In 2015, Guglielmi and Badia discussed optimal strategies in a particular type of service system with two strategic servers. In their setup, each server can either be active or inactive and an active server can be requested to transmit a sequence of packets. The servers have varying probabilities of successfully transmitting when they are active, and both servers receive a unit reward if the sequence of packets is transmitted successfully. Guglielmi and Badia provided an analysis of optimal strategies in four scenarios: where each server does not know the other's successful transmission probability; one of the two servers is always inactive; each server knows the other's successful transmission probability; and they are willing to cooperate. Unfortunately the analysis in Guglielmi and Badia contained errors. In this paper we correct these errors. We discuss three cases where both servers (I) communicate and cooperate; (II) neither communicate nor cooperate; (III) communicate but do not cooperate. In particular, we obtain the unique Nash equilibrium strategy in Case II through a Bayesian game formulation, and demonstrate that there is a region in the parameter space where there are multiple Nash equilibria in Case III. We also quantify the value of communication or cooperation by comparing the social welfare in the three cases, and propose possible regulations to make the Nash equilibrium strategy the socially optimal strategy for both Cases II and III.
翻译:2015年,Guglielmi和Badia用两个战略服务器讨论了特定类型服务系统中的最佳战略。在设置中,每个服务器可以是主动的,也可以是不活跃的,可以请求一个活跃的服务器传输一个包序列。服务器在活动时有不同的成功传输概率,如果包序列传送成功,两个服务器都得到单位奖励。Guglielmi和Badia在四种情况下对最佳战略进行了分析:每个服务器不知道对方的成功传输概率;两个服务器中有一个总是不活跃;每个服务器了解对方的成功传输概率;他们愿意合作。不幸的是,Guglielmi和Badia的分析含有错误。在本文件中,我们纠正这些错误。我们讨论了三个案例,即服务器(I)沟通与合作;(II)既不沟通也不合作;(III)沟通但不合作;沟通但不合作。特别是,我们通过制定巴耶西亚游戏,在第二号案件中获得了独特的纳什平衡战略,并表明在参数空间中有一个区域,在第三号案件中存在多个纳什基利利差的传播概率;以及他们愿意合作。我们还在第三号案件中将最佳通信规则用于社会平衡。