Data underlying the publication: On the optimal selection of generalized Nash equilibria in linearly coupled aggregative games

This data contains simulation results for the optimal selection of a Generalized Nash Equilibrium (GNE) in a linearly coupled aggregative game.<br>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.<br>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.<br>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<br>The data is in format .pkl which serializes the following data:<br>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+PPPx_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 PPPresidual_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 algorithmcost_ppp: dictionary that maps from the tuple (t,n) to a vector containing the final value of the cooperative objective function for the PPP algorithmcost_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 iterationscost_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 iterationT_horiz: length of the horizon of a multi-period Cournot gameexponent_hsdm: vector of length t, containing the exponential terms by which the HSDM stepsize vanishesN: number of agents<br>