Multi-trophic resource selection function enlightens the behavioural game between wolves and their prey.

1. Habitat selection strategies translate into movement tactics, which reckon with the predator-prey spatial game. Strategic habitat selection analysis can therefore illuminate behavioural games. Cover types at potential encounter sites (i.e. intersections between movement paths of predator and prey) can be compared with cover types available (i) within the area of home-range-overlap (HRO) between predator and prey; and (ii) along the path (MP) of each species. Unlike the HRO scale, cover-type availability at MP scale differs between interacting species due to species-specific movement decisions. Scale differences in selection could therefore inform on divergences in fitness rewarding actions between predators and prey. 2. We used this framework to evaluate the spatial game between GPS-collared wolves (Canis lupus) versus caribou (Rangifer tarandus), and wolf versus moose (Alces alces). 3. Changes in cover-type availability between HRO and MP revealed differences in how each species fine-tuned its movements to habitat features. In contrast to caribou, wolves increased their encounter rate with regenerating cuts along their paths (MP) relative to the HRO level. As a consequence, wolves were less likely to cross caribou paths in areas with higher percentage of regenerating cuts than expected based on the availability along their paths, whereas caribou had a higher risk of intersecting wolf paths by crossing these areas, relative to random expectation along their paths. Unlike for caribou, availability of mixed and deciduous areas decreased from HRO to MP level for wolves and moose. Overall, wolves displayed stronger similarities in movement decisions with moose than with caribou, thereby revealing the focus of wolves on moose. 4. Our study reveals how differences in fine-scale movement tactics between species create asymmetric relative encounter probabilities between predators and prey, given their paths. Increase in relative risk of encounter for prey and decrease for predators associated with specific cover types emerging from HRO to MP scale analysis can disclose potential weaknesses in current movement tactics involved the predator-prey game, such as caribou use of cutovers in summer-autumn. In turn, these weaknesses can inform on subsequent changes in habitat selection tactics that might arise due to evolutionary forces.