We introduce a novel deep graphical representation that integrates game theory principles with the laws of statistical physics, enabling feature extraction, and pattern classification within a unified learning framework. In our approach, neurons in a network are analogous to players in a game theory model. Each neuron, viewed as a classical particle governed by the laws of statistical physics, corresponds to a set of actions that represent specific activation values. Neural network layers are conceptualized as sequential cooperative games. The feedforward process in deep learning is interpreted as a sequential game with each game involving multiple players. During training, neurons are evaluated iteratively and filtered based on their contributions to a payoff function, which is quantified using the Shapley value driven by an energy function. Neurons that significantly contribute to the payoff form strong coalitions, and only these neurons are allowed to propagate information to the next layers. The Shapley value facilitates model regularization, thereby improving overall performance. We applied this framework to facial age estimation and gender classification tasks. Experimental results show that our approach outperforms traditional multi-layer perceptron and convolutional neural network models in terms of efficiency and accuracy.