# 5G Price Competition with Social Equilibrium Optimality for Social Networks
###### Abstract  
Due to the leaps of progress in the 5G telecommunication industry, commodity pricing and consumer choice are frequently subject to change and competition in the search for optimal supply and demand. We here utilize a two-stage extensive game with complete information to mathematically describe user-supplier interactions on a social network. Firstly, an example of how to apply our model in a practical 5G wireless system is shown. Then we build a prototype that offers multiple services to users and provides different outputs for suppliers, where in addition, the user and supplier quantities are independently distributed. Secondly, we then consider a scenario in which we wish to maximize social welfare and determine if there is a perfect answer. We seek the subgame perfect Nash equilibrium and show that it exists, and also show that when both sides reach it, social welfare likewise reaches its maximum. Finally, we provide numerical results that corroborate the efficacy of our approach on a practical example in the 5G background. social network; game theory; provider competition; 5G wireless production; equilibrium 20222  
theory to study multi-buyer, multi-seller dynamics in a cognitive radio setting. Then finally, the price competition of multihop wireless networks is studied in [23; 24]. The work [25] by [PERSON] inspired us to design and prove the decentralized algorithm. Nevertheless, our work has many significant differences. First, we used a less-rigorous precondition to prove our convergence. Second, our research shows that there are a finite (rather than infinite) number of globally optimum solutions. Third, with our work, consumers are free to use any resource quantity they choose. Finally, current research only focused on a single OFDM cell in resource allocation optimization, while we prefer to investigate NOMA or uRLLC with a high-speed network and low delay in the 5G background [26]. In this study, we explain the user-supplier interaction in the 5G wireless system using a two-stage extended game with comprehensive information (see [27]). To understand how to apply our model in a practical 5G wireless system, we take a 5G popular technology as a specific example. Then we explain how the two-stage works. Suppliers set their commodity pricing in the first stage, and consumers select the amount and supplier in the second stage. A user may choose the less costly commodity with poor service or the more expensive commodity with superior service. Based on users' responses to suppliers' prices, the suppliers take advantage and maximize profits. With this in mind, we first create a prototype that provides consumers with a variety of services and distinct outputs for providers. A multistage game model is utilized to describe the user-supplier relationship, and the user and supplier quantities are independently distributed. Next, we consider a social welfare maximization situation and determine that there must be an optimal solution. At that point, we move to the supplier competition game, which generates a decentralized algorithm that gradually finds equilibrium. The flowchart of the proposed algorithm is shown in Figure 1. Users make decisions based merely on the suppliers' set price; meanwhile, suppliers determine the pricing based on demand (the user's want). Finally, we present numerical results that demonstrate the efficacy of the suggested approach. Our model aims to address the lack of a strong strategy to address the mismatch between supply and demand in the current 5G market, as well as the insufficient structure of market, which can have extremely negative effects. The model provides the user with a  
Figure 1: The flowchart of the proposed framework. perspective on how to select a supplier, also provides a perspective for suppliers on the needs of users. It targets welfare maximization and provides an efficient way of managing supply and demand-side constraints.