def index
  @rate = Rate.where(:rater_id => current_user.id)

  @ratename = Game.where(:id => @rate.first.rateable_id)

  end

<% @rates.order("created_at desc").each do |rates| %>

      You are playing <%= @ratename.name %></div>

  <% end %>

class Rate < ActiveRecord::Base
  attr_accessible :rateable_id, :rater_id

  belongs_to :user
  belongs_to :game

end

def index
  @rates = current_user.rates.order("created_at desc")
end

<% @rates.each do |rate| %>
  You are playing <%= rate.game.name %>
<% end %>

@ratename = Game.where(:id => @rate.first.rateable_id)

@rates = current_user.rates.order("created_at desc") #will work if you made correct associations (user has many rates)

<% @rates each do |rate| %>
  You are playing <%= rate.game.name %></div>
<% end %>

def index
   @rates = current_user.rates.includes(:game).order("created_at desc")
end


in view

     <% @rates.each do |rate| %>

      You are playing <%= rate.game.name %></div>

  <% end %>