Double Oracle Algorithm for Game-Theoretic Robot Allocation on Graphs
CoRR(2023)
摘要
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.
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