具有非线性价格偏好的消费者面临的垄断者问题研究
On concavity of the monopolist's problem facing consumers with nonlinear price preferences
摘要：
垄断者希望通过寻找最优价格策略来实现利润最大化。在她宣布产品和价格的菜单之后，每个代理$x$将选择购买使他自己的效用最大化的产品$y(x)$，如果是正的。委托人的利润是出售的每种产品所产生的净收益的总和。这些是由生产成本和销售产品的分配决定的，而这又基于匿名代理人的分配以及他们根据委托人的价格菜单所作的选择。在本文中，我们提供了一个充要条件的凸性或凸性的委托人的（双层）最优化问题，假设每个代理的负效用是一个严格增加，但不一定仿射（即拟线性）支付的价格的函数。凹的存在，使问题更适合计算和理论分析，它是获得唯一性和稳定性的结果，特别是校长的策略的关键。即使在准线性的情况下，我们的分析超越了以前的工作，解决凸性以及凸性，通过建立条件，不仅是充分的，而且是必要的，并需要更少的假设代理人的喜好。
英文摘要：
A monopolist wishes to maximize her profits by finding an optimal price policy. After she announces a menu of products and prices, each agent $x$ will choose to buy that product $y(x)$ which maximizes his own utility, if positive. The principal's profits are the sum of the net earnings produced by each product sold. These are determined by the costs of production and the distribution of products sold, which in turn are based on the distribution of anonymous agents and the choices they make in response to the principal's price menu. In this paper, we provide a necessary and sufficient condition for the convexity or concavity of the principal's (bilevel) optimization problem, assuming each agent's disutility is a strictly increasing but not necessarily affine (i.e. quasilinear) function of the price paid. Concavity when present, makes the problem more amenable to computational and theoretical analysis; it is key to obtaining uniqueness and stability results for the principal's strategy in particular. Even in the quasilinear case, our analysis goes beyond previous work by addressing convexity as well as concavity, by establishing conditions which are not only sufficient but necessary, and by requiring fewer hypotheses on the agents' preferences.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
