We study the problem of computing a Maximal Independent Set (MIS) in distributed networks, where each node is a rational agent that receives a payoff depending on whether it is included in the MIS. In classical distributed computing, it is typically assumed that nodes follow the prescribed algorithm faithfully. However, this assumption fails when nodes are rational agents whose utilities depend on the algorithm’s output. In such cases, nodes may deviate from the algorithm if it increases their expected payoff. Classical solutions for MIS assume that nodes generate random bits honestly or rely on unique identifiers to break symmetry. However, in rational settings, nodes may manipulate randomness to gain a strategic advantage, and relying solely on unique identifiers can result in unfairness, where some nodes have zero probability of joining the MIS and thus no incentive to participate. To address these challenges, we propose two algorithms that work under a utility model, where agents are incentivized to compute locally correct solutions while also exhibiting preferences among these solutions. In these algorithms, randomness is generated through interactions between neighboring nodes, which can be viewed as simple games, where no single node can unilaterally change the outcome. This approach allows us to break symmetry while being compatible with rational behavior. For both algorithms, we show that regardless of the execution history that has occurred, no agent can improve its expected utility by deviating from that stage, provided no other agents deviate. This is a much stronger guarantee compared to Trembling Hand Perfect Equilibrium, which is typically used in such scenarios. Both algorithms guarantee that when all the nodes follow the algorithm, every node has a positive probability of joining the MIS, and that the final output is a correct Maximal Independent Set. Finally, for both algorithms, we can guarantee termination in \( O(\log n) \) rounds with high probability under mild additional assumptions, where \(n\) is the number of nodes in the network.