Which of the following are true and which are false? Give brief explanations.

a) In a fully observable, turn-taking, zero-sum game between two perfectly rational players, it does not help the first player to know what strategy the second player is using—that is, what move the second player will make, given the first player's move.

b) In a partially observable, turn-taking, zero-sum game between two perfectly rational players, it does not help the first player to know what move the second player will make, given the first player's move.

c) A perfectly rational backgammon agent never loses.

Expert Solution

a. False. Just consider cake cutting problem in which a child divide cake into 2 pieces and another child select the piece. Since this game is also fully observable zero sum game where sum of profit minus loss of both agent is zero, the strategy played by one agent definitely helps the second agent to make the choice. For example in this game, second child will select bigger piece cake if first child divide cake equally.

b. False, even in partially observable game, knowledge of what second player moves definitely helps the first player. For example in auction, where two or more agent make bids, knowledge of what other agent have biding capacity will definitely maximize the profit that could be made while wining the bid. Here partial observation means that even though the exact amount other people can make is not clear, what their next biding price knowledge will definitely helps in decision making.

c. False, since Backgammon is game of chance and outcome(winning or losing) depends upon outcome of rolling dice which is a random phenomena. And hence even a perfectly rational agent can lose.

venereology answered 2 years ago

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