Game-Theoretic Model for Repeated Helicopter Allocation Between Two Squads

摘要

A platoon commander has a helicopter to support two squads, which encounter two types of missions critical or routine on a daily basis. During a mission, a squad always benefits from having the helicopter, but the benefit is greater during a critical mission than during a routine mission. Because the commander cannot verify the mission type beforehand, a selfish squad would always claim a critical mission to compete for the helicopter which leaves the commander no choice but to assign the helicopter at random. In order to encourage truthful reports from the squads, we design a token system that works as follows. Each squad keeps a token bank, with tokens deposited at a certain frequency. A squad must spend either 1 or 2 tokens to request the helicopter, while the commander assigns the helicopter to the squad who spends more tokens, or breaks a tie at random. The two selfish squads become players in a two- person non-zero-sum game. We find the Nash Equilibrium of this game, and use numerical examples to illustrate the benefit of the token system.