A kinetic equation modelling the collective dynamics of the rock-paper-scissors binary game: well-posedness and asymptotic behaviour

par Hugo Martin (IDP Tours)

jeudi 5 févr. 2026, 13:30 → 14:30 Europe/Paris

E2290 (Tours)

The rock-paper-scissors game has been studied for ages from various points of view. Game theory established a long time ago that two rational players have a unique optimal strategy, which is playing one of the three moves at random, with probability 1/3. This very simple case was extended in different ways. In a (not so) recent  paper, Pouradier Duteil and Salvarani considered a large amount of rational agents, that play a r-p-s game after encountering, and exchange money based on the outcome. This results in a PDE modeling a population structured in wealth, that can be interpreted as a discrete heat equation on the half-line with a diffusion rate depending on the amount of players that are rich enough (i.e. that would be able to pay their dept if they loose they next game), thus introducing a nonlinearity.
The goal of this work was to adapt a methodology that was successfully used on equations arising from biology. The explicit limit obtained depends linearly on the initial condition, and an algebraic decay rate toward this limit was established.