Many researchers treat firm-level competition as the origin of competition between nations. In other words, nations are as strong as their companies. Therefore, competition lies in "firm-level competitiveness." To evaluate firm-level competitiveness, a survey was conducted in this study. Information was gathered from players in the olive oil industry, including olive oil mills, refiners, and exporters. A total of 117 firms completed the questionnaire. The Analytic Hierarchy Process was applied to determine priorities regarding factors affecting international-domestic competition and preferred arenas of competition for firms and to establish a hierarchy with respect to these preferences. The analysis gives a first-to-last ranking of branding, then food safety and quality, and finally price. The exporters emphasized incentives rather than prices as critical factors. Also, the firms stated that they can generally compete with their rivals in terms of quality, technology and food safety requirements. Taking high costs into account, it appears to be very important to continue premium support and subsidies from the standpoint of international competition.