It depends on what you mean by "linguist" and "competition". There is the linguistics olympiad, a skills competition related to linguistics designed for high school students, and they include transliteration exercises where e.g. some words are given in Georgian script and based on that you have to figure out what some other word is. This is not what linguists generally mean by decipherment, instead, the term refers to figuring out an unknown script (Georgian is not unknown, just unknown to the test-takers), one not used in a living language (hence you don't have to decipher Arabic, you just have to learn the writing system).
An example is Persian cuneiform, which was deciphered by Henry Rawlinson (hence the link to his later work on Assyrian. The script was a centuries-old puzzle, and various people made contributions to understanding the inscriptions, focusing on the word for "king" and the names of kings. There was also a puzzle of understanding Egyptian hieroglyphics, the resolution of which helped solve the Persian cuneiform puzzle. The details of the decipherment of Assyrian are not clear to me, so it's not clear that there was a "competition". There is a current prize for deciphering the Indus script, but this is not an organized competition, it is a challenge. There are a small number of undeciphered systems, such as Rongorongo, and it is likely that at any given time, one or more persons are spending time on decipherment of that system. The evidence regarding decipherment of the Voynich manuscript indicates that there probably are multiple efforts at decipherment right now.
Rawlinson was not a linguist as we generally understand the concept, he was an army officer, but you could say that anyone who deciphers a script is perforce a linguist.