All words and photographs supplied by Adam Tarr, MZO TARR Architects.
Over the bank holiday weekend, John Forbes Nash Jr., died in a car crash (age 86), along with his wife. Nash won the Nobel Prize in 1994 for his work in the field of Game Theory.
But what exactly is Game Theory? Well, if anyone has watched the film ‘A Beautiful Mind’ with Russell Crowe, they may have heard of it, as Crowe in fact plays John Nash, one of the fundamental figures within Game Theory. But in true Hollywood style, Russell Crowe aka John Nash, had his epiphany about Game Theory whilst sitting in a bar, when trying to decide which woman he and his friends should ask to dance.
For those of you who are not Russell Crowe fans, Game Theory is the mathematical study of decision-making between people in situations of conflict or cooperation. That means any time a decision is to be made between 2 or more people, you can use Game Theory to help identify which is the best decision or strategy. Think about that when you next buy a car, play football or even pay your taxes. It’s important because we are all constantly making strategic decisions in both our professional and personal lives, most of the time without even realising it. Therefore the application of Game Theory is huge. It is used in:
Business, where it can analyse competitors and help you set the best price for your product;
In biology, when trying to understand the relationships between predators and their prey;
In sport, from which chess move to make next, to where to shoot your penalty in football or even where to serve in tennis;
In politics, it has been used by politicians to understand how to maximise votes and by governments to help create defence strategies;
In fact it can even help with your dating… .
Image credits: Copyright Universal Pictures, Dreamworks SKG, Imagine Entertainment
For starters John Nash didn't invent Game Theory; however, whilst studying Game Theory at Princeton, Nash developed a fundamental concept that would come to be known as the Nash equilibrium. The Nash equilibrium occurs when each player (person) in the game is assumed to know the strategies of the other players, and no player has anything to gain by changing only their own strategy. If I've already lost you, here’s arguably one of the most famous Game Theory examples to better explain.
The ‘Prisoner’s Dilemma’ was a social experiment created by 2 scientists in 1950 to show why two purely
rational individuals might not cooperate with each other, even if it first appears that it is in their best interests to do so. In fact, the prisoner’s dilemma is not simply some abstract research game, but has real world relevance when dealing with issues such as over fishing in the Atlantic and global warming. The Prisoner’s Dilemma is as follows:
2 members of a criminal gang are arrested and put into 2 separate rooms. They are not able to communicate with each other and the police do not have enough evidence to convict either of them on the main charge, so, they must get a confession. The police therefore come up with a deal which they offer to each of the gang members separately. The choices (aka strategies) for each of the gang members are as follows:
1. To betray the other gang member and tell the police he did it, and as long as the other gang member stays quiet, you can go free and he will be sentenced to 3 years;
2. However, if both gang members betray each other by saying the other one did it, you will both get 2 years each in prison;
3. Lastly if you both stay quiet and don’t betray each other, you will both get 1 year each in prison for the lesser crime.
The choices are shown here in a simple matrix below:
Since each gang member cannot control the other gang member’s decision of whether to betray or stay quiet, their best decision or Nash Equilibrium would be to betray (shown below in orange). This decision to betray will mean the prisoner will either get to go free or receive 2 years in prison, whereas the other decision, to remain quiet, will result in either 1 year or 3 years in prison. To ‘Betray’ is the best option the player/gang member can make, taking into account the other players’ potential decision.
Well, let us look at a few projects. MZO TARR Architects embraced the above Prisoner’s Dilemma in an almost literal sense to create a fun, interactive Warming Hut for use along the Assiniboine River, in Winnipeg, Canada to provide shelter for ice skaters.
The Warming Hut consists of two rooms each with a manual wall mounted wheel that controls 2 ceiling louvres. The players have the option to turn the wheel to the right to cooperate (quiet), or left to defect (betray). This motion pivots the louvres to either funnel or block prevailing winds into the zones. However, like the Prisoner’s Dilemma, the final result is also dependent upon the decision made by the player in the other zone.
This is an internal view of the warming hut showing the player/person standing in Zone A choosing whether to betray or remain quiet by turning the wall mounted wheel. This will affect the wind/temperature for the person in zone B, but also the wind/temperature in Zone A. The reason for this is that Zone B has a corresponding wall mounted wheel.
Below is the Cold dilemma matrix for our Warming Hut:
Our second project is a residential tower which without Nash’s Equilibrium could not exist. We were recently approached to design a concept for a residential tower (‘Nash’ Pursuit tower) near Canary Wharf, London for the popular Private Rented Sector. For Londoners, the priorities when choosing a property are location and space. In this context, space refers first to the size and quality of internal space, and secondly, whether there is private outside space.
In the course of our research, we also identified that a tenant is more likely to renew their lease if they have a good relationship with at least one neighbour. With this information about tenant priorities and behaviour in mind, we created a game that encouraged the flat occupants to create garden space above.
The highlighted yellow and green zones within the floor plans below vary in size depending upon how much space the 5 flat owners have been willing to give up. The floors shown are 10, 11, 12 and 13. The internal yellow area is the communal garden space created.
This shared communal space (highlighted in yellow above) in the centre will encourage community spirit as well as offering a certain level of garden privacy. However, flat occupants have to trade part of their private floor space to create it. The amount they trade is up to them; they can trade as much or as little as they choose but to encourage the flat owners, the rules of our game state 2m2 of communal garden would be created for every 1m2 of private space given up. The amount of garden space created, (the ‘Nash Equlibirum’), depends upon the decisions made by the flat owners. Some flat owners of course chose to be selfish, giving up no space in the hope they could use the garden created by the other four flat owners’ more selfless decisions. But the largest spaces in terms of private and communal garden space were created on those floors where tenants were unselfish. Greater collaboration led to better results.
Our ‘Nash’ Pursuit game enables a win-win scenario for both developers and tenants because:-
1. The short-term tenants can revert to the original size of floor space at any time;
2. It enables the tenants to trade private space for a larger shared internal garden for their floor;
3. The landlord benefits, as good neighbourly relationships have been proved to increase lease renewals by 90-95%.
Lastly, the 2 images above show the tower’s Nash Equilibrium at 2 different times. The exterior glass is different because of the different choices made by the tenants. The flat sizes and arrangements are more likely to change when a new tenant moves in.