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Cooperative relaying refers to a technique that allows the source to transmit its messages to the destination via the relaying of multiple cooperative partners and exploits the spatial diversity gains inherent in multiuser wireless systems. In this work, we examine cooperative networks with cooperative and malicious relays and determine the optimal behavior for both kinds of relays using a game-theoretic approach. We formulate the problem as a zero-sum game, determining the optimal relay strategies by identifying the Nash equilibrium of the proposed game under individual power constraints. We prove, with Rayleigh fading, the optimal strategy for malicious relays is to transmit independent Gaussian noise using full power at each relay and for cooperative relays is to independently re-encode the source's message into Gaussian signals and forward them to the destination. Inter-cooperation among relays is unnecessary. The results are verified through numerical simulations.