Intermittent Strategic Cooperation of Two Selfish Agents on Graphs

2026-06-15

AI Summary

This study addresses the problem of intermittent cooperative path planning for two self-interested agents navigating a graph under spatiotemporal constraints, formulated as a shortest-path game. Agents may selectively cooperate at specific nodes to reduce travel time while facing the risk of abrupt cooperation breakdown. Through game-theoretic analysis, the work establishes stringent conditions necessary for stable cooperation, proves that every instance admits at least one pure-strategy Nash equilibrium, and devises a polynomial-time algorithm to efficiently enumerate all relevant equilibria. Building on bargaining theory, a coordination mechanism is further developed. Experimental results demonstrate a pronounced trade-off across equilibria between individual efficiency and social welfare.

Abstract

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.

Problem

• strategic cooperation
• selfish agents
• graph path planning
• Nash equilibrium
• intermittent cooperation

Innovation

• Intermittent Strategic Cooperation
• Two-Agent Path Planning
• Pure Nash Equilibrium
• Polynomial-Time Algorithm
• Bargaining-Theoretic Coordination