Strict preference relation

Definition

Given the preference relation $\succsim_i$ we can define the corresponding strict preference relation $\succ_i$, which describes when player $i$ strictly prefers one outcome to another: $$x \succ_i y \iff x \succsim_i y \text{ and } y \not\succsim_i x$$

References

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