The Zebra Crossing Game – Using Game Theory to Explain a Discrepancy Between Road User Behaviour and Traffic Rules

Abstract In Norway, cyclists are allowed to cycle on pavements, and urban paths are often designated for use by both cyclists and pedestrians. Crossings between pavements/paths and the roadway are normally marked as zebra crossings. At these crossings, the law treats cyclists and pedestrians differently: whereas cyclists must give way to road traffic, the road traffic must give way to pedestrians. On encountering road traffic at these crossings, a cyclist has three options: give way (a); cycle over the zebra crossing (and risk a collision) (b); or (c) force the drivers to yield by dismounting and walking over the zebra crossing (c). The approaching driver has two choices: drive on as the law suggests (x) or give way to the cyclist (y). The solutions prescribed by the traffic rules are a/x or c/y. However, on applying game theory to this situation, it can be shown that neither of these solutions are in perfect equilibrium, and the game theoretic solution to the game is in fact b/y, i.e. that the cyclists cycle over the zebra crossing and the cars yield, contrary to what the traffic rule prescribes. Thus, according to game theoretic reasoning one would expect the normal solution in road traffic to be that drivers yield to cyclists in zebra crossings. In order to test this, we studied crossing behaviour at three zebra crossings, two crossings where cyclists approached from the pavement and one crossing where cyclists came from a combined cycle and walking path. We found that rather than aligning with traffic rules, the actual crossing behaviour aligned with the solution generated by game theory. The results show that game theoretic modelling can be a valuable tool to understand road user interaction. Better understanding and ability to predict road user interactions could help to improve traffic safety.