Wyo. Stat. § 36-5-108
If two (2) or more qualified applicants under W.S. 36-5-101 shall offer the same annual rental for the same lands, and such offers are the highest offers received and are equal to or above the minimum rental fixed by the board, and no preferred right exists in the old lessee, or if the old lessee does not exercise the preferred right, the director shall grant the lease to the applicant holding title to lands nearest to the lands applied for. When a preferred right exists in the old lessee under the provisions of this act, the old lessee shall be given fifteen (15) days notice by registered mail, and if he fails or refuses to file his acceptance together with the balance of the rental due for the first year, within the time specified, the lease shall be awarded automatically to the applicant offering to pay the highest annual rental, or in the event of even offers, shall be disposed of as hereinbefore provided. As used in this section, "preferred right" means as defined in W.S. 36-5-105(h).
W.S. 36-5-108