Behavioural economics meets property rights - who owns the space between airline seats?

This article in The Economist is definitely one to save up for the next time you are teaching behavioural economics, but it offers a great deal more than that. The interaction of demand and supply, property rights, scarce resources and allocative efficiency - to name a few.

How much would you pay to be granted the right to recline your seat on an aeroplane? And how much would you pay to prevent the person in front of you from reclining theirs? Rather than the passenger behind resorting to jamming his knees into the back of the seat in front, or the passenger in front choosing the most awkward moment to tip his seat back towards the person behind him, would it be better if they held an auction over the rights to use of that space before the flight, and so agreed who valued it most highly?

Research shows that an equilibrium may be difficult to arrive at: on average, 'recliners' - the person seated in front - set the price of agreeing not to recline their seat at $41, but if they had to pay to be allowed to recline, rather than being paid not to do so, they were only willing to pay $12.It comes down to their expected utility, according to van Neumann and Morgenstern writing The Theory of Games and Economic Behaviour in 1944, and decision-makers are much more reluctant to give up something that they thought they owned than to pay for something they thought belonged to someone else.

But if we were to haggle over who is allowed to use the space between airline seats, would this just increase inequality - would ownership of the space simply be gained by the person with the higher disposable income? Is that the best outcome, or would the solution suggested in the article, which is to install non-reclinable seats, simply result in the worst of all worlds?