Determine the optimal strategy for the situation by representing it as a game an

Question

Determine the optimal strategy for the situation by representing it as a game and finding the saddle point. State your final answer in the terms of the original question. A Republican and a Democratic candidate are running for office in a heavily Republican county. A recent newspaper poll comparing their views on taxes and welfare reform showed that when compared on taxes or on welfare reform, the Republican leads by 20%. When comparing the Democrat on welfare reform to the Republican on taxes, the Republican leads by 35%. But when comparing the Democrat on taxes to the Republican on welfare reform, the Republican leads by only 10%. Use this information to decide what each candidate should discuss at their next debate. (Let T represent taxes and W represent welfare reform.) The saddle point is the in row and column What should each discuss at their next debate? They both should discuss welfare reform at their next debate. The democratic candidate should discuss taxes, while the republican candidate discusses welfare reform. The democratic candidate should discuss welfare reform, while the republican candidate discusses taxes. They both should discuss taxes at their next debate.

Explanation / Answer

In order to solve this game we can apply the minimax principle and find out the optimum strategy for each players.

First we construct the game payoff matrix as follows: When compared on taxes or welfare reform, the republican leads by 20% that is (tax-tax and welfare-welfare is assign 20%). When comparing the democrat on welfare reform to the republican on taxes, the republican leads by 35% (welfare reform-tax). When comparing the democrat on taxes to the republican on welfare reform, the republican leads by 10% (tax-welfare reform)

By the minimax principle, row minimum are (20% and 10%) and the column maximum are (20% and 35%). By minimax and maximin we get (20%=20%) which showh the value of the game. The solution of the game is (Tax Tax) and value of the game is 20%.

The value of the game is row minimum and column maximum, therefore no one have any incentive to shift from this equilibrium, and both will be at optimum at this level. So this is known as saddle point.

So the saddle point is 20% at row R1 and Column 1.

And they both should discuss taxes at their next deabte, so they can both are betteroff by their best alternative stategies.

Democratic Republican Tax Welfare Minimum Tax 20% 35% 20% Welfare 10% 20% 10% Maximum 20% 35% 20%=20%

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.