完全市场中乘法形式的相对业绩准则
Relative performance criteria of multiplicative form in complete markets
摘要：
研究了完全半鞅市场中效用最大化的$N$ -局中人博弈在乘法形式的相对业绩准则下纳什均衡的存在唯一性.对于一个大类的球员的效用函数，纳什均衡的一般特征，为一个给定的初始财富向量提供了可逆的映射从$\mathbb{R}^N$到$\mathbb{R}^N$。作为一般定理的结果，我们得到了纳什均衡的存在性和唯一性的任意初始财富向量，以及它们的收敛性，如果（i）球员的效用函数接近CRRA，或（ii）球员的竞争权重是小的，相对风险厌恶是有界远离无穷大。
英文摘要：
We consider existence and uniqueness of Nash equilibria in an $N$-player game of utility maximization under relative performance criteria of multiplicative form in complete semimartingale markets. For a large class of players' utility functions, a general characterization of Nash equilibria for a given initial wealth vector is provided in terms of invertibility of a map from $\mathbb{R}^N$ to $\mathbb{R}^N$. As a consequence of the general theorem, we derive existence and uniqueness of Nash equilibria for an arbitrary initial wealth vector, as well as their convergence, if either (i) players' utility functions are close to CRRA, or (ii) players' competition weights are small and relative risk aversions are bounded away from infinity.
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