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Electricity Retailers offer various utility plans in the hope that the increased competition would result in lower prices, improved service, and innovative product offerings. In this paper, we present the retail electric provider's (REP) optimal pricing strategy for residential customers in smart grid, in which the REP offers multiple utility plans for customers with different needs, which includes a flat-rate plan, a multistage plan, and a lump-sum fee plan. The residential customers select the utility plan that maximize their own payoffs by considering their own demands and the pricing strategies of the three plans. In the other way around, the REP optimizes its profit by carefully designing its pricing strategy based on residential customers' decisions. To obtain insights of such a highly coupled system, we consider a system with one REP and a group of customers in need of electricity. We propose a three-stage Stackelberg game model, in which the REP acts as the leader who decides the specific plans to offer at Stage I, then announces the price for each plan in stage II, and finally the customers act as followers that select plans in stage III. We derive the market equilibrium by analyzing customers' decisions among the plans under different pricing schemes. Then, we provide the REP's optimal pricing strategies to maximize its profit. In the end, we give the optimal decisions for REP on the specific plan(s) to offer while considering each customer's evaluation and demand. Both the analytical and simulation results show that the lump-sum fee plan can maximize REP's profit in most cases.

Social reinforcement originating from memory is the key characteristic of behavioral adoption in social contagion. Here, we introduce a non-Markovian susceptible-adopted-recovered (SAR) model to incorporate the memory mechanism. The higher the number of accumulated pieces of exposures an individual is exposed to, the larger is the probability that he/she will adopt the behavior. We observed that when the adopting probability per piece of behavioral information was smaller than a critical value, the final adoption size increased with the behavioral information probability discontinuously. Otherwise, the final adoption size increased with the behavioral information probability continuously. A physical understanding of the mechanism inducing discontinuous spreading was obtained through an edge-based compartment method, which also matched well with the simulation results.

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