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pure strategy Nash Equilibria of this game

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Suppose that a cake is being divided in the following way among two players. Each player writes down a number from zero to one on his piece of paper. Then both players turn over their pieces of paper. If the sum is less than or equal to one, each player gets a share of the cake equal to the number he wrote. If the sum is bigger than one, each player gets nothing.

What are the pure strategy Nash Equilibria of this game? Do they help you at all in predicting the result of the game?

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Suppose that a cake is being divided in the following way among two players. Each player writes down a number from zero to one on his piece of paper. Then both players turn over their pieces of paper. If the sum is less than or equal to one, each player gets a share of the cake equal to the number he wrote. If the sum is bigger than one, each player gets nothing.

What are the pure ...

Solution Summary

The pure strategy Nash Equilibria of this game are noted.

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Game Theory - Normal Form and Nash Equilibriums for Simultaneous Games

You have been offered the chance to participate in a Treasure Hunt game whose rules are as follows. THere are three coloured boxes: red, green and yellow. The game show host must hide a $100 bill in a box of his choice. You have the option of opening one and only one box/ If the money was hidden in that box, you win it. Otherwise, it returns to the host. Each box has a fee which you must pay to the host if you choose to open that box. The fees are $50 for the red box, $20 for the green box, and $0 for the yellow box. Assume that both you and the show host want to maximize expected earnings.

a) Write down the normal form (payoff matrix) of this game.
b) Find the Nash equilibrium.

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