Strategic Equilibrium for a Pair of Competing Servers with Convex Cost and Balking
研究两个指数服务器为争夺到达顾客而进行的博弈，每个服务器选择服务率最大化自身利润，证明在凸成本下存在唯一的纯策略纳什均衡点。
A two-person game is formulated for a queuing situation involving a pair of exponential servers competing for arriving customers. The servers have identical characteristics except for their service rates. Each server is free to select its own service rate. The objective of each server is to select a service rate that will maximize its own profit. Arrivals are Poisson. The probability that an arriving customer enters the queue is allowed to depend on the queue length at the time of arrival. The proportion of arrivals to a given server is shown to be strictly concave in the server's own service rate and decreasing in the other service rate. Furthermore, we show that when the cost function is convex and increasing, there exists a unique pure strategy Nash equilibrium point for the resulting game.