Cyclic Competition and Percolation in Grouping Predator-Prey Populations

Abstract

We study, within the framework of game theory, the properties of a spatially distributed population of both predators and preys that may hunt or defend themselves either isolatedly or in group. Specifically, we show that the properties of the spatial Lett-Auger-Gaillard model, when different strategies coexist, can be understood through the geometric behavior of clusters involving four effective strategies competing cyclically, without neutral states. Moreover, the existence of strong finite-size effects, a form of the survival of the weakest effect, is related to a percolation crossover. These results may be generic and of relevance to other bimatrix games.

Collective strategies and cyclic dominance in asymmetric predator-prey spatial games

“…8b was obtained for the particular values β = 0.4 and α = 0.7 within that time window. Other points inside the coexistence phase may show similar behavior albeit with some arrows reversed and strategies switching roles while keeping some of the sub-loops intransitive and the coexistence stable [41]. An intriguing characteristic of the phase diagram, Fig.…”

“…We checked that the results are essentially the same when they are independently chosen or, as in Ref. [41], when either i or j change at any given attempt. In this regard, it would be important to further check how robust the results are when also changing the updating rule, replacing Eq.…”

“…In Ref. [41], where some preliminary results were presented, we considered a slightly different dynamics in which the two chosen neighbors compare their payoff and that earning the smallest one adopted the strategy of the winner (with the above probability). The difference is that, in Ref.…”

“…The difference is that, in Ref. [41], either i or j would change strategy, while here, only i may be updated.…”

Alliance formation with exclusion in the spatial public goods game

“…Besides inappropriate initial states the system size also may limit the largest emerging characteristic length of the patterns, which can also be a source of misleading conclusions. These problems can only be avoided by applying systematic finite-size analysis [48][49][50]. …”