Game Theory Points HA’s Towards Mergers

Game Theory Points HA’s Towards Mergers

As the world of Maths and Financial Modelling mourns the passing of John Nash (Nobel Prize winning mathematician), it seems apt and coincidental that I’d been exploring the economic concept of “Game Theory” in the context of housing associations (HA’s).

Principally, Game Theory points out that each and every housing association that competes against other housing associations for land and new units has an optimal strategy, and this strategy is predictable. The late John Nash helpfully pointed out, that if all the participants chose their predicted strategy, it would theoretically be worth at least one of the housing associations subsequently amending their strategy – this became known within economics as the Nash Equilibrium.


The Famous Prisoner Example Applied to HA’s

The prisoner example, put succinctly, is a way of explaining why the optimal solution to a problem is often only seen when being one step removed from a situation. In the example two prisoners are being interrogated for a murder. They’ve been charged, but if they stay quiet the police would have to drop the case in a matter of weeks on the grounds of limited evidence. It is clearly a positive result for both parties, but each party can only see the situation from their own perspective. They’d be fearful of being “ratted out” by their fellow suspect and then receiving a 20 year jail sentence. They’d also know that if they co-operated any jail sentence would be halved and only the first to co-operate would receive the recognition in their reduced sentence. It’s for this reason, that during the three weeks of interrogation, the best option through the eyes of each prisoner is to attempt to co-operate quickly in the hope of securing a reduced sentence.

In the context of housing associations it seems obvious that the pressures of “The Housing Crisis” pits ever increasingly ambitious development departments against one another if they operate within the same geographical region. It’s worth pointing out that all HA’s exist for only two purposes, to best serve existing tenants or to increase stock in an attempt to erode the housing crisis. It appears to be a quirk of the charitable housing sector that by each of the housing associations choosing to eradicate the housing crisis – the decision directly detracts from the ability of other housing associations succeeding in doing so. Other charitable sectors do not suffer from this quirk.  Cancer Research UK’s research doesn’t directly push up the price of cancer research done by the Macmillan Foundation, although it can be argued that they indirectly push up the cost of employing scientists et al.

Which Strategy Gets the Best Value out of Section 106’s?

Section 106’s account for circa £3bn in social development each year. When commercial housing developers build sites of ten or more units, we know they are forced into offering a section of the stock at a social level – through section 106 agreements, and as each housing association reviews whether to bid for section 106’s it faces two options.


Option 1: Best Foot Forwards

The HA may adjust its bid to the maximum level it can sustainably afford.  This typically hovers around the present value of the units calculated via a discounted cashflow model. By bidding towards the top end it is more likely to win – and successfully obtain the units. It would then receive units that deliver only marginally positive NPV’s that offer little cross subsidy to the rest of the company.

Or, it may lose having only succeeded in bumping the price up for the housing association that had emerged victorious in the bidding war.


Option 2: Collusion and a Little Running From the Police

However, what happens if the housing associations could collude? What happens if the housing associations could create an agreement where they took it in turns to bid for the section 106 units? The new hurdle to overcome would be bidding just high enough so as to be acceptable to the private developer, this is likely to be around the level that they’d cover costs. Each housing association could then redirect cash and increased surpluses into further social housing developments.

Each successful HA benefits two fold, through a) increased profitability and b) decreased cash outflow.

However, it probably hasn’t gone un-noticed amongst the keen eyed Financial Directors of the social housing sector that collusion is a dirty word that conjures up images of real prison and interrogation scenarios. The ideal scenario would be a legal form of collusion.

The Solution: Mergers. Potentially lots of mergers

When two similar sized housing associations share a desire to grow, they typically compete for the same land and section 106’s. To merge is not only a way of spreading fixed overheads over a greater number of units but also a way of decreasing competition and increasing internal rates of return (IRR’s).

To take this to the extreme, the sector appears in-efficient in each and every borough where two or more housing associations compete. As previously stated, there is a huge amount of goal congruence within the sector, each housing association is only in business to serve two purposes, either to grow (and diminish the housing crisis) or to serve its existing tenants.

It therefore appears clear that the optimum strategy for growth is to merge with all other housing associations that are actively bidding on land within their areas. If we assume that all housing associations have a similar cost of funds to cover when bidding on a project, we can assume that most housing associations calculate the present value of a new development in much the same way and come to much the same conclusion. This means that the presence of only a few HA’s has the effect of pushing the sale price of section 106 agreements up to a similar level of a market filled with tens of HA’s. Therefore, we’d need to eradicate all competition within geographic areas to sufficiently decrease the bidding costs for section 106 sites and in turn all land sites within an area.

A succession of partnerships has slowly brought about the domination of some HA’s within some areas, but none to my knowledge has come about as quickly as I am proposing. The typical partnership model would be to merge, and then take a period of a few years to consolidate, but I’d argue that it should at least be the strategy of some housing associations to merge on mass in order to maximise their effectiveness. As the table below depicts, area dominant housing associations that can obtain cheaper section106 deals may be key to solving the housing crisis. Competition free section 106’s potentially add a present value of £7,000 to each new unit. That’s £7,000 that could be spent on organic development within land led sites.

How Game Theory May be Applied to Housing Associations

How Game Theory May be Applied to Housing Associations


Unfortunately, what I’ve ignored is the decision makers within the above scenarios. Mergers between HA’s tend to result in one CEO and Finance Director collecting their P45, and if we remember the results of the prisoner example, we’ll remember that at an individual level, people tend to act in their own self-interest. However, I don’t rule out that under the guidance of the HCA and economists within the sector we’ll see an ever increasing amount of mergers and partnerships in an attempt to “choose” the optimum strategy when tackling the housing crisis. I believe that the next step in the HCA alleviating what I call the “Goal Congruent Competition Problem” is to at least note and publish the geographical locations where HA’s are actively pursuing development opportunities.

Find out more:

An academic paper entitled “The Use of Game Theory in Voluntary Urban Readjustment Measures” has been published in Germany this month and can be found via google.

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