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摘要翻译：
我们引入了一个知觉和现实之间反馈的进化博弈，我们称之为现实博弈。它是一种机会游戏，不同客观结果（如掷硬币中的正面或反面）的概率取决于对这些结果的下注量。通过改变把赌注量与结果概率联系起来的“现实地图”，就有可能从概率不依赖于赌注的纯粹客观的游戏持续地转移到概率等于赌注量的纯粹主观的游戏。我们研究了自我强化游戏，在这种游戏中，对一个结果下更多的赌注会增加它的赔率，以及自我击败游戏，在这种游戏中，情况恰恰相反。这是研究在均衡和不均衡，有和没有理性的参与者，以及数值和分析。我们引入了一种度量博弈无效率的方法，类似于度量金融市场中套利机会的大小。我们证明了收敛到均衡是一个幂律，收敛速度非常慢：博弈越主观，收敛速度越慢。
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英文标题：
《The Reality Game》
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作者：
Dmitriy Cherkashin, J. Doyne Farmer, Seth Lloyd
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最新提交年份：
2009
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：General Finance 一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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英文摘要：
We introduce an evolutionary game with feedback between perception and reality, which we call the reality game. It is a game of chance in which the probabilities for different objective outcomes (e.g., heads or tails in a coin toss) depend on the amount wagered on those outcomes. By varying the `reality map', which relates the amount wagered to the probability of the outcome, it is possible to move continuously from a purely objective game in which probabilities have no dependence on wagers to a purely subjective game in which probabilities equal the amount wagered. We study self-reinforcing games, in which betting more on an outcome increases its odds, and self-defeating games, in which the opposite is true. This is investigated in and out of equilibrium, with and without rational players, and both numerically and analytically. We introduce a method of measuring the inefficiency of the game, similar to measuring the magnitude of the arbitrage opportunities in a financial market. We prove that convergence to equilibrium is is a power law with an extremely slow rate of convergence: The more subjective the game, the slower the convergence.
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PDF链接：
https://arxiv.org/pdf/0902.0100
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