Address Resolution Protocol (ARP) spoofing attacks have become the most pivotal attacks in deteriorating the performance of computer networks. The objective of this paper is to develop SM-ARP, Stochastic Markovian game model based ARP spoofing attack detection scheme.Although many recent techniques have been developed to detect and protect against ARP spoofing attacks, the practical challenges has led to ineffective utilization. The major challenge is that the attackers employing ARP spoofing tend to alter the attack strategy at each point and increases the difficulty in detection and security implementations. The packet forwarding relaying is one suchattack strategy which is harder to detect using traditionally proven methodologies. This paper tackles the packet forwarding relay strategy based ARP spoofing attack strategy by using the proposed SM-ARPto eliminate the attack in a practically feasible manner. The proposed model utilizes a stationary Markov model for optimizing the packet forwarding behaviour of the networks. When an ARP spoofing attack is initiated, the SM-ARP model tracks the changes in the packet forwarding patterns through cache table and detects the misbehaviours. As a security measure, these misbehaved nodes are entitled to recovery and repair process to restore the network to stabilized state. Experiments are conducted to evaluate the performance of SM-ARP in an application for student marks management system. The results prove that the proposed SM-ARP model improves the detection of ARP spoofing attacks with accuracy of 88.2% and also reduces the complexity and errors.