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One property economists like to see from utility functions and preferences is the transitive property. If $A$ is preferred to $B$, and $B$ is preferred to $C$, then $A$ should be preferred to $C$. Another critical property is one of completeness. Relations are complete if, for all $A$ and $B$, $A$ is related to $B$, $B$ is related to $A$, or both.

Is the game of “rock, paper, scissors” transitive and complete?

A

Rock, paper, scissors is both transitive and complete.

B

Rock, paper, scissors is complete, but not transitive.

C

Rock, paper, scissors is transitive, but not complete.

D

Rock, paper, scissors is neither transitive nor complete.

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