International Society of Dynamic Games

Dynamic Games and Applications Seminar

Agent-Based Dynamic Models of Opinion Formation: Where Are We Now?

November 2, 2023
11:00 AM – 12:00 PM (Montreal Time)

Webinar link

Models of opinion formation explore dynamic effects of social complexity, emphasizing that society is more than the sum of its individuals and illustrating how social influence leads to the emergence of collective behaviors. The term “opinions” refers to numerical characteristics of individuals and their behaviors. Opinions can be continuous (real numbers of vectors) or discrete (drawn from a finite set). Their evolution can be described on either microscopic (agent-based) level or macroscopic (population-wide) level. During the presentation, I will concentrate on microscopic dynamical models that involve continuous opinions. These models have attracted significant attention within the fields of dynamical systems, control theory, and AI. We discuss main achievements in analysis of such models, as well as new challenges.

Dynamic Games and Applications Seminar

Principle of quadratic fines for inspection/corruption games

October 19, 2023
11:00 AM — 12:00 PM (Montreal time)

Webinar link

Games of inspection and corruption are well developed in the game-theoretic literature. In author’s paper “Inspection -corruption game of illegal logging and other violations: generalized evolutionary approach” (Mathematics MDPI 2021, 9(14), 1619) a generalised evolutionary approach was developed based on the general framework of the pressure -resistance games of author’s paper “The evolutionary game of pressure (or interference), resistance and collaboration” (Mathematics of Operations Research), 42 (2017), no. 4, 915 – 944). An evolution of a two-level hierarchy was constructed, where a local inspector can be corrupted and is further controlled by the higher authority. Concerning a mathematical novelty, the model led to a switching generalised replicator dynamics (kinetic equations), where switching occurred on the effective frontier of corruption.

In this framework the “principle of quadratic fines” was discovered stating that the quadratic growth of the fine function allows one to effectively control the level of violations. In the talk we present these ideas together with some recent developments showing the robustness of the principle of quadratic fine by extending the model in various directions.