ECON2550 Game Theory

This online assessment substitutes the traditional two-hour re-sit exam we would have in August. All questions below are mandatory for you to answer. They relate to the material we covered throughout the year.Please submit your answers on Turnitin that is set up for this purpose (turnitin and then online re-sit assessment). When answering the questions, it is good to use both intuition and math just as we did during our lectures/classes (so it is recommended to revise the recorded content/ seminars). You will also need to create payoff matrices and do some calculations (and show your work). For this purpose, you can use Word that allows the user to create tables and do simple math. Also, feel free to assume individual payoffs when these are not given by the specific question. Please use pdf file format when submitting your answers on turnitin. Good luck!Please read the questions carefully and do let me know via email if you need any clarifications in the next couple of weeks (by the end of July).
Subgame Perfection Vs Nash Equilibrium
How does the idea of a subgame perfect Nash equilibrium rule out non- credible threats? [Hint: When answering the question, it may be best to use games/examples we saw during the lectures/seminars throughout the second term].
Penalty-taking
Think of the following simultaneous-move game between a striker that is about to take a penalty and a goalkeeper: the striker can only kick to the left or the right and therefore the goalkeeper can either move to the left or to the right. In this simplified game, if the striker and the goalie choose the same direction (looking at the game from either the striker’s or the goalie’s perspective), the goalkeeper saves the penalty. Otherwise, the striker scores.(a)Derive the mixed strategy Nash Equilibrium of this game when the payoff matrix of the game is as follows (the striker is the row player):(b)If the striker is happier when scoring by kicking to the left, as in the payoff matrix that follows,find the mixed strategy Nash equilibrium. Why is the mixed strategy Nash Equilibrium of the asymmetric penalty game different from the mixed strategy Nash Equilibrium of the symmetric version in (a)? (15 marks)(c)How likely do you think it is that players in games with no Nash equilibrium in pure strategies choose mixed strategies? (25 marks