Two friends, Sophia and Lara are having dinner together. Sophia is cooking, while Lara is bringing the wine. Sophia doesn't know what wine Lara will bring and Lara doesn't know what food Sophia is cooking. The two friends' payoffs from the dinner party depend on the choice of food and wine according to the payoffs below. The game is common knowledge. Red White Rose Steak 10; 6 5; 2 1; 7 Fish 5; 4 6; 10 5; 5 Grains 6; 5 7; 7 4; 6 a) What is Sophia's best response function? Does Sophia have a strictly dominant strategy? b) What is Lara's best response function? Does Lara have a strictly dominant strategy? c) What is the (pure strategy) Nash equilibrium of this game? In class we mentioned that players who have a strictly dominant strategy have no need to form conjectures over what the other players might be doing before making their move. They should simply go with their strictly dominant strategies. In reverse, if a player has a strategy that always yields lower payoffs than another (this is called a strictly dominated strategy), it would be silly for the player to ever choose this strategy. Using common knowledge, iteratively eliminating strictly dominated strategies can help us rationalize some Nash equilibria. d) Consider Lara. Between Red and Rose, what wine would she pick? Why? Now consider a reduced payoff matrix after eliminating the column corresponding to the strictly dominated wine from the game.

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