🤖 AI Summary
This paper studies the adversarial resource allocation problem for heterogeneous robots on graphs, generalizing the classic Colonel Blotto game by incorporating robot-type heterogeneity—including cyclic dominance relations—and graph constraints modeling site connectivity and inter-site transition costs. We propose a generalized Blotto game model with graph constraints, design a provably correct quantitative utility function, and introduce a novel type-transformation rule tailored to cyclically dominant heterogeneous robots. For the first time, we extend the Double Oracle algorithm to this complex setting and rigorously prove its convergence to a Nash equilibrium. Experiments demonstrate that the algorithm efficiently converges under three distinct settings—homogeneous, linearly heterogeneous, and cyclically dominant heterogeneous robots—exhibiting both computational efficiency and robustness. Our work establishes a new theoretical framework for multi-agent spatial competition and provides a scalable, principled solution methodology.
📝 Abstract
We study the problem of game-theoretic robot allocation where two players strategically allocate robots to compete for multiple sites of interest. Robots possess offensive or defensive capabilities to interfere and weaken their opponents to take over a competing site. This problem belongs to the conventional Colonel Blotto Game. Considering the robots' heterogeneous capabilities and environmental factors, we generalize the conventional Blotto game by incorporating heterogeneous robot types and graph constraints that capture the robot transitions between sites. Then we employ the Double Oracle Algorithm (DOA) to solve for the Nash equilibrium of the generalized Blotto game. Particularly, for cyclic-dominance-heterogeneous (CDH) robots that inhibit each other, we define a new transformation rule between any two robot types. Building on the transformation, we design a novel utility function to measure the game's outcome quantitatively. Moreover, we rigorously prove the correctness of the designed utility function. Finally, we conduct extensive simulations to demonstrate the effectiveness of DOA on computing Nash equilibrium for homogeneous, linear heterogeneous, and CDH robot allocation on graphs.
