I tested this (briefly) and was having some problems with the onchange callback (nothing happened). This however works great (register event with Js, not HTML attribute):
<form name="difficulty" action="${pageContext.request.contextPath}/game.do" method="post">
<div id="difficulty">
<label>Difficulty Level</label><br>
<select name="difficultyLevel">
<option value="easy" name="easy">Easy</option>
<option value="medium" name="medium">Medium</option>
<option value="hard" name="hard">Hard</option>
</select>
</div>
</form>
<script type="text/javascript">
document.getElementsByName("difficultyLevel")[0].onchange = function() {
document.getElementsByName('difficulty')[0].submit();
}
</script>