According to the OSPF protocol, the designated router (DR) is the router that acts as the focal point for exchanging routing information on a multi-access network segment, such as a LAN 1 .  The DR election process is based on the following criteria, in order of precedence 1 :

The router with the highest OSPF priority becomes the DR. The default priority is 1, and a priority of 0 means the router will not participate in the election.

If there is a tie in priority, the router with the highest router ID becomes the DR. The router ID is a 32-bit number that uniquely identifies a router in an OSPF domain. It can be manually configured or automatically derived from the highest IP address of a loopback interface or a physical interface.

If there is a tie in router ID, the router that was first to become an OSPF neighbor becomes the DR.

In your scenario, two routers share the same highest priority and start time. This means that they have equal chances of becoming the DR based on the first and third criteria. Therefore, the second criterion will be used to break the tie, which is the router ID.  The router with the highest router ID will become the DR, and the other router will become the backup designated router (BDR), which is ready to take over the role of DR if it fails 1 .