Network Creation Games with Local Information and Edge Swaps
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In the swap game (SG) selfish players, each of which is associated to a vertex, form a graph by edge swaps, i.e., a player changes its strategy by simultaneously removing an adjacent edge and forming a new edge (Alon et al., 2013). The cost of a player considers the average distance to all other players or the maximum distance to other players. Any SG by n players starting from a tree converges to an equilibrium with a constant Price of Anarchy (PoA) within O(n^3) edge swaps (Lenzner, 2011). We focus on SGs where each player knows the subgraph induced by players within distance k. Therefore, each player cannot compute its cost nor a best response. We first consider pessimistic players who consider the worst-case global graph. We show that any SG starting from a tree (i) always converges to an equilibrium within O(n^3) edge swaps irrespective of the value of k, (ii) the PoA is Θ(n) for k=1,2,3, and (iii) the PoA is constant for k ≥ 4. We then introduce weakly pessimistic players and optimistic players and show that these less pessimistic players achieve constant PoA for k ≤ 3 at the cost of best response cycles.
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