Effects of Competition in a Secretary Problem
Effects of Competition in a Secretary Problem
复制标题
竞争对秘书问题的影响
作者：
D. Cownden;D. Steinsaltz
在著名的秘书问题的一个新颖的多人游戏扩展中，多个玩家寻求从一个共同的劳动力池中雇佣秘书。秘书们不接受被搁置，总是立即接受工作机会，一旦被某一家公司拒绝，他们就会离开劳动力市场。所有参与者对秘书的偏好相同，并且所有参与者都寻求在所有n个秘书中获得最佳的概率。我们发现，在纳什均衡中，随着搜索劳动力池的参与者数量N的增长，最优策略收敛于N的简单函数。对于两人的情况，我们还计算了参与者通过合作可以获得多少收益，以及在促进怨恨的支付结构下最优策略如何变化。
In a novel multiplayer extension of the famous secretary problem, multiple players seek to employ secretaries from a common labour pool. Secretaries do not accept being put on hold, always accept job offers immediately, and leave the labour pool once rejected by a single player. All players have an identical preference for secretaries, and all players seek to optimize the probability of obtaining the best of all n secretaries. We find that in the Nash equilibrium, as the number, N, of players searching the labour pool grows, the optimal strategy converges to a simple function of N. For the two-player case we also compute how much players can gain through cooperation and how the optimal strategy changes under a payoff structure that promotes spite.