The predator–prey space game and the costs associated with risk effects are affected by prey 1) proactive adjustments (when prey modify their behaviour in response to an a priori assessment of the risk level) and 2) reactive adjustments (when prey have detected an immediate threat). Proactive adjustments are generally well-studied, whereas the frequency, strength and duration of reactive adjustments remain largely unknown. We studied the space use and habitat selection of GPS-collared zebras Equus quagga from 2 to 48 h after an encounter with lions Panthera leo. Lion–zebra encounters generally occurred close to artificial waterholes (< 1 km). Two hours after an encounter, zebras were more likely to have fled than stay when the encounter occurred in more risky bushy areas. During their flight, zebras selected grasslands more than usual, getting great visibility. Regardless of their initial response, zebras finally fled at the end of the night and reached areas located far from waterholes where encounters with lions are less frequent. The large-scale flights (∼4–5 km) of zebras led to a local zebra depression for lions. Zebras that had fled immediately after the encounter resumed their behaviour of coming close to waterholes on the following day. However, zebras that had initially stayed remained far from waterholes for an extra 24 h, remaining an elusive prey for longer. The delay in the flight decision had different short-term consequences on the lion–zebra game. We reveal that the spatial context of the encounter shapes the immediate response of prey, and that encountering predators induces strong behavioural responses: prey flee towards distant, safer, areas and have a constrained use of key resource areas which are at the heart of the predator–prey game at larger spatio-temporal scales. Nighttime encounters were infrequent (once every 35 days on average), zebra responses were short-lived (< 36 h) but occurred over a large spatial scale (several km).

#### Encounter_ClassificationEM

Data used to classify the immediate spatial responses of zebras after an encounter with lions between stay and flight. Column headings: Id = id of zebras, DateTime = local date and time of the GPS fixes of zebras, DistToLion = distance between zebra and lion at the time of the encounter in m, NetDisplacement = net displacement of zebra two hours after the encounter with lion in m.

#### Encounter_RSF

Data used to determine the habitat features of encounter areas and the habitat determinants of immediate response choice (stay or flight). Column headings: Id = id of zebra, DateTime = local date and time of the GPS fixes of zebras, Encounter = dependent categorical variable indicating if an encounter occurred ("Yes") or not ("No") at a given time, Encounter2 = dependent categorical variable (question 2) indicating if zebras stay ("Stay") or flee ("Flight") after encountering lions, DistWater = distance to artificial waterholes in km, Grassland = binary variable with 1 if zebra was in grassland and 0 if not, Bushland-1 = binary variable, Bushland-2 = binary variable, Bushland-3 = binary variable, Woodland = binary variable, Wooded Bushland = binary variable (reference category).

#### RSF_Lions

Data used to asses habitat selection function of lions (RSF). Column headings: Id = id of lion, DateTime = local date and time of the GPS fixes of lions, Year = year, isNight = binary variable indicating if GPS fixes occurred at nighttime (1) or daytime (0), DistWater = distance to artificial waterhole in km, Case = binary response with 1 for GPS fixes and 0 for random locations, Grassland = binary variable with 1 if location occurred in grassland and 0 if not, Bushland-1 = binary variable, Bushland-2 = binary variable, Bushland-3 = binary variable, Woodland = binary variable, Wooded Bushland = binary variable (reference category).

#### RSF_Zebras

Data used to asses habitat selection function of zebras (RSF). Column headings: Id = id of zebra, DateTime = local date and time of the GPS fixes of zebras, Year = year, isNight = binary variable indicating if GPS fixes occurred at nighttime (1) or daytime (0), DistWater = distance to artificial waterhole in km, Case = binary response with 1 for GPS fixes and 0 for random locations, Grassland = binary variable with 1 if location occurred in grassland and 0 if not, Bushland-1 = binary variable, Bushland-2 = binary variable, Bushland-3 = binary variable, Woodland = binary variable, Wooded Bushland = binary variable (reference category).

#### SSF_DelayedFlight_Immediately

Data used to asses the step selection function (SSF) of zebras using the delayed-flight tactic immediately after an encounter with lions (question 4). Column headings: id = id of zebra, FakeTime = 2-case, case = binary variable with 1 for an observed step and 0 for a random step, strata = id of the stratum where an observed step is paired with 10 random steps, TacticCont = categorical variable indicating if the step occurred after an encounter ("Tactic") or during the proactive phase ("Control"), Grassland = binary variable with 1 if the step ended in grassland and 0 if not, Bushland-1 = binary variable, Bushland-2 = binary variable, Bushland-3 = binary variable, Woodland = binary variable, Spline1-4 = spline variable for step length in m, StepLength = length of the step in m.

#### SSF_ImmediateFlight_Immediately

Data used to asses the step selection function (SSF) of zebras using the immediate-flight tactic immediately after an encounter with lions (question 4). Column headings: id = id of zebra, FakeTime = 2-case, case = binary variable with 1 for an observed step and 0 for a random step, strata = id of the stratum where an observed step is paired with 10 random steps, TacticCont = categorical variable indicating if the step occurred after an encounter ("Tactic") or during the proactive phase ("Control"), Grassland = binary variable with 1 if the step ended in grassland and 0 if not, Bushland-1 = binary variable, Bushland-2 = binary variable, Bushland-3 = binary variable, Woodland = binary variable, Spline1-4 = spline variable for step length in m, Step Length = length of the step in m.

#### SSF_DelayedFlight_NextDay

Data used to asses the step selection function (SSF) of zebras using the delayed-flight tactic the next day after an encounter with lions (question 4). Column headings: id = id of zebra, FakeTime = 2-case, case = binary variable with 1 for an observed step and 0 for a random step, strata = id of the stratum where an observed step is paired with 10 random steps, cluster = id of the cluster (group of non independent strata) used for robust variance, TacticCont = categorical variable indicating if the step occurred after an encounter ("Tactic") or during the proactive phase ("Control"), Grassland = binary variable with 1 if the step ended in grassland and 0 if not, Bushland-1 = binary variable, Bushland-2 = binary variable, Bushland-3 = binary variable, Woodland = binary variable, Spline1-4 = spline variable for step length in m, Step Length = length of the step in m.

#### SSF_DelayedFlight_NextNight

Data used to asses the step selection function (SSF) of zebras using the delayed-flight tactic the next night after an encounter with lions (question 4). Column headings: id = id of zebra, FakeTime = 2-case, case = binary variable with 1 for an observed step and 0 for a random step, strata = id of the stratum where an observed step is paired with 10 random steps, cluster = id of the cluster (group of non independent strata) used for robust variance, TacticCont = categorical variable indicating if the step occurred after an encounter ("Tactic") or during the proactive phase ("Control"), Grassland = binary variable with 1 if the step ended in grassland and 0 if not, Bushland-1 = binary variable, Bushland-2 = binary variable, Bushland-3 = binary variable, Woodland = binary variable, Spline1-4 = spline variable for step length in m, Step Length = length of the step in m.

#### SSF_ImmediateFlight_NextDay

Data used to asses the step selection function (SSF) of zebras using the immediate-flight tactic the next day after an encounter with lions (question 4). Column headings: id = id of zebra, FakeTime = 2-case, case = binary variable with 1 for an observed step and 0 for a random step, strata = id of the stratum where an observed step is paired with 10 random steps, cluster = id of the cluster (group of non independent strata) used for robust variance, TacticCont = categorical variable indicating if the step occurred after an encounter ("Tactic") or during the proactive phase ("Control"), Grassland = binary variable with 1 if the step ended in grassland and 0 if not, Bushland-1 = binary variable, Bushland-2 = binary variable, Bushland-3 = binary variable, Woodland = binary variable, Spline1-4 = spline variable for step length in m, Step Length = length of the step in m.

#### SSF_ImmediateFlight_NextNight

Data used to asses the step selection function (SSF) of zebras using the immediate-flight tactic the next night after an encounter with lions (question 4). Column headings: id = id of zebra, FakeTime = 2-case, case = binary variable with 1 for an observed step and 0 for a random step, strata = id of the stratum where an observed step is paired with 10 random steps, cluster = id of the cluster (group of non independent strata) used for robust variance, TacticCont = categorical variable indicating if the step occurred after an encounter ("Tactic") or during the proactive phase ("Control"), Grassland = binary variable with 1 if the step ended in grassland and 0 if not, Bushland-1 = binary variable, Bushland-2 = binary variable, Bushland-3 = binary variable, Woodland = binary variable, Spline1-4 = spline variable for step length in m, Step Length = length of the step in m.