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A peer-to-peer network is planned around the concept of equivalent peer nodes simultaneously working one and the other clients and servers to different nodes on the system. Lately, different selfish practices of peer-to-peer (P2P) organize nodes have turned out to be progressively extreme, and the presence of free-riding, whitewashing and so forth falls apart the exhibition of the systems. This exploration tends to the free-riding issue in peer-to-peer systems.Free-riding problem in P2P networks have become increasingly challenging the various attempts to address the problem. Free-riding reduces P2P system’s effectiveness, robustness and worsened network congestion, therefore, leading to system instability (Shahriar and Jaumard, 2017). Many existing works have considered the use of game theory approaches to address the problem of free-riding in the peer-to-peer network. Some of the mechanisms of game theory used by many researchers can somehow detect and punish free-riders in P2P networks at the expense of overload of peers and the suffering of bandwidth with the slowness of the communication between peers.This paper presents a new mechanism of the stochastic model of Ayo game theoretic to restrain free riding in partially centralized P2P in second generation of unstructured of P2P network.

Peer (P2P) networks have emerged as an efficient and affordable means of transmitting videos to numerous end-users via the Internet. The dynamic and heterogeneous nature of P2P streaming systems (P2PSS) makes testing, analyzing and verification a cumbersome task. However, formal methods offer efficient approaches to rigorously analyze and verify P2PSS. This paper demonstrates the use of formal verification techniques for analyzing the behavioral properties of P2PSS. We use temporal logics to analyze whether all the possible behaviors within the P2P streaming systems conform to the defined specifications. Specifically, we apply model checking to check the consistency, completeness and certainty of the model if the temporal properties of the proposed system satisfies the required specifications. Furthermore, the P2PSS framework was modeled and verified using Simulink Design Verifier (SDV) in MATLAB simulation tool. The simulations results showed 100% validation for all frames and 50% validation for I-frames prioritisation. Further, the probability of a peer capable of forwarding frames while receiving is at most 0.5.