Figure 3.

Evolution of a ToM

(A) Average $k$-level emerging from evolving a population of $Z=500$ individuals as a function of the selection pressure $\beta$ and the cognition error probability $\epsilon$. Fitting our stationary distribution of Steps to those deduced from behavioral experiments leads to the optimum values (${\beta }^{\ast }\approx 0.31,{\epsilon }^{\ast }\approx 0.19$) depicted with a red circle in panel A. This panel shows how the average recursive reasoning level $k$ changes in the population in the function of $\beta$ and $\epsilon$. Comparison between behavioral experiments and the theoretical best fit is made in panel D. Panels B and C portray the $k$-level distributions as a function of $\epsilon$ and $\beta$, respectively, in each case keeping the other parameter at the optimum value (${\beta }^{\ast }$ and ${\epsilon }^{\ast }$, respectively). This result shows how ToM, specified here as a process of recursively reasoning about beliefs and $k$-levels of others, evolves, illustrating how both parameters influence the selection for lower or higher recursive reasoning levels.