RAILS - Join table with 2 tables and a form - Controller what should I do?

i'm a bit lost and also new to rails and i couldn't find an answer to this. I think it's just my lack of knowledges in rails too.
I got Users , they own games (the opposite is true too) and a join table between them to make the link
Table(Game_User) : (user_id) & (game_id).

A user has many games
A game has many users

I would like to update my form and save the information when the user signed in and add his favorite game among a list (F.select_collection in the form).

I just dont know if the information in the join table was recorded, i dont think so, my tests in the rails console where not concluding. I'm learning by doing but sometimes it's a bit difficult :)

If I missed something just ask me ( I don't have a controller for the Table Join , is it ok ? )

Thanks a lot in advance !!

user.rb

class User < ActiveRecord::Base
  has_many :game, :through => :game_user
  has_many :game_user

game.rb

class Game < ActiveRecord::Base
   has_many :user, :through => :game_user
   has_many :game_user
end

game_user.rb

class GameUser < ActiveRecord::Base
    belongs_to :game
    belongs_to :user
end

games_controller.rb

 before_action :set_game, only: [:show, :edit, :update, :destroy]

  def index
    @games = Game.all
  end

  def show
  end

  def new
    @game = Game.new
  end

  def edit
  end

  def create
    @game = Game.new(game_params)

    respond_to do |format|
      if @game.save
        format.html { redirect_to @game, notice: 'Game was successfully created.' }
        format.json { render :show, status: :created, location: @game }
      else
        format.html { render :new }
        format.json { render json: @game.errors, status: :unprocessable_entity }
      end
    end
  end

  def update
    respond_to do |format|
      if @game.update(game_params)
        format.html { redirect_to @game, notice: 'Game was successfully updated.' }
        format.json { render :show, status: :ok, location: @game }
      else
        format.html { render :edit }
        format.json { render json: @game.errors, status: :unprocessable_entity }
      end
    end
  end

  def destroy
    @game.destroy
    respond_to do |format|
      format.html { redirect_to games_url, notice: 'Game was successfully destroyed.' }
      format.json { head :no_content }
    end
  end

  private
    # Use callbacks to share common setup or constraints between actions.
    def set_game
      @game = Game.find(params[:id])
    end

    def game_params
      params.require(:game).permit(:name, :plateform, :plateform_id, :typegame)
    end
  end

users_controller.rb

class UsersController < ApplicationController
    def index
      @users = User.all
    end

    def show
      @user = User.find(params[:id])
    end

end

Last item , the form for editing the profile of the person (with Devise gem btw)

extract of the form

<div class="panel-title-edit">
      <h1>Edit <%= resource_name.to_s.humanize %></h1>
    </div>
  </div>
  <div class="panel-body-edit">
    <%= form_for(resource, :as => resource_name, :url => registration_path(resource_name), :html => { :method => :put }) do |f| %>
    <%= devise_error_messages! %>

  <div class="form-group">
    <%= f.label :country %><br />
    <%= f.text_field :country, autofocus: true,  class: "form-control" %>
  </div>


  <div class="form-group">
    <%= f.label :game %><br />
    <%= f.collection_select(:game, Game.all, :id, :name, {:multiple => true}, class: "form-control") %>
  </div>

  <div class="form-group">
    <%= f.submit "Update", class: "btn btn-primary" %>
  </div>
<% end %>