%0 Generic %A Benenati, Emilio %A Ananduta, Wicak %A Grammatico, Sergio %D 2024 %T Data underlying the publication: On the optimal selection of generalized Nash equilibria in linearly coupled aggregative games %U %R 10.4121/8a4f4888-418b-4f0b-8d65-b88a43918956.v1 %K simulation %K GNE %K game theory %K Generalized Nash Equilibrium %X <p>This data contains simulation results for the optimal selection of a Generalized Nash Equilibrium (GNE) in a linearly coupled aggregative game.</p><p><br></p><p>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.</p><p><br></p><p>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.</p><p><br></p><p>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</p><p><br></p><p>The data is in format .pkl which serializes the following data:</p><p><br></p><p>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</p><p>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</p><p>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.</p><p>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.</p><p>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.</p><p>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.</p><p>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</p><p>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</p><p>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</p><p>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</p><p>T_horiz: length of the horizon of a multi-period Cournot game</p><p>exponent_hsdm: vector of length t, containing the exponential terms by which the HSDM stepsize vanishes</p><p>N: number of agents</p><p><br></p> %I 4TU.ResearchData