Medical image segmentation is a crucial step in diagnosis and analysis of diseases for clinical applications. Deep convolutional neural network methods such as DeepLabv3+ have successfully been applied for medical image segmentation, but multi-level features are seldom integrated seamlessly into different attention mechanisms, and few studies have fully explored the interactions between medical image segmentation and classification tasks. Herein, we propose a feature-compression-pyramid network (FCP-Net) guided by game-theoretic interactions with a hybrid loss function (HLF) for the medical image segmentation. The proposed approach consists of segmentation branch, classification branch and interaction branch. In the encoding stage, a new strategy is developed for the segmentation branch by applying three modules, e.g., embedded feature ensemble, dilated spatial mapping and channel attention (DSMCA), and branch layer fusion. These modules allow effective extraction of spatial information, efficient identification of spatial correlation among various features, and fully integration of multi-receptive field features from different branches. In the decoding stage, a DSMCA module and a multi-scale feature fusion module are used to establish multiple skip connections for enhancing fusion features. Classification and interaction branches are introduced to explore the potential benefits of the classification information task to the segmentation task. We further explore the interactions of segmentation and classification branches from a game theoretic view, and design an HLF. Based on this HLF, the segmentation, classification and interaction branches can collaboratively learn and teach each other throughout the training process, thus applying the conjoint information between the segmentation and classification tasks and improving the generalization performance. The proposed model has been evaluated using several datasets, including ISIC2017, ISIC2018, REFUGE, Kvasir-SEG, BUSI, and PH2, and the results prove its competitiveness compared with other state-of-the-art techniques.