensors, resulting in unsold resources. Similarly, y represents the probability that the Edge / Cloud Server Resource Provider (ECSP) chooses the "reasonable pricing" strategy, and 1-y represents the probability that it chooses the "unreasonable pricing" strategy. 3) Sensor Device Strategy Selection: The goal of sensors is to maximize the utility of resources purchased from the ECSP within budget constraints. The strategy selection is as follows: Purchase of resources (z): If the ECSP provides resources at a reasonable price and within budget, the sensor will choose to purchase resources to complete its task. Refuse to purchase resources (1-z): If the price of resources is too high and exceeds the sensor's budget, the sensor will choose not to purchase the resources. Similarly, z represents the probability that the sensor chooses the "purchase resources" strategy, and 1-z represents the probability that it chooses the "refuse to purchase resources" strategy. (2) Second stage: After analyzing their strategies, the benefit matrix of each entity under different strategy choices can be obtained. Assume E i,j E represents the expected return, while E i This represents the average expected return for each participant in the game. In this model, i = 1, 2, 3 represent idle users, ECSPs, and sensors, respectively, while j = 1, 2 represent the different strategies chosen by each entity. The specific details are as follows: 1) The expected returns for idle users choosing the "reasonable pricing" strategy and the "unreasonable pricing" strategy are E respectively. 1,1 and E 1,2 Its average expected return is Among them, E g This represents the energy consumed by the g-th idle user when selling resources, specifically expressed as... Where e g B represents the consumption coefficient of idle users; g This indicates that the idle user is co-priced with the ECSP and needs to pay compensation to the ECSP. Combining equations (4), (5), and (6), we can obtain the replication dynamic equation for the idle user, as shown below: 2) The expected returns for ECSP when choosing the "reasonable pricing" strategy and the "unreasonable pricing" strategy are E and E, respectively. 2,1 and E 2,2 Its average expected return is Among them, E j This represents the energy consumption consumed by the j-th ECSP in selling resources, specifically expressed as... Where e j D represents the ECSP consumption coefficient. j This indicates the cost of the resources sold by the ECSP, specifically calculated as follows: c j,a and c j,b These represent the cost of a unit of cache resources and compute resources for that ECSP, respectively. j This indicates that the ECSP still purchased resources even when idle users chose the "unreasonable pricing" strategy, resulting in economic losses for the ECSP due to unreasonable pricing. j This represents the cost incurred by ECSP in purchasing idle resources, calculated as follows: Combining equations (8), (9), and (10), the replication dynamic equations of ECSP can be obtained as follows: 3) Similarly, the expected returns for the sensor choosing the "purchase resources" strategy and the "refuse to purchase resources" strategy are E and E, respectively. 3,1 and E 3,2 Its average expected return is Among them, L i This indicates that the sensor device still purchased resources despite the ECSP's "unreasonable pricing" strategy, resulting in economic losses for the sensor due to the unreasonable pricing. Similarly, combining equations (12), (13), and (14), we obtain the sensor's replication dynamic equation:

6. The method for constructing a replication dynamic function and performing stability analysis as described in claim 5, characterized in that, Step 5) Obtain the Jacobian matrix of the replication dynamic equations for the idle user, ECSP, and sensor obtained in claim 4. Then, substitute each pure policy equilibrium point into this matrix to further calculate the eigenvalues ​​corresponding to each equilibrium point, thereby determining its stability. See below:

7. The method for pricing idle user resources in an IoT edge-cloud continuum based on three-stage evolutionary game theory as described in any one of claims 1-5, characterized in that, The process of optimal resource allocation and pricing based on this method is as follows: 1) Request phase: Sensors with limited device resources submit a request to the ECSP to purchase resource services; 2) Pricing Phase: Idle users determine the initial pricing of resources based on market demand and competitive landscape; Edge / cloud server resource providers (ECSPs) set resource sales prices for sensors after taking into account procurement costs and sensor budget constraints, thus forming a two-tier pricing structure. 3) Competition and Evolution Stage: Based on the resource pricing set by ECSP, the sensor device decides to purchase resources to meet its own needs; the three parties continuously adjust their strategies according to the three-stage evolutionary game model and the replicating dynamic equation, and conduct stability analysis to determine the evolutionary stable strategy (ESS). 4) Resource allocation stage: Based on the game results of the Evolutionary Stable Strategy (ESS), the ECSP provides corresponding computing and storage resources to the sensor, thereby achieving optimal allocation of system resources.

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