### Other Models for NCGs  
Several variants of these two basic models have been defined, with the goal of better characterizing specific aspects of the network formation process. These variants range from limiting the modifications that players are allowed to perform on their current strategies (see in [9; 10; 11]), to budgeting either the number of edges a player can activate or her eccentricity (see in [12; 13; 14]), and finally to considering generalized versions of the basic models on edge-weighted graphs (see in [15; 16]). Generally speaking, all the aforementioned models exhibit a substantial asymptotic increase in their PoAs compared to that of corresponding basic models introduced above.  
Observe that all these models, except for those given in [10; 11], share a severe restriction with the basic model, namely, the NP-hardness for a player to select a best-response strategy. Besides that, they also all assume that players have a _common and complete_ information about the ongoing network. While this is feasible for small-size instances of the game, this becomes unrealistic for large-size networks. This is rather problematic, given the growing size of the inputs in the practice. Moreover, quite paradoxically, the full-knowledge assumption is not simplifying at all: it makes it computationally unfeasible for a player to select a best-response strategy, as said before, or even to check whether she is actually in a NE! To address these delicate issues, a new model which limits a player's full knowledge of the network structure up to a given radius \(k\) from herself has been introduced in [17]. In such a setting, players do not even know the size \(n\) of the network (in distributed computing terminology, the system is _uniform_). The authors provided a comprehensive set of upper and lower bounds to the _Price of Anarchy_ (PoA) for the entire range of values of \(k\), which have been confirmed by a further experimental evaluation in [18]. Critically, these bounds to the PoA refer to a new suitable equilibrium concept that accounts for the limited knowledge of the players. More precisely, as a player has a partial (defective) view of the network, before changing her strategy she has to evaluate whether such a choice is convenient in _every_ realizable network which is compatible with her current view. Then, let \(\sigma_{u}\) be the strategy played by player \(u\), and define \(\Sigma|_{\sigma_{u}}\) to be the set of strategy profiles \(\sigma=(\sigma_{-u},\sigma_{u})\) of the players such that the network \(G(\sigma)\) is realizable according to player \(u\)'s view. Let  
\[\Delta(\sigma_{u},\sigma_{u}^{\prime})=\max_{\sigma\in\Sigma|_{\sigma_{u}}} \{C_{u}(\sigma_{-u},\sigma_{u}^{\prime})-C_{u}(\sigma)\} \tag{3}\]  
denote the worst possible cost difference \(u\) would have in switching from \(\sigma_{u}\) to \(\sigma_{u}^{\prime}\). This means that if \(\Delta(\sigma_{u},\sigma_{u}^{\prime})>0\), then there is some strategy profile \(\sigma\) compatible with \(u\)'s current view for which switching from \(\sigma\) to \((\sigma_{-u},\sigma_{u}^{\prime})\) would increase \(u\)'s cost. Conversely, if \(\Delta(\sigma_{u},\sigma_{u}^{\prime})<0\), player \(u\) can safely change her strategy from \(\sigma_{u}\) to \(\sigma_{u}^{\prime}\) as this will decrease her cost by at least \(|\Delta(\sigma_{u},\sigma_{u}^{\prime})|>0\) in all of the conceivable networks \(G(\sigma)\) that are compatible with \(u\)'s view. Then, the _Local Knowledge Equilibrium_ (LKE) is defined as a strategy profile \(\bar{\sigma}\) such that for every player \(u\) and every strategy \(\sigma_{u}\), we have \(\Delta(\bar{\sigma}_{u},\sigma_{u})\geq 0\). Notice that our equilibrium concept is actually weaker than the classical NE concept as we have that every NE is also a LKE.