Distributed MIS Algorithms for Rational Agents using Games
Nithin Salevemula, Shreyas Pai
TL;DR
This paper tackles computing a Maximal Independent Set in the LOCAL model when nodes are rational agents who value correctness and inclusion. It introduces two resilience strategies: a purely non-cryptographic RPS-based approach and a cryptography-assisted rank-based method, both designed to implement a belief-independent sequential equilibrium and to guarantee termination in $O(\log n)$ rounds under mild conditions. The authors formalize MIS with rational nodes as an extensive-form game, prove equilibrium and robustness properties, and analyze tradeoffs between cryptographic assumptions and message complexity. The work advances distributed algorithm design under self-interested behavior, enabling correct MIS formation without monetary transfers, while highlighting limitations such as potential collusion and the sensitivity to utility modeling.
Abstract
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.