# 效用

## 基礎

${\displaystyle {\text{U}}=\sum _{i=1}^{n}u(x_{i})p_{i}}$，當中

${\displaystyle u(x_{i})}$ 係指第 ${\displaystyle i}$ 個可能結果嘅效益，${\displaystyle u(x_{i})}$${\displaystyle x_{i}}$${\displaystyle i}$ 帶嚟嘅價值）嘅函數，而 ${\displaystyle p_{i}}$ 係第 ${\displaystyle i}$ 個可能結果發生嘅機會率[註 1]。用日常用語講，即係話個選擇嘅 ${\displaystyle {\text{U}}}$ 等如「將每個可能結果發生嘅機會率乘嗰個結果嘅效益，再將呢啲乘出嚟嘅數冚唪唥加埋嗮一齊」[1]

## 註釋

1. ${\displaystyle \sum }$加總
2. 有關類似嘅統計分析，可以睇睇多層模型嘅概念。

## 英詞

1. expected utility
2. utility encoding

## 引用來源

1. Morgenstern, O., & Von Neumann, J. (1953). Theory of games and economic behavior. Princeton university press.
2. Devisch, O. T., Timmermans, H. J., Arentze, T. A., & Borger, A. W. (2009). An agent-based model of residential choice dynamics in nonstationary housing markets. Environment and Planning A, 41(8), 1997-2013.
3. Tobler, P. N., Christopoulos, G. I., O'Doherty, J. P., Dolan, R. J., & Schultz, W. (2009). Risk-dependent reward value signal in human prefrontal cortex 互聯網檔案館歸檔，歸檔日期2021年5月17號，. (PDF). Proceedings of the National Academy of Sciences, 106(17), 7185-7190.