Deligkas, Argyrios; Eiben, Eduard; Skretas, George Minimizing Reachability Times on Temporal Graphs via Shifting LabelsInternational Joint Conference on Artificial Intelligence (IJCAI) 2023: 5333–5340
We study how we can accelerate the spreading of information in temporal graphs via delaying operations; a problem that captures real-world applications varying from information flows to distribution schedules. In a temporal graph there is a set of fixed vertices and the available connections between them change over time in a predefined manner. We observe that, in some cases, the delay of some connections can in fact decrease the time required to reach from some vertex (source) to another vertex (target). We study how we can minimize the maximum time a set of source vertices needs to reach every other vertex of the graph when we are allowed to delay some of the connections of the graph. For one source, we prove that the problem is W[2]-hard and NP-hard, when parameterized by the number of allowed delays. On the other hand, we derive a polynomial-time algorithm for one source and unbounded number of delays. This is the best we can hope for; we show that the problem becomes NP-hard when there are two sources and the number of delays is not bounded. We complement our negative result by providing an FPT algorithm parameterized by the treewidth of the graph plus the lifetime of the optimal solution. Finally, we provide polynomial-time algorithms for several classes of graphs.
Bilò, Davide; Bilò, Vittorio; Döring, Michelle; Lenzner, Pascal; Molitor, Louise; Schmidt, Jonas Schelling Games with Continuous TypesInternational Joint Conference on Artificial Intelligence (IJCAI) 2023: 2520–2527
In most major cities and urban areas, residents form homogeneous neighborhoods along ethnic or socioeconomic lines. This phenomenon is widely known as residential segregation and has been studied extensively. Fifty years ago, Schelling proposed a landmark model that explains residential segregation in an elegant agent-based way. A recent stream of papers analyzed Schelling’s model using game-theoretic approaches. However, all these works considered models with a given number of discrete types modeling different ethnic groups. We focus on segregation caused by non-categorical attributes, such as household income or position in a political left-right spectrum. For this, we consider agent types that can be represented as real numbers. This opens up a great variety of reasonable models and, as a proof of concept, we focus on several natural candidates. In particular, we consider agents that evaluate their location by the average type-difference or the maximum type-difference to their neighbors, or by having a certain tolerance range for type-values of neighboring agents. We study the existence and computation of equilibria and provide bounds on the Price of Anarchy and Stability. Also, we present simulation results that compare our models and shed light on the obtained equilibria for our variants.
Bilò, Davide; Cohen, Sarel; Friedrich, Tobias; Gawendowicz, Hans; Klodt, Nicolas; Lenzner, Pascal; Skretas, George Temporal Network Creation GamesInternational Joint Conference on Artificial Intelligence (IJCAI) 2023: 2511–2519
Most networks are not static objects, but instead they change over time. This observation has sparked rigorous research on temporal graphs within the last years. In temporal graphs, we have a fixed set of nodes and the connections between them are only available at certain time steps. This gives rise to a plethora of algorithmic problems on such graphs, most prominently the problem of finding temporal spanners, i.e., the computation of subgraphs that guarantee all pairs reachability via temporal paths. To the best of our knowledge, only centralized approaches for the solution of this problem are known. However, many real-world networks are not shaped by a central designer but instead they emerge and evolve by the interaction of many strategic agents. This observation is the driving force of the recent intensive research on game-theoretic network formation models. In this work we bring together these two recent research directions: temporal graphs and game-theoretic network formation. As a first step into this new realm, we focus on a simplified setting where a complete temporal host graph is given and the agents, corresponding to its nodes, selfishly create incident edges to ensure that they can reach all other nodes via temporal paths in the created network. This yields temporal spanners as equilibria of our game. We prove results on the convergence to and the existence of equilibrium networks, on the complexity of finding best agent strategies, and on the quality of the equilibria. By taking these first important steps, we uncover challenging open problems that call for an in-depth exploration of the creation of temporal graphs by strategic agents.
Gadea Harder, Jonathan; Krogmann, Simon; Lenzner, Pascal; Skopalik, Alexander Strategic Resource Selection with Homophilic AgentsInternational Joint Conference on Artificial Intelligence (IJCAI) 2023: 2701–2709
The strategic selection of resources by selfish agents is a classic research direction, with Resource Selection Games and Congestion Games as prominent examples. In these games, agents select available resources and their utility then depends on the number of agents using the same resources. This implies that there is no distinction between the agents, i.e., they are anonymous. We depart from this very general setting by proposing Resource Selection Games with heterogeneous agents that strive for joint resource usage with similar agents. So, instead of the number of other users of a given resource, our model considers agents with different types and the decisive feature is the fraction of same-type agents among the users. More precisely, similarly to Schelling Games, there is a tolerance threshold \(\tau \in [0,1]\) which specifies the agents' desired minimum fraction of same-type agents on a resource. Agents strive to select resources where at least a \(\tau\)-fraction of those resources' users have the same type as themselves. For \(\tau=1\), our model generalizes Hedonic Diversity Games with a peak at \(1\). For our general model, we consider the existence and quality of equilibria and the complexity of maximizing social welfare. Additionally, we consider a bounded rationality model, where agents can only estimate the utility of a resource, since they only know the fraction of same-type agents on a given resource, but not the exact numbers. Thus, they cannot know the impact a strategy change would have on a target resource. Interestingly, we show that this type of bounded rationality yields favorable game-theoretic properties and specific equilibria closely approximate equilibria of the full knowledge setting.