Figure 2
The figure shows three pairs of text boxes arranged in three rows. The first box, positioned at the top left (in the first row), contains the following text: “C and T engage in a noncooperative game by selecting recycling rates tau subscript c and tau subscript t, forming a competitive scenario (tau subscript c, tau subscript t).” A right-pointing arrow from this box points to the second box (in the first row), containing the following text: “M, C, and T jointly determine cooperative strategies: C S R effort level theta, new battery price rho, and retired battery transfer price f subscript c and f subscript t, thereby constructing characteristic functions.” A downward arrow from this box points to the third box, positioned on the right in the second row. The text within the box reads: “Profit distribution values are allocated via the Shapley value method, with M, C, and T receiving profits defined as f subscript m (tau subscript c, tau subscript t), f subscript c (tau subscript c, tau subscript t), and f subscript t (tau subscript c, tau subscript t), respectively.” A left-pointing arrow from this box leads to the fourth box positioned on the left (in the second row). The text in the box reads: “The profit allocations f subscript c (tau subscript c, tau subscript t) and f subscript t (tau subscript c, tau subscript t) for C and T serve as their payoff functions in the noncooperative phase.” A downward arrow from this box points to the fifth box positioned on the left in the third row. The text within the box reads: “The Nash equilibrium recycling rates tau subscript c asterisk and tau subscript t asterisk are solved, yielding optimal profits f subscript m asterisk (tau subscript c asterisk, tau subscript t asterisk), f subscript c asterisk (tau subscript c asterisk, tau subscript t asterisk), and f subscript t asterisk (tau subscript c asterisk, tau subscript t asterisk).” A right-pointing arrow from this box points to the sixth box (in the first row), containing the following text: “The equilibrium solutions are fed back into the cooperative phase, yielding globally optimal strategies: C S R effort level theta asterisk, new battery price rho asterisk, and retired battery transfer price f subscript c asterisk and f subscript t asterisk.” The first, fourth, and fifth boxes are arranged in a vertical series on the left and are labeled “Noncooperative game part.” The second, third, and sixth boxes are arranged in a vertical series on the right and are labeled “Cooperative game part.” The boxes on the left and right are separated by a dotted vertical line. All six boxes are collectively labeled “Noncooperative-cooperative biform game.” Additional dotted vertical lines are present on the extreme left and right sides of the two vertical series of boxes, respectively.Noncooperative-cooperative biform game solution framework. Source(s): Created by authors