A Bidding Game in a Continuum Limit Order Book
A Bidding Game in a Continuum Limit Order Book
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连续限价订单簿中的竞价游戏
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Giancarlo Facchi
中科院分区：
文献类型：
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作者：
A. Bressan;Giancarlo Facchi
本文涉及限价订单簿的连续模型，将其视为 $n$ 玩家的非合作博弈。外部买家要求给定资产的随机金额 $X > 0$。只要价格不超过给定的上限$overline{P}$，该金额将以最低可用价格购买。一个或多个卖家以不同的价格提供不同数量的资产，竞相履行收到的订单，而订单的大小是事先未知的。本文的第一部分讨论了单个参与者的测值最优定价问题的解决方案，证明了存在性结果并导出了最优性的充分必要条件。第二部分专门讨论纳什均衡。对于一般类别的随机变量$X$和任意数量的参与者，证明了相应的纳什均衡的存在性和唯一性，明确地确定了每个参与者的定价策略。对于不同类别的随机变量，表明没有纳什等价...
The paper is concerned with a continuum model of the limit order book, viewed as a noncooperative game for $n$ players. An external buyer asks for a random amount $X > 0$ of a given asset. This amount will be bought at the lowest available price, as long as the price does not exceed a given upper bound $overline{P}$. One or more sellers offer various quantities of the asset at different prices, competing to fulfill the incoming order, whose size is not known a priori. The first part of the paper deals with solutions to the measure-valued optimal pricing problem for a single player, proving an existence result and deriving necessary and sufficient conditions for optimality. The second part is devoted to Nash equilibria. For a general class of random variables $X$ and an arbitrary number of players, the existence and uniqueness of the corresponding Nash equilibrium is proved, explicitly determining the pricing strategy of each player. For a different class of random variables, it is shown that no Nash equi...