You cannot use PHP code within jQuery (not in this case at least). There is a plugin for jQuery (http://plugins.jquery.com/files/jquery.cookie.js.txt) based on the parameters that are given you can setup a cookie or a session for the current user. For instance:
$('#element').click(function(e) {
e.preventDefault();
$.cookie('Ticket[]', $('#IDGame').val();
});
This code assumed the $IDGame is stored in a (hidden) textfield with ID = IDGame. This is the proper way using jQuery with sessions and cookies. If you want to use PHP Code per sé, than you should consider loading a PHP file with the getJSON function and sending the ID as a parameter to the file and adding a new key to the session in the background.
$IDGamefrom? Is it sent to the server using a query parameter? Do you check its validity?