Econ Papers Daily / 期刊论文
重排序问题中的一致性原则
The consistency principle in the reordering problem
摘要
We investigate implications of the consistency principle for the reordering problem, also known as the queueing problem with an initial queue. The consistency principle specifies how an allocation rule should respond when an agent leaves the problem. We introduce four different consistency properties for the reordering problem and characterize three allocations rules, the pairwise equal-splitting rule (Curiel et al. Eur J Operat Res 40:344-351, 1989), the maximum price rule and the minimum price rule. Balanced consistency requires that for each pair of agents i and j , the impact on agent i ’s net utility when agent j leaves the initial queue and the agents behind her move forward by one position, should be equal to the impact on agent j ’s net utility when agent i leaves the initial queue and the agents behind her move forward by one position. Balanced cost reduction requires that if an agent leaves the initial queue and the agents behind her move forward by one position, then the total net utilities of the remaining agents should be reduced by the amount equal to the net utility of the departing agent. Smallest-cost consistency (respectively, largest-cost consistency ) requires that if an agent with the smallest (respectively, largest) unit waiting cost leaves the initial queue and the agents behind her move forward by one position, then the net utilities of the remaining agents should not be affected. We show that either balanced consistency or balanced cost reduction , together with the three basic properties of queue-efficiency , budget-balance and Pareto indifference , characterizes the pairwise equal-splitting rule. On the other hand, together with the three basic properties, smallest-cost consistency characterizes the maximum price rule and largest-cost consistency the minimum price rule.
中文摘要
我们探讨了一致性原则在重排序问题（即带有初始队列的排队问题）中的含义。一致性原则规定了当一位代理人离开问题时，分配规则应如何响应。我们为重排序问题引入了四种不同的一致性属性，并刻画了三种分配规则：两两均分规则（Curiel等人，欧洲运筹学杂志40:344-351，1989）、最高价格规则和最低价格规则。平衡一致性要求，对于每对代理人i和j，当代理人j离开初始队列且其后的代理人向前移动一位时，对代理人i净效用的影响，应等于当代理人i离开初始队列且其后的代理人向前移动一位时，对代理人j净效用的影响。平衡成本减少要求，如果一位代理人离开初始队列且其后的代理人向前移动一位，则剩余代理人的总净效用应减少，减少量等于离开代理人的净效用。最小成本一致性（分别地，最大成本一致性）要求，如果具有最小（分别地，最大）单位等待成本的代理人离开初始队列且其后的代理人向前移动一位，则剩余代理人的净效用不应受到影响。我们表明，平衡一致性或平衡成本减少，连同队列效率、预算平衡和帕累托无关性这三个基本属性，共同刻画了两两均分规则。另一方面，连同这三个基本属性，最小成本一致性刻画了最高价格规则，而最大成本一致性则刻画了最低价格规则。