## 2 Related Works  
### Traditional Pricing Models and Strategies  
Traditional pricing models have been extensively applied across various economic domains, particularly in product pricing and market strategy optimization [34]. Classical pricing approaches primarily include static pricing methods, regression-based dynamic pricing models, and pricing game strategies derived from game theory [35]. While each of these methods demonstrates value under specific market conditions, limitations are evident when addressing high-dimensional state modeling and real-time feedback [36]. Static pricing methods represent one of the earliest and most widely adopted pricing strategies. The core idea involves predefining prices based on historical data and market patterns, without accommodating dynamic market changes [37]. Such methods are typically suitable for relatively stable markets with predictable demand [38]. However, in volatile markets influenced by complex consumer behavior and competitive pricing, static pricing approachesoften lack efficiency and adaptability [39]. Consequently, these models generally rely on averages or heuristic rules derived from historical data but lack the capacity for dynamic adjustments. To address these shortcomings, regression-based dynamic pricing models have been introduced [40]. These models dynamically adjust prices by establishing functional relationships between price, sales, and demand. Regression analysis is commonly used to model the dependency between pricing and demand. A representative linear regression model is expressed as  
\[y=\beta_{0}+\beta_{1}x_{1}+\beta_{2}x_{2}+\ldots+\beta_{n}x_{n}+\epsilon, \tag{1}\]  
where \(y\) denotes sales or demand, \(x_{1},x_{2},\ldots,x_{n}\) represent feature variables related to price and market conditions, \(\beta_{0},\beta_{1},\ldots,\beta_{n}\) are regression coefficients, and \(\epsilon\) is the error term. This approach assumes a linear or otherwise regressive relationship between price and demand. However, in practical scenarios, the relationship between pricing and consumer demand is often nonlinear and influenced by various factors, such as psychological behavior and seasonal market fluctuations. Therefore, regression-based dynamic pricing methods tend to lack accuracy and stability when faced with such complexity. Pricing game strategies derived from game theory have been widely applied in competitive market scenarios, especially under multi-agent competition [41]. Game theory offers a systematic framework for analyzing strategic behavior among market participants, where pricing is often a critical decision variable [42]. Typical game-theoretic models involve defining the players, strategy spaces, and payoff functions, from which equilibrium pricing can be derived [43]. For example, in a classical Nash equilibrium model, each participant chooses the optimal strategy considering the strategies of others. The payoff function can be expressed as  
\[u_{i}(p_{1},p_{2},\ldots,p_{n})=\text{profit function}(p_{i},p_{1},p_{2},\ldots,p _{n}), \tag{2}\]  
where \(u_{i}\) denotes the profit of the \(i\)-th participant, \(p_{1},p_{2},\ldots,p_{n}\) are the pricing strategies of all participants, and the profit function reflects how revenue varies under different pricing scenarios. Although game-theoretic approaches provide a theoretical framework for analyzing pricing competition, practical application is constrained by the dynamic nature of markets, nonlinear price feedback, and the unpredictability of competitor behavior. These models often assume fully rational agents, thereby overlooking the complexity of consumer behavior and the presence of irrational market factors, which limits their applicability in complex real-world environments [44].