09:45 AM - 10:10 AM
Value-function based non-cooperative games
Generalizing the family of network interdiction games communicated to us by Andrew Liu and his collaborators,
this paper studies a two-stage non-cooperative game wherein the objective function of each player's optimization problem contains a value function of a second-stage linear program parameterized by the first-stage variables,
through a (possibly piecewise) linear function that upper bounds the second-stage decision variable. We investigate the solution existence of this game and methods for computing such solutions. The latter methods include Lemke's algorithm for problems with affine structures and best-response schemes in general.
10:10 AM - 10:35 AM
Theoretical and computational comparisons of formulations for Stackelberg bimatrix games
Stackelberg Games confront contenders, a leader and a follower, with opposed objectives, each wanting to optimize their rewards. The objective of the game is for the leader to commit to a reward-maximizing strategy anticipating that the follower will best respond.
A Stackelberg game can be modeled as a bilevel bilinear optimization problem. We present different single level reformulations and compare their LP relaxations from both theoretical and computational points of view.
10:35 AM - 11:00 AM
A branch-and -bound algorithm for a bilevel location-allocation model.
We propose an exact branch-and-bound framework for determining the optimal locations and service levels associated with facilities, taking into account user behaviour and competition. In this bilevel maximization setting, we obtain a valid upper bound on the objective through the linearization of the lower level nonlinear terms. At each node of the enumeration tree where an integer solution (number of servers) is achieved, a feasible solution is computed by solving the follower's mathematical program. Preliminary numerical results will be presented and discussed.