Preference relation

Definition

A preference relation of player $i$ over a set of outcomes $O$ is a binary relation denoted by $\succsim_i$.

$x \succsim_i y$ as "player $i$ either prefers $x$ to $y$ or is indifferent between the two outcomes"

Assumptions

Complete

The preference relation $\succsim_i$ over $O$ is complete, that is, for any pair of outcomes $x$ and $y$ in $O$, either $x \succsim_i y$, or $y \succsim_i x$, or both.

Reflexive

The preference relation $\succsim_i$ over $O$ is reflexive, that is, $x \succsim_i x$ for every $x \in O$.

Transitive

The preference relation $\succsim_i$ over $O$ is reflexive, that is, for any triplet of outcomes $x$, $y$, and $z$ in $O$, if $x \succsim_i y$ and $y \succsim_i z$ then $x \succsim_i z$.

Compare

• Strict preference relation
• Indifference relation

References

1. M. Maschler, E. Solan, and Shmuel Zamir, Game Theory, Cambridge University Press, 2013, p. 10.