Cloud and edge computing service providers (SPs) provide heterogeneous computing services to users, which forms the computing market. However, users’ service selections among SPs are unbalanced, resulting in inefficient resource utilization. In this paper, we analyze users’ service selection behaviors and design efficient pricing mechanisms to optimize the social welfare of the computing market. Considering the huge number of users and heterogeneous service providers, users can hardly acquire complete information to make their decisions, and we model users’ interactions as a dynamic service selection evolutionary game. Analyzing the evolutionary stable state (ESS) of the game and designing efficient pricing mechanisms for edge-cloud computing markets are challenging due to the implicit relationship between prices and users’ service selection dynamics, and the heterogeneity of service providers and user populations. We first investigate a single-population scenario where users are homogeneous, for which we prove that the ESS is unique. We design a static pricing mechanism which depends on SPs’ marginal costs and computation capacities, and a dynamic pricing mechanism which also depends on SPs’ real-time congestion tax. We prove that under our pricing mechanisms, the ESS is the socially optimal state and is globally asymptotic stable. We then analyze the general multi-population scenario where users are heterogeneous, for which we prove that the ESS exists but may be not unique. We design a static pricing mechanism (and a dynamic pricing mechanism) which depends on SPs’ marginal costs and the social-optimal average delay costs (and the real-time average delay costs). We prove that under our pricing mechanisms, the socially optimal state is an ESS and is asymptotically stable. Simulation results validate the effectiveness of our designed pricing mechanisms.

With the proliferation of edge computing, many business entities deploy their own edge servers to compete for users, which forms multi-server edge computing networks. However, no prior work studies the competition among heterogeneous edge servers and how the competition affects users’ selfish computation offloading behaviors in such a network from an economic perspective. In this paper, we model the interactions between edge servers and users as a two-stage game. In Stage I, edge servers with heterogeneous marginal costs set their service prices to compete for users, and in Stage II, each user selfishly offloads its task to one of the edge servers or the remote cloud. Analyzing the equilibrium of the two-stage game is challenging due to edge servers’ heterogeneity and the congestion effect caused by resource sharing among users. We first investigate the equilibrium when edge servers follow the serve-as-arrive (SAA) model (i.e., serving all offloaded tasks simultaneously), and then extend our analysis to the serve-in-queue (SIQ) model (i.e., serving offloaded tasks one by one following the M/M/1 queue rule). Under the SAA model, we prove that users’ selfish computation offloading game in Stage II is a potential game and admits a unique Nash equilibrium (NE), for which we derive the explicit expressions. Furthermore, for edge servers’ price competition game in Stage I, we characterize the conditions for the uniqueness of the NE and derive its explicit expression. Under the SIQ model, we derive the unique NE of users’ selfish computation offloading game, and show that the NE of edge servers’ price competition game may not always exist. We compare the equilibrium under the two service models and show that at equilibrium, edge servers with low marginal costs can achieve higher profits under the SIQ model when edge servers’ computation capacity is large or the delay incurred on the cloud is moderate; however, edge servers with high marginal costs can obtain higher profits under the SAA model in most cases.

As edge computing provides crucial support for delay-sensitive and computation-intensive applications, many business entities deploy their own edge servers to compete for users, which forms multi-server edge computing networks. However, no prior work studies the competition among heterogeneous edge servers and how the competition affects users’ selfish computation offloading behaviors in such a network from an economic perspective. In this paper, we model the interactions between edge servers and users as a two-stage game. In Stage I, edge servers with heterogeneous marginal costs set their service prices to compete for users, and in Stage II, each user selfishly offloads its task to one of the edge servers or the remote cloud. Analyzing the equilibrium of the two-stage game is challenging due to edge servers’ heterogeneity and the congestion effect caused by resource sharing among users. We first prove that in Stage II, users’ selfish computation offloading game is a potential game and admits a unique Nash equilibrium (NE), for which we derive the explicit expression. We then analyze edge servers’ price competition game in Stage I and characterize the conditions for the uniqueness of the NE. We show that at equilibrium, users only choose low-priced edge servers, and hence edge servers with low marginal costs can win the price competition, which reflects the improvement of economic efficiency in competitive markets. Moreover, it is surprising that the equilibrium prices do not monotonically increase with the task execution delay. This is because a long execution delay gives a chance to edge servers with high marginal costs to win the competition, which results in more fierce competition among edge servers.