State-Based Quasi-Potential Game

This paper expands the quasi-potential game framework to state-based spaces, focusing on the synchronous dynamics between state-based games. Two novel concepts, state-based quasi-potential game (SQPG) and strongly state-based quasi-potential game (SSQPG), are proposed. A formal definition of synchronization in state-based games is first established, along with its necessary and sufficient conditions. The concept of strong synchronization is then introduced as an extension, together with its criteria. A representative example demonstrates the proposed theoretical results. This research enriches the theoretical framework of state-based games and increased the flexibility in game design as well.