Intermittent Strategic Cooperation of Two Selfish Agents on Graphs
For researchers in multi-agent path planning and game theory, this work provides a formal analysis of strategic cooperation under fragility, though the problem is highly specific and the results are incremental.
The paper introduces the Intermittent Strategic Cooperation-Based Two-Agent Path Planning (IC2PP) problem, a shortest-path game on graphs where two self-interested agents can cooperate intermittently to reduce travel times. It characterizes the structure of Pure Nash Equilibria, proves existence of at least one PNE in every instance, and provides a polynomial-time algorithm for enumerating all relevant PNEs, with empirical comparisons of equilibrium outcomes.
We study strategic space- and time-constrained cooperation between two self-interested agents through the Intermittent Strategic Cooperation-Based Two-Agent Path Planning (IC2PP) problem, a shortest-path game on graphs in which agents navigate toward individual targets while optionally cooperating at specific nodes to reduce their own travel times. Although such cooperation can strictly benefit both agents, it is strategically fragile: agents may deviate at any point along their paths. Modeled as a 2-player game, we characterize the structure of Pure Nash Equilibrium (PNE) joint strategies in IC2PP, and show that stable cooperation must follow a highly constrained form. We further prove that at least one PNE exists in every instance of IC2PP, and present a polynomial-time algorithm for enumerating all relevant PNEs. When multiple equilibria arise, we study coordination mechanisms based on bargaining-theoretic selection concepts and empirically compare equilibrium outcomes in terms of individual travel times and social welfare.