PAPER CODE NO. MATH 331 MAY 2020 EXAMINATIONS NON-PHYSICAL APPLICATIONS I (MATHEMATICAL ECONOMICS) TIME ALLOWED : Two Hours and a Half INSTRUCTIONS TO CANDIDATES This paper contains SEVEN questions, all carrying equal weight. Full marks will be awarded for complete solutions to FIVE questions. Candidates may attempt all questions, but only the best FIVE solutions will be taken into account. Candidates are only permitted to use calculators deemed acceptable, and affixed with an official holographic sticker, by the Department of Mathematical Sciences. PAPER CODE …Math331…… PAGE 1 OF 6 CONTINUED Examiner: Dr D M Lewis Tel: ext 4014 (Maths Sci.) 1. A rustic poker game for two players, and , begins with both players staking ￡1 into the kitty. In this game there are two hats, each containing two cards. Hat No. 1, used in the first round of bidding, contains a card marked 1 and a card marked 5. Hat No. 2 used in the second round
of bidding, contains a card marked 3 and another card marked 5. When selecting a card from a hat both players are careful not to show it to their opponent. Player goes first and has the choice of either calling “Raise ￡3”, putting ￡3 into the kitty and selecting a card from hat No. 1, or calling “Stick”, in which case he does nothing. Now it is Player ’s turn. He too can choose to call “Raise ￡3” pay and select a card from Hat No. 1, or just call “Stick”. That concludes the first round of bidding. If (and only if) both players raised in round 1, then a second round of bidding commences, with Hat No.1 replaced by Hat No. 2. The procedure is the same. Player goes first, then Player . Each player can “Raise ￡3” or “Stick” and any selections are made from Hat No. 2. Once all the bidding has concluded the game ends. The players turn over their cards and compute their scores. A player’s score is given by the total on their cards (if any) minus the amount of money they contributed to the kitty (including their initial stake) to get them. The player with the highest score wins the kitty, if the scores are level the kitty is shared. a) Draw a game tree for this game including the information sets, payoffs, and the
relevant probabilities of the possible wining/losing scenarios.