论文标题
在具有非线性网络效果的多项式logit模型下定价
Pricing under a multinomial logit model with non linear network effects
论文作者
论文摘要
我们研究了在多项式logit模型下定价的问题,在该模型中,我们将网络效应纳入了消费者的决策。当卖家竞争或合作时,我们分析这两个案例。特别是,我们特别注意总体预期收入以及在网络效应参数的变化下如何影响无购买选项的行为。例如,我们证明无购买选项的市场份额正在减少网络效应的价值,这意味着,服装成员之间的沟通更强会增加预期的销售量。我们还分析了当网络效应纳入市场时,如何更改客户的效用,并比较显示竞争和垄断价格的情况。我们使用随机近似算法的工具来证明购买可用产品的概率会收敛到独特的固定分布。我们模拟卖方可以使用这种固定分配来建立其策略。发现在这些情况下,纯净的NASH均衡代表了竞争中的定价策略,并且最佳(最大化总收入)的固定价格是协作案例的特征。
We study the problem of pricing under a Multinomial Logit model where we incorporate network effects over the consumer's decisions. We analyse both cases, when sellers compete or collaborate. In particular, we pay special attention to the overall expected revenue and how the behaviour of the no purchase option is affected under variations of a network effect parameter. Where for example we prove that the market share for the no purchase option, is decreasing in terms of the value of the network effect, meaning that stronger communication among costumers increases the expected amount of sales. We also analyse how the customer's utility is altered when network effects are incorporated into the market, comparing the cases where both competitive and monopolistic prices are displayed. We use tools from stochastic approximation algorithms to prove that the probability of purchasing the available products converges to a unique stationary distribution. We model that the sellers can use this stationary distribution to establish their strategies. Finding that under those settings, a pure Nash Equilibrium represents the pricing strategies in the case of competition, and an optimal (that maximises the total revenue) fixed price characterise the case of collaboration.