Description and Application of a Mathematical Method for the Analysis of Harmony

Table 1

Harmony degree calculation for various scenarios of the “tragedy of the commons.”

Scenario			a	b	I	j	HD	Directions
1	200	100	1	0	1	0	1	and . Optimal action.
2	120	100	0.82	0.18	1	0.18	0.79	Certain “differences” occur.
3	200	80	0.86	0.14	1	0.14	0.84	Certain “differences” occur.
4	200	60	0.69	0.31	1	0.31	0.59	Larger “differences” occur.
5	160	80	1	0	1	0	1	and . Optimal action.
6	100	50	1	0	1	0	1	and . Optimal action.
7	200	150	0.86	0.14	0.5	0.14	0.41	Harmony goal is exceeded, and some “differences” occur.
8	250	100	0.86	0.14	0.5	0.14	0.41	Harmony goal is exceeded, and some “differences” occur.
9	300	150	1	0	0	0	0	Harmony goal is significantly exceeded.
10	250	180	0.87	0.13	0	0.13	0	Harmony goal is significantly exceeded, and some “differences” occur.