Abstract
Games with strategic substitutes (GSS) are generally more intractable than games with strategic complements (GSC). This well-known fact is revisited from two new perspectives, a network one and a computational one. From the network perspective, it is shown that every GSC, under certain mild conditions, can be embedded into a larger GSS, such that the set of the pure strategy Nash equilibria of the former is the projection of that of the latter. From the computational perspective, it is shown that the two focal equilibria of a GSC with linear best responses can be computed in polynomial time, while computing a pure strategy Nash equilibrium of a GSS with linear best responses is PPAD-hard. These results indicate that strategic substitutability is more fundamental than strategic complementarity, in the sense that the class of GSS is much broader than the class of GSC. Combined with the previous results in the literature, our paper provides a more complete picture about the relationship between GSC and GSS.
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