It's an agreement done by the State's AGs.
Only if state law allows it. California, Connecticut, Hawaii, Maryland, Massachusettes, New Jersey, Illinois, Oregon, Rhode Island, and New York state Attorney Generals are prohibited by law to make such agreements, for example.
The only states up for discussion are Maine, Nevada and Wisconsin. All the other states whose state law allows for any reciprocity at all already recognize the Oklahoma permit.
In Maine, it is the Chief of State Police that enters into the reciprocity agreements, not the Attorney General, Title 25 MRSA, Part 5, Chapter 252, Subsection 2001-A:
Maine State Police
Gaming and Weapons Section
164 State House Station
Augusta, Maine 04333-0164
(207) 624-7210
In Nevada, it is the Nevada Department of Public Safety and the Nevada Sheriffs’ and Chiefs’ Association must agree to it, NRS 202.3689:
Nevada Department of Public Safety, 333 West Nye lane . Suite 100 . Carson City, NV 89706 . (775) 684-6262
Wisconsin law requires the other state to conduct an FBI NICS check prior to issuing the permit for it to be recognized in WI. I suspect that Oklahoma does not do an actual NICS check.
http://www.doj.state.wi.us/dles/cib/conceal-carry/reciprocity
Wisconsin Department of Justice
P.O. Box 7857
Madison, WI 53707-7857
Phone: (608) 266-1221
While you are waiting for the various legislatures to change the state laws, you can open carry in Nevada with no permit required, and when outside a vehicle you can open carry in Maine and Wisconsin with no permit required.