This data contains simulation results for the optimal selection of a Generalized Nash Equilibrium (GNE) in a linearly coupled aggregative game.
The test is performed by using the Hybrid Steepest Descent Method (HSDM) for fixed point selection, combined with the preconditioned proximal point (PPP) algorithm for GNE seeking.
The test case is a Cournot game, where the agents compete over 3 limited utilities whose price increases linearly with the consumption. Among the set of solutions, the agents cooperatively optimize a quadratic cost.
The test is performed over T randomly generated tests with indexes t=1,...,T. Each test differs for the exponential term by which the HSDM stepsize vanishes. Each test is performed for N random initialization points, with indexes n=1,...,N
The data is in format .pkl which serializes the following data:
x_hsdm: dictionary that maps from the tuple (i, t, n) to the value for agent i, where t is the test index, n is the initialization point index, computed using HSDM+PPP
x_ppp: dictionary that maps from the tuple (i, t, n) to the value for agent i, where t is the test index, n is the initialization point index, computed using PPP
residual_hsdm: dictionary that maps from the tuple (t,n) to a vector containing the sequence of residuals for the hsdm+PPP algorithm. The residual is a measure of distance from the computed point to the GNE set.
residual_ppp: dictionary that maps from the tuple (t,n) to a vector containing the sequence of residuals for the PPP algorithm. The residual is a measure of distance from the computed point to the GNE set.
sigma_hsdm: dictionary that maps from the tuple (t, n) to the value of the aggregative variable, where t is the test index, n is the initialization point index, computed using HSDM+PPP.
sigma_ppp: dictionary that maps from the tuple (t, n) to the value of the aggregative variable, where t is the test index, n is the initialization point index, computed using PPP.
cost_hsdm: dictionary that maps from the tuple (t,n) to a vector containing the final value of the cooperative objective function for the hsdm+PPP algorithm
cost_ppp: dictionary that maps from the tuple (t,n) to a vector containing the final value of the cooperative objective function for the PPP algorithm
cost_hsdm_history: dictionary that maps from the tuple (t,n) to a vector containing the sequence of values of the cooperative objective function for the hsdm+PPP algorithm obtained along the iterations
cost_ppp_history: dictionary that maps from the tuple (t,n) to a vector containing the sequence of values of the cooperative objective function for the hsdm+PPP algorithm obtained along the iteration
T_horiz: length of the horizon of a multi-period Cournot game
exponent_hsdm: vector of length t, containing the exponential terms by which the HSDM stepsize vanishes
N: number of agents