It’s a fairly common situation: two competing agencies working for the same client. What happens? They stab each other in the back – subtly sabotaging each other’s work, criticising each other’s work to the client, talking up their own capabilities in contrast.

Meanwhile, the agency teams suffer an unpleasantly hostile working relationship, the client pays for resource dedicated to skirmishing that could have been directed into servicing their needs, and everyone’s joy is sapped by the depressing experience of producing adequate but uninspiring work that could have been great.

All the agencies had to do was work together and everyone would have benefited – including the client, whose budget for both agencies may well have expanded as a result of the cooperative effort.

So why didn’t they?

Incentivising nastiness

At the heart of the problem is the simple fact that, individually, we are paid to make money for our agency, not to help our clients.

Don’t get me wrong – in the long run, helping our clients is the best way to make money for our agency, but often an individual’s performance is measured against short-term targets rather than long-term gains.

This translates into account managers being pressured from above to grow their accounts by undermining the accounts of competing suppliers. And even if there’s no pressure to go on the offence, there’s the fear of being on the defense – losing business to the aggressive tactics of the competition.

When faced with this situation, however the other agency behaves, the outcome will be better for you if you play nasty. They play nice? You screw them. They play nasty? You keep from being screwed. It’s a no-brainer.

The thing is, they’re faced with the exact same situation. And it’s a no-brainer for them too.

So if you both act rationally for short-term benefits, you’ll both play nasty. And if you both play nasty, you’ll both get a fairly undesirable outcome. But if you both just played nice, you’d both get a fairly desirable outcome.

In game theory, this scenario is called the Prisoner’s Dilemma, and its solution hinges on a simple fact: we don’t face these situations just once, but rather face them over and over again.

Finding a solution

Looking for the best strategy for repeated instances of the Prisoner’s Dilemma, a political scientist named Robert Axelrod organised a tournament in which different strategies could be competed against each other.

In a study of the other most successful strategies in the tournament, Axelrod found five recurring traits. Successful strategies…

· …are never the first to play nasty.

· …counter-attack when the competition plays nasty.

· …return to playing nice if the competition stops playing nasty.

· …often trial a return to playing nice to give the competition a chance to do the same.

· …don’t seek to reap more benefit than the competition.

So, what does that mean for you?

Benefiting in the real world

Take a little advice from mathematics in your relationships with other agencies…

1. Treat other agencies the way you’d like to be treated. Don’t look for opportunities to undermine other agencies. Hell, if you think they did a good job, tell them and the client that you think so.

2. But don’t be a doormat. If you learn that another supplier has started trying to push you out of business you already handle, you push right back.

3. Favour reconciliation. If things are hostile, be eager to end hostilities. They might not expect that, so there’s a good chance you’ll have to let them know. Have a coffee or a beer, tell them the situation’s bad for everyone and work together on ending it.

4. Let your agency’s work do the talking. Most important point of all. Another agency can only really push you out of business if you don’t deliver good work (you don’t deserve the client) or your client can’t recognise good work (the client doesn’t deserve you). Either way, a team that prioritises quality over politics will win the long game.

Remember, qualities like humility, respect, friendliness, forgiveness and integrity aren’t for suckers – they’re good for business.

You can’t argue with that: it’s maths.

Ryan Sproull is a digital strategist at Zuni.