You and I play the following game. Hidden from you, I put a coin in my hand: with probability p itis a 10 pence coin and otherwise it is a 20 pence coin. You now guess which coin is in my hand:you guess it is 20 pence with probability s and otherwise you guess it is a 10 pence coin.You get to win the coin if you guess correctly and otherwise win nothing. What (in terms of p ands) is your expected gain in pence from playing this game once with me?Challenge: suppose we are going to play repeatedly and you want to maximise your gain and Iwish to minimise my loss. What value of p should I choose and what value of s should youchoose? (This question is somewhat ill-defined, but it does have an interesting possible answer.)(Note: anything labelled "challenge" will not be part of the hand-in.)

Given Information- P(putting 10 pence coin in hand) = p P(putting 20 pence coin in hand) = 1 - p…

Answered: You and I play the following game.…

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter17: Making Decisions With Uncertainty

Section: Chapter Questions

Problem 17.5IP

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Consider the following Bayesian game. There are two players 1 and 2. Both players choose whether to play A or B. Two states are possible, L and R. In the former, players play a stag-hunt game, and in the latter, players play a matching pennies game. Suppose that Player 2 knows the state, while Player 1 thinks that the state is L with probability q and R with probability 1 ! q. Payo§s in each state respectively satisfy: Player 1 is the row player, and their payo§ is the first to appear in each entry. Player 2 is thecolumn player and their payo§ is the second to appear in each entry. (a) What is the set of possible strategies for the two players in this game? (b) Find all the pure strategy Bayes Nash equilibria for any value of q 2 (0, 1).
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For the following questions consider this setting. The deciding shot in a soccer game comes down to a penalty shot. If the goal-keeper jumps in one corner and the striker shots the ball in the other, then it is a goal. If the goalie jumps left and the striker shoots left, then it is a goal with probability 1/3. If the goalie jumps right and the striker shots right, it is goal with probability 2/3. Say the goalie's strategy is to jump left with probability 1 and the striker shoots left with probability 0.5, then the probability of a goal is (round to two digits) If the striker shoots in either corner with probability 0.5 and the goalie likewise shoots in either corner with probability 0.5, then the probability of a goal is (round to 2 digits)

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