Tariff Versus Sanction Under Bounded Rationality

We formulate the design of a taxation mechanism as a Stackelberg game assuming: a) perfect competition, with exogenous prices; b) imperfect competition, captured through a variational inequality approach, with endogenous prices. Three settings of the mechanism are considered: (i) benchmark involving no taxation, (ii) optimum tariff, (iii) optimum sanction. The expected utility maximization formulation of the game is extended further by relying on cumulative prospect theory to account for the bounded rationality of the stakeholders. We derive closed-form mappings linking the outcomes of the three settings. Additionally, we assess the impact of bounded rationality through a new performance metric, the Price of Irrationality. Numerical results are derived on a randomized instance of a gas trading game between Europe, Asia, and Russia.