论文标题
预期的多停车表示偏爱彩票的偏好
Expected multi-utility representations of preferences over lotteries
论文作者
论文摘要
让$ \ succsim $是一组简单彩票的二进制关系，而可计数的结果集$ z $。我们在$ \ succsim $上提供必要和足够的条件，以确保存在$ u $ u $ u $ u $ u $ u $ u $ u $ u u $ u：z \ to \ mathbf {r} $，以便$ p \ ucs q \ uccsim q \，\，\，\，\，\，\，\，\ long long long long frightrightArlow \ _ \ Mathbf {e} _q [u] \，\ text {对于所有简单彩票$ p，q $ in u $$ in u $$ in u $$。在这种情况下，集合$ u $本质上是唯一的。然后，我们表明，如果$ z $无法数量，模拟表征将无法保持。这为Dubra，Maccheroni和OK在[J.经济。理论〜\ textbf {115}（2004），no。〜1，118--133]。最后，我们表明，$ \ succsim $上的不同连续性要求允许对设定的实用程序功能的可能选择（例如，所有公用事业功能均具有限制）的某些限制，提供了广泛的预期多功能表示。
Let $\succsim$ be a binary relation on the set of simple lotteries over a countable outcome set $Z$. We provide necessary and sufficient conditions on $\succsim$ to guarantee the existence of a set $U$ of von Neumann--Morgenstern utility functions $u: Z\to \mathbf{R}$ such that $$ p\succsim q \,\,\,\Longleftrightarrow\,\,\, \mathbf{E}_p[u] \ge \mathbf{E}_q[u] \,\text{ for all }u \in U $$ for all simple lotteries $p,q$. In such case, the set $U$ is essentially unique. Then, we show that the analogue characterization does not hold if $Z$ is uncountable. This provides an answer to an open question posed by Dubra, Maccheroni, and Ok in [J. Econom. Theory~\textbf{115} (2004), no.~1, 118--133]. Lastly, we show that different continuity requirements on $\succsim$ allow for certain restrictions on the possible choices of the set $U$ of utility functions (e.g., all utility functions are bounded), providing a wide family of expected multi-utility representations.
