1. You and a rival engaged in a game in which there are three possible outcomes: you win, your rival wins (you lose), and the two of you tie. You get a payoff of 50 % if you win, a payoff of 20

% if you tie, and a payoff of zero if you lose. What is your expected payoff of the following situations:

1. There is a 50 % chance that the game ends in a tie and 10 % chance that you win) there is thus 40 % chance that you lose).
2. There is an 80 % chance that you lose and 10 % chance that you win or that you tie.

1. Assume two car manufacturing companies considering introducing an electric vehicles to a local market. Car manufacturer A is ahead in the development process and manufacturer B is considering whether to enter the competition. If manufacturer B stays out, it earns zero profit, whereas A enjoys a monopoly and earns a profit of Birr 2 billion. If B decides to enter and develop the rival airplane, then A has to decide whether to accommodate B peaceably or to wage a price war. In the event of peaceful competition, each firm will make a profit of Birr 500 million. If there is a price war, each will Birr 200 million because the prices of electric vehicles will fall so low that neither firm will be able to recoup its development costs. Draw the tree for this game.

1. Explain the difference between game theorys use as a predictive tool and its use as a prescriptive tool. In what types of real-world settings might these two uses be most important?

1. In a sequential move game, the player who moves first is sure to win. Is this statement true or false? State the reason for your answer in a few brief sentences, and give an example of a game that illustrates your answer.

1. Consider the strategic game described below. In each case, how you would classify the game according to the six dimensions: whether moves are sequential or simultaneous, whether the game is repeated, whether there is imperfect or incomplete (asymmetric) information, whether the rules are fixed,, and whether cooperative agreements are possible. If you do not have enough information to classify a game in a particular dimension, explain why.

1. Rock-Paper-Scissors: On the count of three, each player makes the shape of one of the three items with his hand. Rock beats scissors, scissors beat paper, and paper beats rock.
2. Roll-call voting: Voters cast their votes orally their names are called. In a two candidate elections, the candidate with the most votes wins.
3. Sealed-bid auction: Bidders seal their bids in envelopes for a bottle of wine. The highest bidder wins the item and pays his bid.

1. Suppose two players J and K, take part in a sequential-move game. J moves first and K moves second, and each player moves only once.

1. Draw a game tree in which J has two possible actions (Up or Down) at each node and K has three possible actions (Top, Middle, or Bottom) at each node. How many of each node type decision and terminal nodes are there?
2. Draw a game tree for a game in which J and K each have three possible actions (Sit, Stand, or Jump) at each node. How many of the two nodes are there?
3. Draw a game tree for a game in which J has four possible actions (North, South, East, or West) at each node and K has two possible actions (Go or Stay) at each node. How many of the two nodes are there?

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