Edge storage presents a viable data storage alternative for application vendors (AV), offering benefits such as reduced bandwidth overhead and latency compared to cloud storage. However, data cached in edge computing systems is susceptible to intentional or accidental disturbances. This paper proposes a decentralized integrity auditing scheme to safeguard data integrity and counter the traditional reliance on centralized third-party auditors (TPA), which are unfit for distributed systems. Our novel approach employs edge servers (ES) as mutual auditors, eliminating the need for a centralized entity. This decentralization minimizes potential collusion with malicious auditors and biases in audit outcomes. Using a strategic game model, we demonstrate that ESs are more motivated to audit each other than TPAs. The auditing process is addressed as a Nash Equilibrium problem, assuring accurate integrity proof through incentives for ESs. Our scheme's security and performance are rigorously assessed, showing it is secure within the random oracle model, offers improved speed, and is cost-effective compared to existing methods.