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• 天元讲堂（8.15-17）杨健教授系列报告
• 浏览量：370 发布人：佚名 发布时间：2017-08-07 14:21:11
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报告人：杨健，2000 年于美国University of Texas, Austin 获管理学博士学位。现任职于罗格斯大学，商学院 管理科学与信息系统系

#1 TITLE: Dynamic Inventory and Price Controls Involving Unknown Demand on Discrete Nonperishable Items

时间：2017815 16:00 - 17:00

地点：维格堂319

ABSTRACT: We study adaptive policies that handle dynamic inventory and price controls when the random demand for discrete nonperishable items is unknown.  Pure inventory control is achieved by targeting newsvendor ordering quantities that correspond to empirical demand distributions learned over time. On the basis of it we conduct the more complex joint inventory-price control, whereupon demand-affecting prices are chosen. We identify policies that strive to balance between exploration and exploitation, and measure their performances by regrets, i.e., the prices to pay for not knowing demand distributions {\em a priori}. Also derived are bounds in the orders of $T^{1/2}$, $T^{2/3}$, $T^{3/4}$, and $T^{5/6}$ for the regrets, depending on how thoroughly unknown the demand distributions are and whether nonperishability has indeed been accounted for. Our simulation sheds lights on the true growth rate of regrets, and also hints at directions for future research.

#2 TITLE: Cooperative Game with Nondeterministic Payoffs

时间：2017816 16:00 - 17:00

地点：维格堂319

ABSTRACT: We study a non-traditional cooperative game where payoffs from coalitions are nondeterministic and players have preferences over their allocations. The long-standing concept of core can be generalized to reflect players' contentment with their allocations. When preferences are expressible through utility functions, the new setup is still a generalization of the non-transferable utility (NTU) game; when players' preferences are reasonably aligned, however, knowledge on the latter can help with the identification of core members of the former game.  When utility functions are translation-invariant, a traditional auxiliary game can be used to predict the nonemptiness of the game's core. With probabilistic structures, nondeterministic payoffs become random variables, utility functions attain risk-attitude connotations, and the timing of players' allocation agreements becomes an issue. Under conditions that ultimately point to the coherent risk measure, we show how the game's core can be related to that of the traditionally defined auxiliary. When individuals both contribute to coalitions in additive fashions and share a common mean-deviation utility, we show that increased risk aversion will promote the formation of the grand coalition. Core members can also be identified by solving nonlinear or even linear programs.

#3 TITLE: Game-theoretic Modeling of Players' Ambiguities on External Factors

时间：2017817 16:00 - 17:00

地点：维格堂319

ABSTRACT: We propose a game-theoretic framework that incorporates both incomplete information and general ambiguity attitudes on factors external to all players. Our starting point is players' preferences on payoff-distribution vectors, essentially mappings from states of the world to distributions of payoffs to be received by players. There are two ways in which equilibria for this preference game can be defined. When the preferences possess ever more features, we can gradually add ever more structures to the game. These include real-valued utility-like functions over payoff-distribution vectors,  sets of probabilistic priors over states of the world, and eventually the traditional expected-utility framework involving one single prior. We establish equilibrium existence results, show the upper hemi-continuity of equilibrium sets over changing ambiguity attitudes, and uncover relations between the two versions of equilibria. %Players' ambiguity attitudes figure large in these results. Some attention is paid to the enterprising game, in which players exhibit ambiguity seeking attitudes while betting optimistically on the favorable resolution of ambiguities. The two solution concepts are unified at this game's pure equilibria, whose existence is guaranteed when strategic complementarities are present. The current framework can be applied to settings like auctions involving ambiguity on competitors' assessments of item worths.