We introduce a new function on the set of pairs cluster variables via f-vectors, which is called compatibility degree (of complexes). The natural generalization classical introduced by Fomin and Zelevinsky. In particular, we prove that has duality property, symmetry embedding property one has. also conjecture exchangeability property. As pieces evidence this conjecture, establish for algebras r...

While a taxonomic approach to maximizing stimulus-response (S-R) compatibility is frequently applied to improve system design, it can fall short because no taxonomy is ever complete. A model-based approach may uncover additional system flaws and can help us to understand the sources of S-R compatibility. A satisfactory model is defined as one that is acceptable on two vital dimensions: It is bo...

We analyse firms’ incentives to provide two-way compatibility between two network goods with different intrinsic qualities. We study how the relative importance of vertical differentiation with respect to the network effect influences the price competition as well as the compatibility choice. The final degree of compatibility allows firms to manipulate the overall differentiation. Under weak ne...