As a follow-up to the pedestrian stand-off game, I have created a simple model of the scenario. It is an agent-based model, where agents wandering randomly in space play a single turn of the pedestrian stand-off each time they meet.
In the video above, each circle is an agent, and represents a single pedestrian. When two agents meet, each one decides whether it will be passive or aggressive for the specific interaction. If an agent decides to be polite, as signified by its color turning green, it pauses its movement to let the other pass. If both choose to be polite, then they spend some time standing still, and after a while, resume their courses. Finally, if both choose to be aggressive, as signified by their color turning red, then they collide into one another. The decision on whether an agent will be passive or aggressive is based on a probability parameter, controlled by the user before running the model.
The model incorporates a payoff system to calculate the effectiveness of each politeness probability. The payoff matrix is the same as in the previous post, where for players I & II playing strategy A or P, w is better than p is better than c is better than d.
Payoff matrix for the pedestrian stand-off game
For this model, numeric integer values were assigned to each payoff in order to calculate each outcome. More specifically, w=0, p=1, c=3 and d=5. For each individual agent, it is better to have a score as low as possible. By aggregating the scores of all agents, an estimation of the efficiency of the current politeness probability can be produced. In the video, the probability for an agent being polite was set to 0.4, so that 4 out of 10 times an agent will be polite and give way to the other agent.
The model was run 5 times for each tenth of the percentile probability, and each iteration was run for 200 interactions. The average score of the 5 iterations produced the score for the specific probability. In the graph below, the different scores for each probability are given.
Average score against politeness probabilities
As seen in the graph, the average score (in other words, time spent negotiating an interaction) is at its lowest for a probability of 0.3. In essence, the crowd spent less time in interactions when every agent let the others pass 3 out of 10 times, and acted aggressively 7 out of 10 times. Although the average score is at its lowest, there were still a lot of collisions and stand-stills (almost half of the total interactions), as can be seen in the video as well. So, if someone was planning on using this formula in the real world, I would suggest taking the results with a grain of salt, and having their apologies at the ready.