In Problems 9-18, which rows and columns of the game matrix are recessive? − 3 5 3 − 1 0 − 1
In Problems 9-18, which rows and columns of the game matrix are recessive? − 3 5 3 − 1 0 − 1
Solution Summary: The author explains that there are no recessive rows and columns for the provided payoff matrix, as the corresponding elements of none of the rows are less than or equal to that of another row.
2. Consider the two-person zero-sum game with the following 2x2 pay-off matrix:
1 2
1 а11 а12
2 a21 a22
Show that if the game has no pure strategy and saddle point, player II should play
strategy 1 with the following probability;
a22-a12
(a1-a12)+(a22-az1)
91
Suppose that we further alter the game from question 2 as follows: now whenever
both players select the same strategy, both receive a payoff of 2. Note that this is
no longer a zero-sum game.
(a) Give the payoff matrix for this game. As usual, you should list Rosemary's
payoffs first and Colin's payoffs second in each cell.
(b) Underline the best responses for each player to each of the other players' strate-
gies in your payoff matrix. Then, find and give all Pure Nash equilibria for the
modified game.
A three-finger Morra game is a game in which two players simultaneously show one, two, or three fingers at each round. The outcome depends on a predetermined set of rules. Here is an interesting example: If the numbers of fingers shown by A and B differ by 1, then A loses one point. If they differ by more than 1, the round is a draw. If they show the same number of fingers, A wins an amount equal to the sum of the fingers shown.
Determine the optimal strategy for each player. (Enter your probabilities as fractions.)
Player A should show one finger with probability _____ , two fingers with probability _____ , and three fingers with probability ______ .
Player B should show one finger with probability _______ , two fingers with probability ________ , and three fingers with probability ________ .
Find the expected value of the game.
The expected outcome is the player A will win __________ points per round, on average.
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