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For each statement give 2x2 matrix that shows it is false. (I'd start by looking at the games I put up in class, Prisoner's Dilemma, Battle of the Sexes, World's Dumbest Game, etc.) When I talk about Pareto efficiency or domination assume it's strong.
(a) If an outcome is a Nash equilibrium outcome, one player or the other gets the highest payoff the player can get in the matrix.
(b) For each outcome consider the sum of the two payoffs. A Nash equilibrium always gives the two players their highest sum.
(c) A Pareto-efficient outcome will be a Nash equilibrium.(d) A Nash equilibrium outcome will be Pareto-efficient.(e) There can never be two Nash equilibria in the same Row.(f) There is no 2x2 game where all four outcomes are Nash equilibrium outcomes.(g) If an outcome is Pareto-efficient it cannot be in a dominated row or in a dominated column. (h) There is no 2x2 game where all four outcomes are Pareto-efficient.
(i) There is no 2x2 game where one player has a dominating strategy and the other player does not.
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Messages are in the form of a sequence of decimal numbers, M = (a1, a2,..., at). The hash value h is calculated as mod n. Calculate the hash function of the above for M=(189
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