Why an artist dressed in a bear suit deserves to get his paws on this year's Turner Prize

There are banners all over the platforms at Lime Street station in Liverpool, proclaiming the arrival of the Turner Prize. For this year only, Britain's leading art competition has gone north to herald Liverpool's year as the European City of Culture for 2008. The exhibition by the four shortlisted artists opens today at Tate Liverpool but, on the larger banners at the station, you may notice some smaller print. It reads: "We're open to you. Are you open to us?"

It is hard to think of another art form taking such a chippy attitude to its potential audience, and it belies the usual Tate propaganda about there being an insatiable demand for contemporary art. If a gallery has to chide its visitors in, on pain of being "closed-minded", there is evidently still a problem – though whether the problem is supposed to be with the art or with the especially recalcitrant people of Liverpool, I'm not sure.

Inside the gallery, everything is being made as nice as possible. To ease your visit, it has installed a temporary café in its top-floor exhibition space. There is no admission fee and there is even a black cab near the entrance to the show, with a video screen on its back seat, showing films of people sitting in the back seats of Liverpool taxis, talking about art. That should do the trick.

The four shortlisted artists are Mark Wallinger, Mike Nelson, Zarina Bhimji and Nathan Coley. This means that in one way this year's Turner really is different: it finally looks like a prize. For the first time, two of the artists in the running – Wallinger and Nelson – have been shortlisted before. That's what you'd expect with a proper annual art competition. The same names will turn up more than once. Someone may even win more than once. But since the Turner was relaunched in 1990, artists have hardly ever been shortlisted twice. No one has ever won twice. No winner has been shortlisted again. It has not behaved like a contest at all – more like a rolling showcase for new talent, disguised as a contest. So this is an encouraging sign, although this time the contest is very unequal.

It's hard to convey Wallinger's work in a small display. Its range is so various, its invention so consistently sharp and dense and surprising. He is shortlisted specifically for his reconstruction in Tate Britain of Brian Haw's anti-war protest in Parliament Square. That piece has been dismantled now. In Liverpool, he is showing Sleeper, a film of a performance work done in the Neue Nationalgalerie in Berlin.

Up all night for 10 nights, dressed in the costume of a brown bear, the artist moved around within the gallery's large glass-walled foyer, trapped but visible to passing pedestrians, as if in a big zoo enclosure. The brown bear is Berlin's emblem and there are various ideas in play (about nation, history, identity). But the impact of the piece exceeds its meanings. The idea seems to come out of nowhere. The absurdity but odd dignity of the costume, the comic-melancholic routines with which the poor, allegorical animal keeps itself awake, add up to a transfixing piece of silent theatre.

Mike Nelson is another artist with a real and rich imagination, though a more consistent trademark. His medium is interiors, into which the viewer enters. He constructs fictional spaces in art galleries, sequences of carefully furnished rooms, dramatic environments, full of thresholds and sudden turnings. Sometimes he works in a highly realistic mode, capturing with uncanny accuracy some low-rent locale, some weirdo's den. Sometimes he takes off into fantasy, symbolism and spectacle. He understands the subdued storytelling that a place can hold. He can fuse these excitements with a sculptural sense of volume and scale.

There is a strain of cliché in his imagination. The mood is too often menacing, druggy, paranoiac – too obviously bad-dreamy. The piece in this show has a characteristically jokey, crazy title – AMNESIAC SHRINE or The misplacement (a futurological fable): mirrored cubes – inverted – with the reflection of an inner psyche as represented by metaphorical landscape 2007 – although it was unfortunately still under construction when I visited. But Nelson's inventions always have a new and strong identity. That can't be said for the other two candidates.

Zarina Bhimji's work is sensitive, a little bit atmospheric, a little bit disquieting, but without any particular character. Her recent pieces are responses to historically charged locations. The photos and a short film she shows here were made in India, Zanzibar and east Africa. The photos are what any arty photographer doing "images of colonial legacy" would come up with.

The short film, Waiting, belongs to a well-known contemporary art genre: the poetic, spooky study of an old building empty of people but resonant with human presence (see work by Tacita Dean, Jane and Louise Wilson etc). The location here is a rope factory – light, dust, machinery, air currents, organic textures, stillness, nice shifts of focus, all perfectly fine but strange to find it up for a top prize. It's not the strangest, though.

There is always some overlap between the personality of the artist and the personality of the hopeless bore. It is not surprising to find art made in a spirit of proactive dullness. And, because hopeless bores also turn up on prize juries and stick up for their own, such art may prosper too. I am trying to demystify what might seem inexplicable: the career of Nathan Coley.

He may well be the most boring artist in Britain – more boring than Simon Starling (who won in 2005), more boring even than Liam Gillick (shortlisted in 2002). His work is so dull to look at that you swiftly turn to a print-out in search of an explanation – and find the work is wholly explained by its explanation but not made the slightest bit more interesting. Coley is concerned with how the built environment embodies political power. So are many people. But you can't make a little model of a terraced house, stick the word "Hope" on one side and "Glory" on the other and imagine it says anything at all.

This year's prize is given on 3 December. Wallinger is the most gifted artist of his generation and it will be silly if he does not win. But, even with the best-run art contests, silly things happen.

Turner Prize 2007 Exhibition, Tate Liverpool, Albert Dock, Liverpool L3, until 1 January