How do coaster table pagers order themselves?
Although this system may be offline from the internet the Server to Client communications must be shared over a 433 MHz channel using 4 digit address and data.

For IoT communication, these other forms were not used with the reasons given for IoT
https://www.getkisi.com/blog/internet-of-things-communication-protocols

In this case, the communication bandwidth is low but addressable.  Without knowing the intellectual property (IP) of this design, one can only guess how it is done. But most likely it is some form of server ( the listener to polls) to client ( the responder to polls) of communication.


  How do coaster table pagers order themselves?   



they respond to all inputs according to user interface and Server communication using the RF channel



  how do the pagers self orient?



by the response to sequential polling from server and response on client LED display



  What are some mechanisms that can facilitate this kind of connectivity and ordering?



Embedded "round-robin" Servo protocols and Wireless dedicated shared RF channels for Tx/Rx antenna.


Another example of a documented round-robin protocol which may be applied to a shared serial channel or a distribution channel or a shared wireless half-duplex channel

http://cdn.meccano.com/open-source/Meccano_SmartModuleProtocols_2015.pdf