Media Coverage
September 2011
Gaming the System
Why are you always in the slowest lane? I know you, the humble reader, are definitely always in the slowest lane. We have the maths to prove it. The unfortunate thing, however, is that every other reader is, likewise, always in the slowest lane.
In my previous column, I described how players were exploring and implementing various routing and scheduling principles to leverage an advantage in an online game. But what if the output of the game defines the principles that drive real-world scheduling and optimisation?
Game theory, formalised by von Neuman in the 1920’s, refers to the analysis of models where a player’s success is dependent on the decisions they make in relation to the other players decisions. The formulation of the games and the strategies used help to explain why we make the decisions we do.
Game theory goes a long way to explaining bizzare traffic phenomena, such as the reason why reducing the number of routes available to drivers can often improve overall network performance, why traffic can seemingly speed up at certain parts of the road network with no apparent cause, and why the removal of traffic signs and traffic lights can increase overall safety and reduce travel time respectively.
Transport management games are largely considered non-cooperative games: that is, the players act independently of each other, both knowing the strategies for success, but whose success depends on the decisions made by others. To hark back to the “slowest lane” example, consider the following game:
Two players are on a highway with two lanes. Traffic extends both in front of them and behind them. One lane is moving fast and one lane is moving slowly. The objective of both players is to increase their speed.
The players have two means of doing this. One – which in game theory would be labelled the user-optimal approach – would be to change into the lane that is moving quickly. However, the tradeoff here is that any move would increase network congestion overall, as drivers in the fast lane would have to slow down to allow the player in; likewise, a move from the fast to the slow lane would cause the fast lane to back up while the player waits to enter the slow lane.
The alternative is to remain within the lane. While this will result in their personal speed being less than optimal, it will decrease the average speed across the network as drivers will not constantly brake or slow to accomodate moving traffic. This is the system optimal approach, and is ideal outcome.
What would you do?
The pay-off structure below (using the notation of Player 1 Score, Player 2 Score, with the higher score being preferable) can be seen in the matrix below:
|
Player 1 Stays |
Player 1 Moves |
Player 2 Stays |
3, 3 |
5,0 |
Player 2 Moves |
0,5 |
1,1 |
If Player 1 moves and Player 2 stays, he gains the most significant boost. If Player 1 moves and Player 2 moves, Player 1 still gains a marginal speed boost. Therefore, in terms of maximising his own speed, the best strategic option is to move.
Unfortunately, the exact same strategy applies to Player 2. Therefore, both move, thereby increasing their speed but increasing congestion on the network. They’ve hit the Nash equilibrium - the point where a player’s strategy cannot be improved given the other players strategy – which is actually the least desirable outcome for the network as a whole.
A similar game has been used to describe the high incidence of fatal accidents amongst motorists where large vehicles are available. Statistical data shows that the overall risk of fatal injuries is minimised when two drivers crash in smaller vehicles. However, drivers can also decrease their individual risk by driving a larger vehicle. Because there is no guarantee that other drivers are going to buy small vehicles, all the drivers buy big vehicles, negating the personal gain while maximising the overall risk of fatal injury.
The issue is that traffic optimisation is often approached with a system-optimal frame of mind, which fails to address user-optimal tendencies. Interestingly, the controversial ring road toll system is by no means an anomaly in terms of traffic management: congestion pricing, where one charges users a premium during peak periods to reduce congestion as described, has been met with a similar amount of dissent worldwide.
If you have any comments or questions, please e-mail me at rick.de.klerk@opsi.co.za.
