Introduction

This is a study of the problem of fire continuously spreading in a closed environment and the emerging behavior of people given the existence of only one exit. The actual model is motivated by a series of social science applications ranging from environmental education to epidemiology to development economics.

Model

There are three main components to our model:

The environment
The population of agents
The source of action: FIRE

Each element of our model is governed by either structural and/or behavioral rules and the object of the simulations (the observed statistic) is the average number of deceased agents over two basic scenarios and three parameter settings that differ in terms of the collaborative characteristics of the agents and the physical rate of fire spread.

The environment (world) is set up as a 21x21 rectangular bounded real space in which the (0,0) coordinate represents the center. The unique exit is assumed to be connected to the coordinates (10,0) and the unique fire starts at position (-10, 0).

The population consists of 20 agents randomly distributed over the above environment governed by the following behavioral rules:

An agent remains stationary unless he/she encounters a fire in an adjacent cell OR receives a warning signal (a yell) from another agent
If non-stationary, the agent moves toward the exit attempting to avoid the fire if possible
There are no conflicting movements among agents. The space is assumed large enough such that agents don’t “bump” into each other while moving.

The fire occupies one square unit of space and at each time step spreads to each of its Moore neighbors with probability fire-spread.

We simulate two main scenarios in which agents either choose to be “considerate people” and upon learning of the spreading fire, they warn other agents of the imminent danger on their way out OR they choose to be “selfish people”, in which case they don’t warn others. However "selfish agents" move twice as fast as “considerate people”. The population is either entirely considerate or entirely selfish (there is no mixing scenario for simplicity).

We experimented with three different rates of fire spread. The average number of deceased agents is reported as our computed statistic in the table below.

Average number of deceased agents

Type of agents	Rate of fire spread
Type of agents	25%	50%	75%
“Considerate”	5.7	10.9	10.1
“Selfish”	12.5	13.7	14.4

* The statistic is obtained by averaging the results of 10 iterations with different random number seeds, and each iteration is run for 50 time steps.

The actual model was created in Net.Logo and can be accessed here. More documentation of the model is available at this link as well.

Conclusions

A natural result that has emerged is that an increased rate of fire spread will generally result in a higher average number of deceased people. One can also clearly see that being considerate pays off at least given these parameters. Of course our scenario assumes that everyone is considerate and this may not be true in mixed populations. Additionally, it pays off more at lower rates of fire spread due to the fact that communication speed is faster relative to the fire spread. Finally, it appears that the gap between average deceased people who are considerate and those who are selfish levels off with the increase in the fire spread rate. This again seems to be a plausible result. Most of the lives saved from the considerate population come from the fact that the early warning signal allows individuals far away from the fire to escape. As the fire rate increases this early warning signal is simply not fast enough to outstrip the rapid fire movement.

Potential extensions

Their are many possible future extensions to this model. One could certainly think of allowing different costs of being considerate and their effects on agents’ individual and aggregate behavior. Other extensions include introducing a heterogeneous population (e.g. combining considerate and selfish people within the randomized population), allowing agents to interact (communicate) over different types of networks, allowing them to take up physical space in the lattice, allowing the fire to burn out and generally creating smarter agents with more complex decision rules.

Social science applications

In general this model can be viewed as comparing two different populations, one in which education about hazards is the norm, and one in which selfish actions are the norm but the population gains some benefit because it doesn't spend time in education. Of course the danger is personal, i.e. individuals die, but the observed statistic is collective, i.e. number of dead agents.

As stated in the introduction, the motivational aspects of this exercise stems from a number of similarities within fields like epidemiology, economics and environmental sciences. For instance, there seems to be a relation to SIR models except the results could apply more to behavior modifications than the normal vaccination models since agents are required to act upon receiving information about the imminent hazard. In development economics, the spread of know-how and knowledge in general could be regarded as essential factors in determining the growth rates and path dependences (e.g. “considerate people” could diffuse the know-how faster with positive effects – i.e. the role of education). Finally, a considerate population will allow more individuals to escape from local environmental hazards such as the threat of radon or sick-building syndrome. In all of these cases, assuming that the parameters of the model can be tied to empirical evidence, it seems that considerate populations perform better than selfish ones.