Blockchain technology is a decentralized ledger system that finds applications in various domains such as banking, e-governance, and supply chain management. The consensus algorithm plays a crucial role in any blockchain network as it directly impacts the network's performance and security. There have been several proposed consensus mechanisms in the literature, including Proof of Work (PoW), Proof of Stake (PoS), Robust Proof of Stake (RPoS), and Delegated Proof of Stake (DPoS). Both Ethereum and Bitcoin utilize the PoW consensus mechanism, where nodes compete to solve puzzles in order to generate blocks, consuming significant processing power. On the other hand, the PoS consensus mechanism selects miners based on the stakes they hold, making it more energy efficient. However, PoS has drawbacks such as vulnerability to coin age accumulation attacks and the potential for partial centralization. In this work, we present a consensus mechanism known as Delegated Proof of Stake with Downgrading Mechanism using Game Theory (DDPoS (GT)). This mechanism employs a two-step game strategy to divide nodes into strong and weak nodes, as well as attack and non-attack nodes. Later, the results of the two games are combined to enhance protocol efficiency and security. Experimental results using a private Ethereum-based network demonstrate that DDPoS (GT) performs better than PoS and DPoS in terms of transaction latency, average block waiting time, and fairness.