Continuity (Utility Theory)

utility-theory

Definition

Continuity (Utility Theory)

If some lottery $B$ is between $A$ and $B$ in preference, then there is some probability $p$ for which the agent will be indifferent between getting $B$ for sure and the lottery yields $A$ with probability $p$ and $C$ with probability $1-p$:

$$A\succ B\succ C⟹\exists p:[p,A;1-p,C]\sim B$$