Price of information in games of chance: A statistical physics approach.

Luca Gamberi, Alessia Annibale, Pierpaolo Vivo
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Abstract

Information in the form of data, which can be stored and transferred between users, can be viewed as an intangible commodity, which can be traded in exchange for money. Determining the fair price at which a string of data should be traded is an important and open problem in many settings. In this work we develop a statistical physics framework that allows one to determine analytically the fair price of information exchanged between players in a game of chance. For definiteness, we consider a game where N players bet on the binary outcome of a stochastic process and share the entry fees pot if successful. We assume that one player holds information about past outcomes of the game, which they may either use exclusively to improve their betting strategy or offer to sell to another player. We find a sharp transition as the number of players N is tuned across a critical value, between a phase where the transaction is always profitable for the seller and one where it may not be. In both phases, different regimes are possible, depending on the "quality" of information being put up for sale: we observe symbiotic regimes, where both parties collude effectively to rig the game in their favor, competitive regimes, where the transaction is unappealing to the data holder as it overly favors a competitor for scarce resources, and even prey-predator regimes, where an exploitative data holder could be giving away bad-quality data to undercut a competitor. Our analytical framework can be generalized to more complex settings and constitutes a flexible tool to address the rich and timely problem of pricing information in games of chance.

机会博弈中的信息价格:统计物理方法。
数据形式的信息可以在用户之间存储和传输,可以被视为一种无形的商品,可以用它来交换金钱。在许多情况下,确定一串数据交易的公平价格是一个重要而开放的问题。在这项工作中,我们开发了一个统计物理框架,允许人们分析地确定在机会游戏中玩家之间交换信息的公平价格。为了明确起见,我们考虑一个游戏,其中N个玩家对随机过程的二进制结果下注,如果成功,他们将分享入场费。我们假设一个玩家拥有关于过去游戏结果的信息,他们可以专门使用这些信息来改进他们的投注策略,或者将其出售给另一个玩家。我们发现,当玩家数量N在一个临界值上调整时,在交易总是对卖家有利的阶段和交易可能不有利的阶段之间,会出现一个急剧的转变。在这两个阶段,不同的制度是可能的,这取决于出售信息的“质量”:我们观察到共生制度,双方有效地串通操纵游戏,使其对自己有利;竞争制度,交易对数据持有者没有吸引力,因为它过度支持竞争对手获取稀缺资源;甚至是捕食者制度,剥削性数据持有者可能会放弃质量差的数据,以削弱竞争对手。我们的分析框架可以推广到更复杂的环境中,并构成一个灵活的工具来解决机会游戏中丰富而及时的定价信息问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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