How can you use algorithmic game theory to optimize aviation operations research?

1 Slot allocation

Slot allocation is the problem of assigning landing and take-off slots to airlines at congested airports. The objective is to maximize the social welfare, which is the sum of the values that airlines assign to their preferred slots, while respecting the capacity constraints of the airport. AGT can help to design slot allocation mechanisms that are incentive-compatible, meaning that airlines have no reason to lie about their true values, and Pareto-efficient, meaning that no airline can be made better off without making another worse off. One example of such a mechanism is the simultaneous ascending auction, which allows airlines to bid for slots in multiple rounds until no one wants to raise their bids.

2 Route assignment

Route assignment is the problem of assigning flight paths to airlines in a given airspace. The objective is to minimize the total delay, fuel consumption, and environmental impact of the flights, while respecting the safety and operational constraints of the airspace. AGT can help to design route assignment mechanisms that are strategy-proof, meaning that airlines have no reason to manipulate their flight plans, and budget-balanced, meaning that the total payments from the airlines equal the total costs of the airspace. One example of such a mechanism is the Vickrey-Clarke-Groves (VCG) mechanism, which charges each airline the marginal cost of its flight path on the other airlines.

3 Frequency planning

Frequency planning is the problem of determining how often to operate flights on each route in a given market. The objective is to maximize the profit, which is the difference between the revenue and the cost of operating the flights, while considering the demand and the competition from other airlines. AGT can help to design frequency planning mechanisms that are Nash equilibrium, meaning that no airline can increase its profit by unilaterally changing its frequency, and socially optimal, meaning that the total profit is maximized. One example of such a mechanism is the Cournot model, which assumes that each airline chooses its frequency based on the expected reaction of the other airlines.

4 Network design

Network design is the problem of determining which routes to operate and how to connect them in a given network. The objective is to maximize the network value, which is the sum of the values that passengers assign to their preferred routes, while considering the costs and the capacities of the network. AGT can help to design network design mechanisms that are stable, meaning that no airline or group of airlines can benefit by leaving or joining the network, and efficient, meaning that the network value is maximized. One example of such a mechanism is the Shapley value, which allocates the network value to each airline based on its marginal contribution to the network.