United Way of River City (UWRC) is considering inviting River City General (RCG), a major medical center, to join its annual federated fundraising campaign. To do so, RCG must discontinue its own campaign but is assured a fair share of the proceeds from the UWRC campaign. The expectation is that the joint campaign will raise more funds than the sum of two separate campaigns. However, if UWRC decides to invite RCG but RCG declines, UWRC will gain a public relations benefit (and raise more funds than otherwise) and RCG will suffer from damaged community relations and be less successful in its own campaign than it would have been were it not invited. If RCG expresses a wish to join the campaign but UWRC does not to extend the invitation, then RCG will be viewed favorably but UWRC will suffer a public relations problem that will make its campaign less successful than if the issue had never come up. The payoff matrix is: a) Are there dominant strategies for either player? If so, what strategies are dominant for each player (7 points)? b) Are there any Nash equilibria? If so, list them (tell me which cells are Nash equilibria, using the standard labels for rows and columns ( R for right, L for left, T for top, and B for bottom) (6 points). c) What do you predict each player will do and why (6 points)? d) How sensitive is this result to the sizes of the estimated pay-offs to each party? Experiment with the numbers in the matrix to determine the circumstances under which the solution would be different. United Way of River City (UWRC) is considering inviting River City General (RCG), a major medical center, to join its annual federated fundraising campaign. To do so, RCG must discontinue its own campaign but is assured a fair share of the proceeds from the UWRC campaign. The expectation is that the joint campaign will raise more funds than the sum of two separate campaigns. However, if UWRC decides to invite RCG but RCG declines, UWRC will gain a public relations benefit (and raise more funds than otherwise) and RCG will suffer from damaged community relations and be less successful in its own campaign than it would have been were it not invited. If RCG expresses a wish to join the campaign but UWRC does not to extend the invitation, then RCG will be viewed favorably but UWRC will suffer a public relations problem that will make its campaign less successful than if the issue had never come up. The payoff matrix is: a) Are there dominant strategies for either player? If so, what strategies are dominant for each player (7 points)? b) Are there any Nash equilibria? If so, list them (tell me which cells are Nash equilibria, using the standard labels for rows and columns ( R for right, L for left, T for top, and B for bottom) (6 points). c) What do you predict each player will do and why (6 points)? d) How sensitive is this result to the sizes of the estimated pay-offs to each party? Experiment with the numbers in the matrix to determine the circumstances under which the solution would be different