2 research outputs found
Robustness against Agent Failure in Hedonic Games
We study how stability can be maintained even after any set of at most k
players leave their groups, in the context of hedonic games. While stability
properties ensure an outcome to be robust against players' deviations, it has
not been considered how an unexpected change caused by a sudden deletion of
players affects stable outcomes. In this paper, we propose a novel criterion
that reshapes stability form robustness aspect. We observe that some stability
properties can be no longer preserved even when a single agent is removed.
However, we obtain positive results by focusing on symmetric friend-oriented
hedonic games. We prove that we can efficiently decide the existence of robust
outcomes with respect to Nash stability under deletion of any number of players
or contractual individual stability under deletion of a single player. We also
show that symmetric additively separable games always admit an individual
stable outcome that is robust with respect to individual rationality.Comment: 17 page
Topological Influence and Locality in Swap Schelling Games
Residential segregation is a wide-spread phenomenon that can be observed in
almost every major city. In these urban areas residents with different racial
or socioeconomic background tend to form homogeneous clusters. Schelling's
famous agent-based model for residential segregation explains how such clusters
can form even if all agents are tolerant, i.e., if they agree to live in mixed
neighborhoods. For segregation to occur, all it needs is a slight bias towards
agents preferring similar neighbors. Very recently, Schelling's model has been
investigated from a game-theoretic point of view with selfish agents that
strategically select their residential location. In these games, agents can
improve on their current location by performing a location swap with another
agent who is willing to swap. We significantly deepen these investigations by
studying the influence of the underlying topology modeling the residential area
on the existence of equilibria, the Price of Anarchy and on the dynamic
properties of the resulting strategic multi-agent system. Moreover, as a new
conceptual contribution, we also consider the influence of locality, i.e., if
the location swaps are restricted to swaps of neighboring agents. We give
improved almost tight bounds on the Price of Anarchy for arbitrary underlying
graphs and we present (almost) tight bounds for regular graphs, paths and
cycles. Moreover, we give almost tight bounds for grids, which are commonly
used in empirical studies. For grids we also show that locality has a severe
impact on the game dynamics