An evolutionary game model of market strategy mutation under sanctions pressure

Prolonged sanctions pressure is changing the behavior of companies and entrepreneurs. But existing models do not explain well how exactly they adapt: some ignore that firms act differently, others assume that the market is frozen in place, even though real data from 2022–2024 show a rapid shift in strategies — from working with old partners to parallel imports. Classical game theory does not explain this. Therefore, the author wants to create a model based on evolutionary game theory, where sanctions pressure affects the payoffs of different strategies. The goal is to build such a model that shows how market strategies change under sanctions pressure through random "mutations" (failures, trial steps). To do this, the author needs to: classify strategies by how well they help survive, describe how the popularity of strategies changes over time accounting for random changes (ε = 0.05–0.15), and find the thresholds at which the market switches from one stable behavior pattern to another. The method is based on discrete replicator dynamics (how strategies are copied depending on their success) with a probability of random changes of 5–15%. The 4×4 payoff matrix is calculated from expert interviews (5 people) and surveys from Rosstat, HSE University, and RANEPA for 2022–2024. The data come from three industries (automotive, pharmaceuticals, finance), chosen based on available public information about the share of imports and the speed at which new practices spread. The results show that at sanctions pressure levels S<0.2 the compliance strategy dominates with a share above 0.8, at 0.35<S<0.65 parallel import dominates with a share of 0.5–0.7, and at S>0.75 the shadow strategy reaches a share of 0.8; a bifurcation is detected at S=0.35 with a region of bistability where the outcome depends on initial conditions, and the speed of adaptation is maximized at ε=0.05–0.10. The main conclusion is that the evolutionary transition between strategies exhibits a threshold rather than smooth character, which explains the observed sectoral heterogeneity. The obtained results can be used by regulators to forecast structural shifts in industries following the introduction of new sanctions packages. Limitations of the model include the expert-based nature of calibration, the exogeneity of the parameter S, and the assumption of an infinite population, while future research directions encompass endogenizing sanctions pressure, calibrating on real panel data for 2022–2024, and expanding the set of strategies.