Samsung appears to be the only big player in the OLED market right now! While there is some competition, it appears to be almost non-existent as the South Korean conglomerate manufactured 95 percent of all OLED panels that shipped in Q1 2016:
According to market research firm UBI Research, Samsung Display shipments accounted for 95% of all total OLED panel shipments in Q1 2016, with OLED shipments totaling in at around 91.3 million units. Samsung Display OLED shipments were at 86.7 million in Q1, and this is best explained by the rise in OLED panel adoption in smartphones. Chinese smartphone makers have adopted OLED displays in an alarming number, with the number of OLED smartphones having more than tripled from just 5 in 2015 to 17 in 2016 — and the year is just getting started.