Discrete preference games with logic-based agents: Formal framework, complexity, and islands of tractability

Analyzing and predicting the dynamics of opinion formation in the context of social environments are problems that attracted much attention in literature. While grounded in social psychology, these problems are nowadays popular within the artificial intelligence community, where opinion dynamics are often studied via game-theoretic models in which individuals/agents hold opinions taken from a fixed set of discrete alternatives, and where the goal is to find those configurations where the opinions expressed by the agents emerge as a kind of compromise between their innate opinions and the social pressure they receive from the environments. As a matter of facts, however, these studies are based on very high-level and sometimes simplistic formalizations of the social environments, where the mental state of each individual is typically encoded as a variable taking values from a Boolean domain. To overcome these limitations, the paper proposes a framework generalizing such discrete preference games by modeling the reasoning capabilities of agents in terms of weighted propositional logics. It is shown that the framework easily encodes different kinds of earlier approaches and fits more expressive scenarios populated by conformist and dissenter agents. Problems related to the existence and computation of stable configurations are studied, under different theoretical assumptions on the structural shape of the social interactions and on the class of logic formulas that are allowed. Remarkably, during its trip to identify some relevant tractability islands, the paper devises a novel technical machinery whose significance goes beyond the specific application to analyzing opinion formation and diffusion, since it significantly enlarges the class of Integer Linear Programs that were known to be tractable so far.