On the stability of resource undermatching in human group-choice
The notebook simulates the model presented at the ACC’14, which captures empirical patterns of the aggregate group-level behavior of individuals competing for resources. When, on a logarithmic plot, there is strict matching between the ratios of the number of individuals choosing any two options (xi/xj) and number of available resources for these options (wi/wj), then the pattern is called an Ideal Free Distribution with no undermatching. The video below illustrates the dynamics of how this stationary state is reached based on local decision-making.
The left plot shows the evolution of the opportunity cost as perceived by single individuals; the center plot the number of resources available per individual and the right plot the ratios for various option pairs. The diagonal dotted line represents the strict match between choices and resources.
However, empirical patterns show that the IFD state is reached with some degree of understating. Undermatching can be described as a globally balanced state in which the perceived cost of the best forgone alternatives is approximately the same for all individuals. The video below illustrates the dynamics for the case with undermatching then there are no dynamics once the IFD is reached.
The right plot shows how the ratio of individuals choosing two different options relates to number of locally available resources on the logarithmic plot. The dots indicate deviations in group-choice behavior from the diagonal line which represents strict matching. It illustrates that there is low discriminability of resources, represented by a = 0.57. When the state reaches the IFD (at around k = 115), variations in the number of resources per individual are small for any option, but the ratio of resources between two options does not match the ratio of individuals choosing these options. Individuals choosing the option with the most resources enjoy higher resources rates.
Depending on the distribution of resources, it can be the case that individuals keep on changing options even after reaching the IFD with understating. The video below illustrates this case.
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