Computing some role assignments of Cartesian Product of Graphs

In social networks, a role assignment is such that individuals play the same role, if they relate in the same way to other individuals playing counterpart roles. As a simple graph models a social network role assignment rises to the decision problem called r -Role Assignment whether it exists such an assignment of r distinct roles to the vertices of the graph. This problem is known to be NP-complete for any fixed r ≥ 2. The Cartesian product of graphs is one of the most studied operation on graphs and has numerous applications in diverse areas, such as Mathematics, Computer Science, Chemistry and Biology. In this paper, we determine the computational complexity of r -Role Assignment restricted to Cartesian product of graphs, for r = 2,3. In fact, we show that the Cartesian product of graphs is always 2-role assignable, however the problem of 3-Role Assignment is still NP-complete for this class.

Thematic role assignment in non-default verb classes: A cross-linguistic comparison of English and German

The influence of sentential cues (such as animacy and word order) on thematic role interpretation differs as a function of language (MacWhinney et al. 1984). However, existing cross-linguistic research has typically focused on transitive sentences involving agents, and interpretation of non-default verb classes is less well understood. Here, we compared the way in which English and German native speakers – languages known to differ in the cue prominence of animacy and word order – assign thematic roles. We compared their interpretation of sentences containing either default (agent-subject) or non-default (experiencer-subject) verb classes. Animacy of the two noun phrases in a sentence was either animate-inanimate and plausible (e.g. “The men will devour the meals...”) or inanimate-animate and implausible in English (e.g. “The meals will devour the men…”). We examined role assignment by probing for either the actor or undergoer of the sentence. Mixed effects modelling revealed that role assignment was significantly influenced by noun animacy, verb class, question type, and language. Results are interpreted within the Competition Model framework (Bates et al. 1982; MacWhinney et al. 1984), and show that English speakers predominantly relied on word order for thematic role assignment. German speakers relied on word order to a comparatively lesser degree, with animacy a prominent cue. Non-default verbs (experiencer-subject) promoted a non-default comprehension strategy regarding the prominence of sentential cues, particularly in German. Intriguingly, responses were modulated by the probe task, with undergoer probes promoting object-initial interpretations, particularly for German speakers. This suggests that task focus may retroactively influence sentence interpretation.

Eliciting Fairness in N-Player Network Games through Degree-Based Role Assignment

From social contracts to climate agreements, individuals engage in groups that must collectively reach decisions with varying levels of equality and fairness. These dilemmas also pervade distributed artificial intelligence, in domains such as automated negotiation, conflict resolution, or resource allocation, which aim to engineer self-organized group behaviors. As evidenced by the well-known Ultimatum Game, where a Proposer has to divide a resource with a Responder, payoff-maximizing outcomes are frequently at odds with fairness. Eliciting equality in populations of self-regarding agents requires judicious interventions. Here, we use knowledge about agents’ social networks to implement fairness mechanisms, in the context of Multiplayer Ultimatum Games. We focus on network-based role assignment and show that attributing the role of Proposer to low-connected nodes increases the fairness levels in a population. We evaluate the effectiveness of low-degree Proposer assignment considering networks with different average connectivities, group sizes, and group voting rules when accepting proposals (e.g., majority or unanimity). We further show that low-degree Proposer assignment is efficient, in optimizing not only individuals’ offers but also the average payoff level in the population. Finally, we show that stricter voting rules (i.e., imposing an accepting consensus as a requirement for collectives to accept a proposal) attenuate the unfairness that results from situations where high-degree nodes (hubs) play as Proposers. Our results suggest new routes to use role assignment and voting mechanisms to prevent unfair behaviors from spreading on complex networks.