The London 2012 Olympic Games have been sold to us at least partly on the premise that sport brings people together and is therefore good for humanity. And although I can see that major sporting events do bring people together in terms of their shared passion for a particular event, they also surely reinforce barriers too, as supporters of one team or nation are encouraged to differentiate themselves from the opposition's supporters. We just need to look at the terrible violence that has historically taken place at certain international football matches to witness the ugly side of sport. So much for community relations.

Fortunately, however, London 2012 is not just about sport. It's also about culture, which arguably has a much better track record (no pun intended) at bringing people together. Under the umbrella of the Cultural Olympiad itself, theatre is well represented, including the World Shakespeare Festival, which is being produced by the RSC in collaboration with over 50 arts organisations and 260 amateur groups (and includes the Globe to Globe Festival, which I wrote about last week); and Unlimited, the UK's largest ever programme celebrating arts, culture and sport by disabled and deaf people.

Then, on top of those official, UK-wide programmes, there are non-Olympics-affiliated local events such as the capital's World Stages Festival, which was announced this week. World Stages sees eight London theatres working together with 12 UK and international co-producers to create eight large-scale productions, each taking as its focus the experience of a different London community.

It's no coincidence that so many of the exciting and ambitious theatre projects that will be taking place next year involve collaboration – whether locally, nationally or internationally – inter-community discourse, and welcoming foreign companies to the UK to perform in foreign languages. Whatever differences exist between people, storytelling is something that we all share, making theatre a good basis for exchange of ideas and experiences. Even if we don't all agree about the topic under discussion, theatre has the power to get us talking, which is always an excellent start.

Reaching new audiences and widening participation is central to many of these projects. In terms of Globe to Globe, that means sending ambassadors into communities; the theatres involved in World Stages are drawing on the existing relationships they have with the communities around them to get people involved. It won't be an easy process – audience development is painstaking work – but the fact that international companies are involved, and that some of the work will be in languages other than English, is a great help. The fact that these theatres will be putting their money where their mouth is and offering plenty of tickets for those on low incomes is also very important.

But it's not just about audiences – it's also about theatre itself. David Micklem, artistic director of BAC, one of the theatres involved in World Stages, yesterday talked to me very enthusiastically about the partnerships the festival has been creating within the London theatre community. The planning for World Stages began before the recession, the change of government and the subsequent arts funding cuts – ie. in a moment when collaboration was a choice rather than a necessity – but it's a happy coincidence that the relationships being developed as part of World Stages have the potential to make survival in the future that little bit more feasible through sharing resources and expertise.

And in the short-term of course, even if this is the only project these theatres ever collaborate on, it's a wonderful opportunity to do work on a larger scale than would ever be possible alone. Babel, for instance, the show that BAC is producing with WildWorks (the team behind the National Theatre Wales's The Passion, which took place in April this year) along with the Lyric Hammersmith, Theatre Royal Stratford East and the Young Vic, will involve a professional and community cast of 500 and will play to audiences of 1000 per performance. Such a project, needless to say, is far beyond the reach of any of these theatres working independently.

I'm excited about the Olympics, but I'm also fairly certain that the three weeks of the Games will be a bit of a nightmare. London will be gridlocked, most people won't actually get the chance to see any of the events and the whole spectacle is costing enormous sums of money that the UK economy may never see again. The cultural events taking place, however, both the official and non-official ones, are another story, and one that I'm far more hopeful about: taking place over many months throughout the UK (World Stages excepted of course), they will entertain tens of thousands of people, get communities talking to each other and enrich the UK's cultural life through engaging with new audiences and artists. I know it's not a competition, but if it was, culture would clearly win: Theatre 1-0 Sport.