信息產(chǎn)品的最優(yōu)廣告

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摘要翻譯：
在銷(xiāo)售信息產(chǎn)品時(shí)，銷(xiāo)售者可以提供一些免費(fèi)的部分信息來(lái)改變?nèi)藗兊墓纼r(jià)，從而有可能增加整體收入。我們通過(guò)揭示部分信息來(lái)研究廣告信息產(chǎn)品的一般問(wèn)題。我們考慮作為決策者的買(mǎi)家。決策問(wèn)題的結(jié)果取決于買(mǎi)家不知道的世界狀態(tài)。買(mǎi)家可以做出自己的觀察，從而可以對(duì)世界的狀態(tài)持有不同的個(gè)人信仰。有一個(gè)信息賣(mài)家可以訪(fǎng)問(wèn)世界的狀態(tài)。賣(mài)家可以通過(guò)透露部分信息來(lái)推廣信息。我們假設(shè)賣(mài)方選擇了一個(gè)長(zhǎng)期的廣告策略，然后向它承諾。賣(mài)方的目標(biāo)是最大化預(yù)期收益。我們?cè)趦蓚�(gè)背景下研究這個(gè)問(wèn)題。（1）賣(mài)方以某一類(lèi)型的買(mǎi)方為目標(biāo)。在這種情況下，尋找最優(yōu)廣告策略相當(dāng)于尋找一個(gè)簡(jiǎn)單函數(shù)的凹閉包。該函數(shù)是兩個(gè)量的乘積，即似然比和不確定性代價(jià)。在此基礎(chǔ)上，我們證明了最優(yōu)機(jī)構(gòu)的一些性質(zhì)，這些性質(zhì)允許我們用有限大小的凸程序求解最優(yōu)機(jī)構(gòu)。如果世界的狀態(tài)具有一定數(shù)量的可能實(shí)現(xiàn)，或者買(mǎi)方面臨具有一定數(shù)量的選擇的決策問(wèn)題，那么凸規(guī)劃將具有多項(xiàng)式大小。對(duì)于一般問(wèn)題，我們證明了尋找最優(yōu)機(jī)制是NP難的。（2）當(dāng)賣(mài)方面對(duì)不同類(lèi)型的買(mǎi)方，并且只知道其類(lèi)型的分布時(shí)，我們給出了一個(gè)近似算法，當(dāng)預(yù)測(cè)可能的買(mǎi)方類(lèi)型不太困難時(shí)，我們將進(jìn)行購(gòu)買(mǎi)。對(duì)于一般問(wèn)題，我們證明了求常因子逼近是NP難的。
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英文標(biāo)題：
《Optimal Advertising for Information Products》
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作者：
Shuran Zheng and Yiling Chen
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最新提交年份：
2021
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分類(lèi)信息：

一級(jí)分類(lèi)：Computer Science        計(jì)算機(jī)科學(xué)
二級(jí)分類(lèi)：Computer Science and Game Theory        計(jì)算機(jī)科學(xué)與博弈論
分類(lèi)描述：Covers all theoretical and applied aspects at the intersection of computer science and game theory, including work in mechanism design, learning in games (which may overlap with Learning), foundations of agent modeling in games (which may overlap with Multiagent systems), coordination, specification and formal methods for non-cooperative computational environments. The area also deals with applications of game theory to areas such as electronic commerce.
涵蓋計(jì)算機(jī)科學(xué)和博弈論交叉的所有理論和應(yīng)用方面，包括機(jī)制設(shè)計(jì)的工作，游戲中的學(xué)習(xí)（可能與學(xué)習(xí)重疊），游戲中的agent建模的基礎(chǔ)（可能與多agent系統(tǒng)重疊），非合作計(jì)算環(huán)境的協(xié)調(diào)、規(guī)范和形式化方法。該領(lǐng)域還涉及博弈論在電子商務(wù)等領(lǐng)域的應(yīng)用。
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一級(jí)分類(lèi)：Economics        經(jīng)濟(jì)學(xué)
二級(jí)分類(lèi)：Theoretical Economics        理論經(jīng)濟(jì)學(xué)
分類(lèi)描述：Includes theoretical contributions to Contract Theory, Decision Theory, Game Theory, General Equilibrium, Growth, Learning and Evolution, Macroeconomics, Market and Mechanism Design, and Social Choice.
包括對(duì)契約理論、決策理論、博弈論、一般均衡、增長(zhǎng)、學(xué)習(xí)與進(jìn)化、宏觀經(jīng)濟(jì)學(xué)、市場(chǎng)與機(jī)制設(shè)計(jì)、社會(huì)選擇的理論貢獻(xiàn)。
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英文摘要：
  When selling information products, the seller can provide some free partial information to change people's valuations so that the overall revenue can possibly be increased. We study the general problem of advertising information products by revealing partial information. We consider buyers who are decision-makers. The outcomes of the decision problems depend on the state of the world that is unknown to the buyers. The buyers can make their own observations and thus can hold different personal beliefs about the state of the world. There is an information seller who has access to the state of the world. The seller can promote the information by revealing some partial information. We assume that the seller chooses a long-term advertising strategy and then commits to it. The seller's goal is to maximize the expected revenue. We study the problem in two settings. (1) The seller targets buyers of a certain type. In this case, finding the optimal advertising strategy is equivalent to finding the concave closure of a simple function. The function is a product of two quantities, the likelihood ratio and the cost of uncertainty. Based on this observation, we prove some properties of the optimal mechanism, which allow us to solve for the optimal mechanism by a finite-size convex program. The convex program will have a polynomial-size if the state of the world has a constant number of possible realizations or the buyers face a decision problem with a constant number of options. For the general problem, we prove that it is NP-hard to find the optimal mechanism. (2) When the seller faces buyers of different types and only knows the distribution of their types, we provide an approximation algorithm when it is not too hard to predict the possible type of buyers who will make the purchase. For the general problem, we prove that it is NP-hard to find a constant-factor approximation.
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PDF鏈接：
https://arxiv.org/pdf/2002.10045

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