Game Theory Approaches for Transportation Problems

This dissertation considers three separate game theory problems in transportation. In the first problem, a combinatorial auction market has been proposed for fractional ownership of autonomous vehicles. The proposed combinatorial auction has two unique features. First, the items are continuous time slots defined by bidders and second, the spatial information of bidders has been incorporated so that sharing becomes a viable plan. A conflict-based formulation of the winner determination problem has been proposed, for which an effective solution approach based on a heuristic and a maximal-clique based relaxation has been presented. The second part of the dissertation examines a pessimistic bilevel toll pricing problem for mitigating the risk of transporting hazardous materials. Since the optimistic hazmat toll pricing problem creates multiple optimal solutions for the inner problem, risk hedging against the behavioral uncertainty of hazmat carriers is desired. Considering hazmat carriers as satisficing decision-makers, an approximate pessimistic problem has been formulated. The optimal solution existence of optimistic and pessimistic problems have been studied. Moreover, solution approaches based on disjunctive programming have been presented. In the third problem, we study the effect of satisficing behavior on transportation network systems. When network users are satisficing decision-makers, the resulting traffic pattern which is called satisficing user equilibrium may deviate from the (perfectly rational) user equilibrium and the total system travel time can be worse than in the case of the perfectly rational user equilibrium. We call the ratio between the total system travel times of the worst-case satisficing user equilibrium traffic pattern and the perfectly rational user equilibrium the price of satisficing, for which we provide an analytical bound. We compare the analytical bound with numerical bounds for several transportation networks