Correction to: Humanities and Social Sciences Communications https://doi.org/10.1057/s41599-021-00730-z.

The following typographical errors have been corrected in the published paper.

  1. 1.

    Under paragraph IV of the section “Stylized Assumptions”, the original stated:

    Then we let ai(ei1,…, ein0) be strictly decreasing, strictly convex functions on domain [0,∞)n

    This has been corrected to:

    Then we let ai(ei1,…, ein) be strictly decreasing, strictly convex functions on domain [0,∞)n

  2. 2.

    Under Theorem 1 (Social dilemmas), the original stated:

Then there exist δei1ej2 > 0 such that the welfare of w1 and w2, W1 and W2

This has been corrected to:

Then there exist δei1,δej2 > 0 such that the welfare of w1 and w2, W1 and W2