Uniform Sampling of the Infinite Noncooperative Game on Unit Hypercube and Reshaping Ultimately Multidimensional Matrices of Player’s Payoff Values

IF 0.5 Q4 ENGINEERING, ELECTRICAL & ELECTRONIC Electrical Control and Communication Engineering Pub Date : 2015-07-01 DOI:10.1515/ecce-2015-0002
V. Romanuke
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引用次数: 5

Abstract

Abstract The paper suggests a method of obtaining an approximate solution of the infinite noncooperative game on the unit hypercube. The method is based on sampling uniformly the players’ payoff functions with the constant step along each of the hypercube dimensions. The author states the conditions for a sufficiently accurate sampling and suggests the method of reshaping the multidimensional matrix of the player’s payoff values, being the former player’s payoff function before its sampling, into a matrix with minimally possible number of dimensions, where also maintenance of one-to-one indexing has been provided. Requirements for finite NE-strategy from NE (Nash equilibrium) solution of the finite game as the initial infinite game approximation are given as definitions of the approximate solution consistency. The approximate solution consistency ensures its relative independence upon the sampling step within its minimal neighborhood or the minimally decreased sampling step. The ultimate reshaping of multidimensional matrices of players’ payoff values to the minimal number of dimensions, being equal to the number of players, stimulates shortened computations.
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单位超立方体上无限非合作博弈的均匀抽样及博弈者收益值的最终多维矩阵的重塑
摘要给出了单位超立方体上无限非合作对策的近似解的一种方法。该方法基于沿每个超立方体维度以恒定步长均匀采样玩家的收益函数。作者陈述了足够精确采样的条件,并提出了将采样前玩家的收益函数的多维矩阵重构为具有尽可能少的维数的矩阵的方法,其中还提供了一对一索引的维护。给出了有限对策的NE(纳什均衡)解作为初始无限对策逼近的有限NE-策略的要求,作为近似解一致性的定义。近似解一致性保证了其在最小邻域内或最小减小采样步内的相对独立性。将玩家收益值的多维矩阵最终重塑为最小维度,即与玩家数量相等,可以缩短计算时间。
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来源期刊
Electrical Control and Communication Engineering
Electrical Control and Communication Engineering ENGINEERING, ELECTRICAL & ELECTRONIC-
自引率
14.30%
发文量
0
审稿时长
12 weeks
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