Swap Stability in Schelling Games on Graphs

We study a recently introduced class of strategic games thatis motivated by and generalizes Schelling’s well-known resi-dential segregation model. These games are played on undi-rected graphs, with the set of agents partitioned into multi-ple types; each agent either occupies a node of the graph andnever moves away or aims to maximize the fraction of herneighbors who are of her own type. We consider a variant ofthis model that we call swap Schelling games, where the num-ber of agents is equal to the number of nodes of the graph, andagents mayswappositions with other agents to increase theirutility. We study the existence, computational complexity andquality of equilibrium assignments in these games, both froma social welfare perspective and from a diversity perspective

Diversity-seeking Jump Games in Networks

Recently, many researchers have studied strategic games inspired by Schelling's influential model of residential segregation. In this model, agents belonging to $k$ different types are placed at the nodes of a network. Agents can be either stubborn, in which case they will always choose their preferred location, or strategic, in which case they aim to maximize the fraction of agents of their own type in their neighborhood. In the so-called Schelling games inspired by this model, strategic agents are assumed to be similarity-seeking: their utility is defined as the fraction of its neighbors of the same type as itself. In this paper, we introduce a new type of strategic jump game in which agents are instead diversity-seeking: the utility of an agent is defined as the fraction of its neighbors that is of a different type than itself. We show that it is NP-hard to determine the existence of an equilibrium in such games, if some agents are stubborn. However, in trees, our diversity-seeking jump game always admits a pure Nash equilibrium, if all agents are strategic. In regular graphs and spider graphs with a single empty node, as well as in all paths, we prove a stronger result: the game is a potential game, that is, improving response dynamics will always converge to a Nash equilibrium from any initial placement of agents

Topological Distance Games

We introduce a class of strategic games in which agents are assigned to nodes of a topology graph and the utility of an agent depends on both the agent's inherent utilities for other agents as well as her distance from these agents on the topology graph. This model of topological distance games (TDGs) offers an appealing combination of important aspects of several prominent settings in coalition formation, including (additively separable) hedonic games, social distance games, and Schelling games. We study the existence and complexity of stable outcomes in TDGs -- for instance, while a jump stable assignment may not exist in general, we show that the existence is guaranteed in several special cases. We also investigate the dynamics induced by performing beneficial jumps.Comment: Appears in the 37th AAAI Conference on Artificial Intelligence (AAAI), 202

Navigating the Topology of 2x2 Games: An Introductory Note on Payoff Families, Normalization, and Natural Order

The Robinson-Goforth topology of swaps in adjoining payoffs elegantly arranges 2x2 ordinal games in accordance with important properties including symmetry, number of dominant strategies and Nash Equilibria, and alignment of interests. Adding payoff families based on Nash Equilibria illustrates an additional aspect of this order and aids visualization of the topology. Making ties through half-swaps not only creates simpler games within the topology, but, in reverse, breaking ties shows the evolution of preferences, yielding a natural ordering for the topology of 2x2 games with ties. An ordinal game not only represents an equivalence class of games with real values, but also a discrete equivalent of the normalized version of those games. The topology provides coordinates which could be used to identify related games in a semantic web ontology and facilitate comparative analysis of agent-based simulations and other research in game theory, as well as charting relationships and potential moves between games as a tool for institutional analysis and design.Comment: 8 pages including 4 figures in text and 4 plate

Schelling games on graphs

We consider strategic games that are inspired by Schelling's model of residential segregation. In our model, the agents are partitioned into k types and need to select locations on an undirected graph. Agents can be either stubborn, in which case they will always choose their preferred location, or strategic, in which case they aim to maximize the fraction of agents of their own type in their neighborhood. We investigate the existence of equilibria in these games, study the complexity of finding an equilibrium outcome or an outcome with high social welfare, and also provide upper and lower bounds on the price of anarchy and stability. Some of our results extend to the setting where the preferences of the agents over their neighbors are defined by a social network rather than a partition into types