You can only imagine the conversations between Mary Harney and Bupa's Martin O'Rourke. O'Rourke, sitting there, knowing that Harney used to lead a political party that symbolises Ireland's emergence from the economic dark ages to the broad, sunlit (privatised) uplands of free markets and fair competition that promote the greatest good for the greatest number.

But in the present instance, Harney is defending something at least part of her must know is daft . . . the dominance of a bloated former state monopoly, VHI, that is given special advantages over its rivals. One of those key advantages is that VHI doesn't have to follow the same rules as its competitors, such as being required by law to maintain cash reserves or indeed even be solvent.

Harney, on the other hand, knew that Bupa had come into Ireland knowing full well that they would one day be forced to figure out how to handle VHI's disproportionately high number of older people who are naturally more expensive to insure . . . to make sure VHI doesn't have to raise premiums to the point where many of them have no insurance.

The problem is that neither side convinced the other it was serious. Harney didn't believe Bupa would make good on its threat to leave.

Bupa didn't believe that Harney would let them go.

It's a game of 'chicken'.

James Dean drives one car, some other bloke in the other, driving straight at each other at high speed on a California highway. If one car swerves first, that driver loses face, but both are still alive. If both cars swerve simultaneously, honour is satisfied and there are no winners or losers. If neither car swerves, both drivers die.

The rational decision is not to play, but if you don't have a choice, find an outcome both sides can live with, so to speak. In this case, Martin O'Rourke's car has 475,000 Bupa members and 300 employees as passengers.

Harney's car has the elderly population of Ireland. The taxpayer winds up having to clean up the mess in either case, because while we may leave the odd patient sitting on a trolley, we don't turn them away from acute care.

Game theorists, such as Thomas Schelling, who won the 2005 Nobel Prize for economics for his 1960 book The Strategy of Conflict, that arguably kept the world from being incinerated in 1962 by helping guide superpower brinkmanship, would see the Bupa-Harney game as having wound up with this result because neither side has demonstrated its commitment. No one is quite sure where the bottom line is. Neither Harney nor Bupa is moving their foot towards the brake. The Irish Times leader on Friday suggested that Bupa is bluffing. Oliver Tattan of Vivas, the other player in the health insurance market, is pretty convinced they're not and is making plans accordingly.

Fortunately, game theory also makes a helpful suggestion in situations like this. If the game is likely to produce no winner, change the game.

Bupa and the department are arguing over how much it should have to pay in order to meet the goal of keeping older people insurable in a competitive market. There is a way out.

They can look to New York state, which in 1993 decided on a policy of 'risk adjustment' to distribute a pool of older people, people who were HIV positive, chronic ailments and neonatal emergencies amongst any insurer who wanted to play in the market.

The state is divided into seven geographical pools and in each region the riskiest insured are distributed proportionately among the players.

New York did something even more radical with car insurance for under-25 male drivers when I grew up there.

Called the 'assigned risk' pool, you were told who your insurer would be. It wasn't cheap but if you wanted to drive you needed it . . . unless you were planning to play chicken.

A risk adjustment strategy like New York's could work in Ireland, and could solve the present impasse. But as everybody well knows, the first step is breaking up the VHI. That's a whole different game . . . and the one that should have been played first.