On independent cliques and linear complementarity problems

In recent work (Pandit and Kulkarni [Discrete Applied Mathematics, 244 (2018), pp. 155–169]), the independence number of a graph was characterized as maximum \(\ell _1\) norm solutions Linear Complementarity Problem (LCP) defined suitably using parameters graph. Solutions this LCP have another relation, namely, that they corresponded to Nash equilibria public goods game. Thus \( \ell _1 \) has an important economic interpretation total investment over all Motivated by this, we consider perturbation corresponds game with imperfect substitutability. We identify combinatorial structures on correspond (equivalently, maximizing equilibria) new LCP. show these “independent cliques" – collections cliques such no two vertices from distinct are adjacent. When becomes null, collapse singletons recover earlier relation independent sets. Independent been studied before generalization Our establishes intricate connection between cliques, LCPs games.