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 -