Session Stickiness in a Stateful Microservice

I have created a simple Spring Boot Microservice for a game of Rock Paper Scissors. It involves in memory storage of registered players as well as the rounds that they play. Now, if I have to use it with a frontend in a scalable cloud environment I am going to require session stickiness. There are unique ids to players as well as the session that the two opponents play with. How can I ensure session stickiness when I have multiple instances of this microservice running in my cluster ?