TY - GEN

T1 - Network creation games with local information and edge swaps

AU - Yoshimura, Shotaro

AU - Yamauchi, Yukiko

N1 - Funding Information:
This work was supported by JSPS KAKENHI Grant Number JP18H03202.
Publisher Copyright:
© Springer Nature Switzerland AG 2020.

PY - 2020

Y1 - 2020

N2 - In the swap game (SG), selfish players, each of which is associated with 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(n3) 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(n3) 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.

AB - In the swap game (SG), selfish players, each of which is associated with 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(n3) 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(n3) 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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U2 - 10.1007/978-3-030-54921-3_20

DO - 10.1007/978-3-030-54921-3_20

M3 - Conference contribution

AN - SCOPUS:85089412120

SN - 9783030549206

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 349

EP - 365

BT - Structural Information and Communication Complexity - 27th International Colloquium, SIROCCO 2020, Proceedings

A2 - Richa, Andrea Werneck

A2 - Scheideler, Christian

PB - Springer

T2 - 27th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2020

Y2 - 29 June 2020 through 1 July 2020

ER -