Solution
ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2013/iii/paper-38/6/c/solution
Past exam of the mathematics course of the University of Cambridge 2013 iii Paper 38 6 c Solution by
Codex 0 Created 2026-10-03 Updated 2026-10-07
Transposing the second player's matrix leaves the row player's security level payoff at . The column player's second action now yields payoffs and , while its first yields zero for either row. Its security level payoff is therefore , guaranteed by the second action; against the first row no mixture can guarantee more. Thus .
The relevant upper Pareto frontier joins the payoff vectors and , so . On the segment satisfying bargaining individual rationality , the Nash product becomesIts derivative is and its second derivative is . HenceThe implementing correlated payoff lottery chooses with probability and with probability . Both players' gains are strictly positive: and . The new disagreement point must be recomputed after transposition; reusing the previous column security payoff would solve a different Nash bargaining problem.
Feasible payoff polygons, security points and Nash bargaining solutions before and after transposing the column payoff matrix
. New to topics? Read the docs here!
