How to paginate Tag’s page

One developer unknown by me had left us with a pagination function that paginate the tags page publishing more pages than the needs, i think it paginate like every tag has all posts listed, so from a certain page every new page is a 404 error.
This is the code we have, i’ve tried to put a $tag variable without success:

global $wp_query;
$paged  = get_query_var('paged') ? get_query_var('paged') : 1;
$cat    = get_query_var('cat') ? get_query_var('cat') : '';
$tag    = get_query_var('tag') ? get_query_var('tag') : ''; // my test for tag variable

$args = array(
	  'paged' => $paged
	, 'order' => 'desc'
	, 'orderby' => 'date'
	, 'type' => 'post'
	, 'cat' => $cat
	, 'tag' => $tag
	, 'post_status' => array('publish')
	);
$the_query = new WP_Query( $args );

// here goes the WHILE LOOP

wp_pagenavi( array( 'query'=> $the_query));