Apart from the arbitration agreement itself, the arbitration rules selected by the parties will govern the arbitration. Arbitral rules tend to have two specific purposes: (1) the promulgation of a specific set of rules to govern the arbitration process; and (2) the administration of the arbitration itself (i.e., naming or challenging an arbitrator). S. I. Strong, Research and Practice in International Commercial Arbitration, §2.38 (2009). Researchers should be cautious, however, as the arbitration agreement may be varied by the parties. Researchers should pay close attention to those rules that state, "unless otherwise agreed in writing by the parties." This could signify an instance where the parties have deviated from the standard arbitration rule. See Margaret Moses. Introduction to International Commercial Arbitration, 7 (2017).
These are some of the leading arbitral institutions, all of which have promulgated their own rules. Researchers should note that there is no requirement to have the arbitration overseen by an arbitral institution (this would lead to an "ad hoc" arbitration), and also that while institutional arbitrations generally are governed by the institutional rules, there may be exceptions. Strong, supra at §2.39.
The Detroit Mercy Law Library's collection includes subscriptions to Westlaw and Kluwer Arbitration, with practical tools helpful in conducting research on arbitral rules.