For me, one of the most interesting economic issues of recent weeks is not Greece, or the failure of Osborne's fiscal austerity, or NGDP targeting, or any of that bigthink guff. It is Danny O'Donoghue's claim that The Voice will attract more talent next year than other talent shows.

I don't think this is true.Let's grant Danny's premise that The Voice is more musically credible than the X Factor. Does it follow that the best singers will go into The Voice?

No. We can think of the problem facing singers as being much like the hawk-dove game, where good singers are hawks and poor ones doves: let's rename it the Kate-Jedward game.

If Jedwards know The Voice will be populated by Kates, they'll not enter as they know they'll lose.They'd prefer to compete against other Jedwards.

But think of the expected payoff to Kates from competing against other Kates. We can write it as p(Vv) - (1-p)Cv, where p is the probability of winning, Vv is the prize on The Voice and Cv is the cost of defeat on The Voice.

The problem here is that p is low, as Kate is competing against other great singers. It's not obvious that this would be offset by a high Cv; the benefits of getting exposure on a more credible music show and being tutored by better people. It's quite possible, therefore, that for reasonable values of p, Vv and Cv, some Kates would rather go onto the X Factor, where p is higher as they'll be up against more doves.

But of course, if many Kates do this, p won't be much higher on the X Factor.

The solution here is for singers to use a mixed strategy. Some will enter the tough competition - The Voice - and some the easy one. The two can therefore co-exist. In this sense, Danny is wrong.

But there are (at least) two factors here which make things more complicated than a standard hawk-dove game.

One is that singers don't know their true ability or - what is not the same thing! - their chances of winning. Overconfident singers would prefer the show with the higher pay-off to winning, whilst underconfident ones would prefer the weaker competition. This might well cause overconfident Jedwards to enter The Voice whilst underconfident Kates enter the X Factor. This would reinforce the tendency for the two to co-exist.

The other problem is that in a standard hawk-dove game, the best thing for a hawk is to be the sole hawk in a field of doves. But this is not true in our case. The best thing for a Kate is to be up against enough other Kates to make a competition attractive to viewers, but not against so many as to dilute the chances of winning.The payoff to competing against other Kates is thus n-shaped in their number.

The issues here are - of course - not about TV shows, but about the economy generally. There are (at least) three implications here:

1.Apparently quite simple choices quickly become tricky when we allow for strategic interaction, uncertainty about probabilities, payoffs and costs and cognitive biases.

2. It is not always true that a stable equilibrium will arise if identical people, facing the same incentives, choose the same behaviour. Sometimes, stability arises only when apparently identical people faced with the same incentives actually behave differently.This applies to the banking system (pdf).

3.There are costs to competition. A mixed strategy, yielding a mixed population of hawks and doves is evolutionarily stable. But this only arises after a lot of hawks and doves have been killed by entering the "wrong" competition.