DTM.4:5.3 - Compatibility changes a threshold but does not guarantee uptake

Suppose a switching group bears conversion costs while old-standard partners keep their process unchanged. Over one horizon, its gain relative to continuing is g(f)=2−0.5−3(1−f), where f is the adopter share. Assume equally weighted encounters in a homogeneous population, so f also gives the group’s relevant partner share on the new standard. The gain is positive only above f=0.5.

An available adapter costing 0.4 and reducing the conversion coefficient to 0.2 gives gₐ(f)=2−0.5−0.4−0.2(1−f). At f=0.2, g=−0.9 while gₐ=0.94.

This is a threshold of the group’s comparison, not yet a population stability result. Add the explicit event rule that a fraction e of the remaining groups receive a feasible, authorized offer and adopt when the gain is positive. Then one step gives:

f_next = f + (1−f)e × indicator(g>0).

For f=0.2 and e=0.25, the share remains 0.2 without the adapter and becomes 0.4 with it. For e=0, neither positive gain nor a favorable threshold produces uptake.

This constructed rule omits departure, unequal partners and changing expectations. To conclude persistence or reversibility, supply those mechanisms where they matter and repeat the corresponding question. ECO.8 retains the coordination and allocation of costs; the engineering method establishes compatibility.