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>

本数据集包含线性耦合聚合博弈中广义纳什均衡（Generalized Nash Equilibrium, GNE）最优选择的仿真结果。
本次测试采用混合最速下降法（Hybrid Steepest Descent Method, HSDM）进行不动点选择，并结合预处理近似点（Preconditioned Proximal Point, PPP）算法求解广义纳什均衡。
测试场景为古诺博弈（Cournot game），智能体围绕3种有限效用展开竞争，其价格随消费量线性增长。在所有解集中，智能体将协同优化一个二次代价函数。
本次测试共生成T组随机测试样本，样本索引为t=1,…,T。每组测试的区别在于HSDM步长衰减的指数项不同。每组测试将针对N个随机初始化点进行，初始化点索引为n=1,…,N。
数据集采用.pkl格式存储，序列化后的数据包含以下字段：
- x_hsdm：字典类型，以元组(i, t, n)为键，映射至智能体i的求解值，其中t为测试索引、n为初始化点索引，该值通过HSDM+PPP算法计算得到。
- x_ppp：字典类型，以元组(i, t, n)为键，映射至智能体i的求解值，其中t为测试索引、n为初始化点索引，该值通过PPP算法计算得到。
- residual_hsdm：字典类型，以元组(t,n)为键，映射至一个向量，存储HSDM+PPP算法的残差序列，残差用于衡量当前计算点与GNE解集的距离。
- residual_ppp：字典类型，以元组(t,n)为键，映射至一个向量，存储PPP算法的残差序列，残差用于衡量当前计算点与GNE解集的距离。
- sigma_hsdm：字典类型，以元组(t, n)为键，映射至聚合变量的取值，其中t为测试索引、n为初始化点索引，该值通过HSDM+PPP算法计算得到。
- sigma_ppp：字典类型，以元组(t, n)为键，映射至聚合变量的取值，其中t为测试索引、n为初始化点索引，该值通过PPP算法计算得到。
- cost_hsdm：字典类型，以元组(t,n)为键，映射至一个向量，存储HSDM+PPP算法的协同目标函数最终值。
- cost_ppp：字典类型，以元组(t,n)为键，映射至一个向量，存储PPP算法的协同目标函数最终值。
- cost_hsdm_history：字典类型，以元组(t,n)为键，映射至一个向量，存储HSDM+PPP算法迭代过程中协同目标函数的序列值。
- cost_ppp_history：字典类型，以元组(t,n)为键，映射至一个向量，存储PPP算法迭代过程中协同目标函数的序列值。
- T_horiz：多周期古诺博弈的时域长度。
- exponent_hsdm：长度为T的向量，存储HSDM步长衰减所使用的各指数项。
- N：智能体总数。