Need help troubleshooting with Jackson

I have a HashMap which I initialize once in static block from a json file. Then I work with my local HashMap to save users requests.

static {
  TypeFactory typeFactory = mapper.getTypeFactory();
  MapType mapType = typeFactory.constructMapType(ConcurrentHashMap.class, String.class, GooglePlayGame.class);
  try {
       games = mapper.readValue(new File("games.json"), mapType);
        } catch (IOException e) {
          log.error(e.getMessage());
        }
    }

When I decide to stop app and launch it again, I can add new pair of "key-value" to this map, but when I'm trying to append changes into my json file, everything that was already in json file is duplicated + new value. This code:

try(JsonGenerator g = mapper.getFactory().createGenerator(
                  new PrintWriter(new BufferedWriter(new FileWriter(new File("games.json"), true))))) {
    mapper.writeValue(g, games);
    } catch (IOException e) {
      log.error(e.getMessage());
    }

I understood why it's happening (because of static initialization every new launch, and then I write to file all hashmap again and again), but I don't know how to fix this. I want to append new pairs to existing json file.

For example: Adding first request, all fine:

{"Machinarium":
   {"Title":"Machinarium",
    "Updated":"28 February, 2019",
    "Version":"2.5.6","Requirements":"4.1,
     "Contacts":"support@amanita-design.net"
}

Then I restart app and got another request, my json file now looks like:

{"Machinarium":
   {"Title":"Machinarium",
    "Updated":"28 February, 2019",
    "Version":"2.5.6","Requirements":"4.1,
     "Contacts":"support@amanita-design.net",
....
},
{"Machinarium":
   {"Title":"Machinarium",
    "Updated":"28 February, 2019",
    "Version":"2.5.6","Requirements":"4.1,
     "Contacts":"support@amanita-design.net",
....
},
"Samorost 3":
   {"Title":"Samorost 3",
    "Updated":"November 14, 2019",
     "Version":"1.0",
     "Requirements":"4.3,
...}

As you can see, duplicate here.

So the goal is: create HashMap -> get user request -> write this request(pair "key-value") to local hashmap -> write hashmap (or every pair separately? hmm) to json file. Then when app starts again: initialize hashmap from this json file with saved requests -> get new user request -> add new requests to json file.

I need to write each pair one by one to file (not all map), but how?