Distributed MIS Algorithms for Rational Agents using Games

We study the problem of computing a Maximal Independent Set (MIS) in distributed networks where each node is a rational agent whose payoff depends on whether it joins the MIS. Classical distributed algorithms assume that nodes follow the prescribed protocol, but this assumption fails when nodes are strategic and may deviate if doing so increases their expected utility. Standard MIS algorithms rely on honest randomness or unique identifiers to break symmetry. In rational settings, however, agents may manipulate randomness, and relying solely on identifiers can create unfairness, giving some nodes zero probability of joining the MIS and thus no incentive to participate. To address these issues, we propose two algorithms based on a utility model in which agents seek locally correct solutions while also having preferences over which solution is chosen. Randomness in our algorithms is generated through pairwise interactions between neighboring nodes, viewed as simple games in which no single node can unilaterally affect the outcome. This allows symmetry breaking while remaining compatible with rational behavior. For both algorithms, we prove that at every stage of the execution, given any history, no agent can increase its expected utility through a unilateral deviation, assuming others follow the algorithm. This gives a stronger guarantee than Trembling-Hand Perfect Equilibrium. When all nodes follow the protocol, every node has a positive probability of joining the MIS, and the final output is a correct MIS. Under mild additional assumptions, both algorithms terminate in $O(\log n)$ rounds with high probability.