### Abstract

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(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.

Original language | English |
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Title of host publication | Structural Information and Communication Complexity - 27th International Colloquium, SIROCCO 2020, Proceedings |

Editors | Andrea Werneck Richa, Christian Scheideler |

Publisher | Springer |

Pages | 349-365 |

Number of pages | 17 |

ISBN (Print) | 9783030549206 |

DOIs | |

Publication status | Published - 2020 |

Event | 27th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2020 - Paderborn, Germany Duration: Jun 29 2020 → Jul 1 2020 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 12156 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 27th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2020 |
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Country | Germany |

City | Paderborn |

Period | 6/29/20 → 7/1/20 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Structural Information and Communication Complexity - 27th International Colloquium, SIROCCO 2020, Proceedings*(pp. 349-365). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12156 LNCS). Springer. https://doi.org/10.1007/978-3-030-54921-3_20