Problem 3 (2 points): Reduce the following payoff matrix for a zero-sum game between two people by dominance. a b c P 1 l S Q 4 -4 2 R 3 3 ]0 S 5 5 4 Problem 5 (2 points): Consider an Input-Output model with 3 sectors (sector 1 is machinery, sector 2 is agriculture, and sector 3 is services) and a technology matrix A. If the external demand for agriculture increases by 1, demand for services increases by 2 but demand for machinery decreases by 3, by how much the production in all three sectors will change? Express your answer in a matrix form that depends on A. Hint: there is a formula in the textbook (and Power Point slides) that gives an answer to this question, you just need to include the specic numbers where you can Certainly . I can explain why there Is no dominant strategy in a certain row of 9 payoff matrix in the context of game theory . In game theory , a dominant strategy for a player is a strategy that always provides a higher payoff ( or at least equal ) than any other strategy, regardless of the choices made by the other players . When there is no dominant chategy in a row, it means that no single strategy is consistently better than the others , and the choice of strategy may depend on the choices made by the opponent Here's an example to illustrate why there might be no dominant stategy in a row of payoff matrix : Consider a simple two-player game where player A har tus strategies ( x andy ), and Player B also har two strategies ( W andZ ) . The payoff matrix might look like this : W Z X (3. 1) (2, 2 ) Y (0.4 ) ( 4.3 ) In this example , let's focus on playes A's row ( x and y ) . Player A doesn't have a dominant strategy because , for each column ( W and Z ) , there is no single strategy ( x ory ) that consistently provider a higher payoff. . If Player B chooser W. then Player A prefers X (370 ). . If Player B chooses X, then player A prefers y ( 472 ) So , the choice of Player Air strategy depends on what Player A does. If Player B chooses W, Player A prefers X ; if Player B chooser 2. Player A prefers y. This lack of dominance illustrates that Player Air optimal strategy depends on the strategies chosen by player B, and there is no single bertstrategy for player A in all scenarios . In rommary, the absence of a dominant strategy in a row of a payoff matrix means that the choice of strategy for that player is influenced by the strategies chosen by the opponents , making it a strategic decision based on the context of the game . Prepared and written by : Jayron Rebates course Hero Tutor