Hello there, please answer all the questions with explanations step by step, please provide step by step explanations and make references to all the study notes and follow up with any questions. Please think about how you explain this to someone who has not done this before! then I will vote 5 star so no worries, also may you make reference to any study websites with the names as I understand you cannot post the links to the study websites, thank you! Please note the first screenshot is the question and the second screenshot is the answer, please explain the answer step by step and clearly and make sure all of them is correct, as it acts like a guide to lead you to the correct answer. Please explain all the concepts clearly and thank you so much for your time. This is all the required from this. Please also explain what does the symbols means, thanks

1. Backwards induction (a) The references for the experiments using chess players to play the centipede game are given below. Read them and summarise what they say. a Palacios-Huerta, 1., & Volij, O. (2009). Field centipedes. American Economic Review, 99, 16191635 a Levitt, 8., List, J., 85 Sadoff, S. (2011). Checkmate: ex ploring backward induction among chess players. American Economic Review, 101, 975990 (b) Two students are sitting in a pub arguing over who should buy the next round. To settle the argument they decide to play the following game. They place 21 pennies on the table and take turns to remove them. Each player can remove either 1, 2 or 3 coins when it is their turn. The person who picks up the last coin wins and the loser buys the next round. 1. If there are 7 coins left explain why it is optimal to take off 3 leaving 4. Why does this also mean that you want to leave your opponent with 8 coins? Continue this reasoning backwards to nd the subgame perfect strategies. ii. If both players use subgame perfect strategies who wins? iii. Extend this to the general case where you can remove up to 3: coins and you start with n (> 33) coins on the table and also to the case where you lose if you pick up the last coin. iv. Is it reasonable to assume that we use backwards induction to work out the subgame perfect equilibrium when we play this game? 1. Backwards induction 0)) i. ii. iii. iv. 4 is a losing position as whatever you do your opponent will be able take off the remaining coins. 8 is therefore also a losing position as whatever you do, your opponent will leave you with 4. Working backwards, all multiples of 4 are losing positions. Subgame perfect strategies, if you are currently not on a multiple of 4 leave your opponent on a multiple of 4. If you are on a multiple of 4 then taking off 1 or 2 or 3 is the same as you will lose if your Opponent plays Optimally (so take off whatever and hope your opponent makes a mistake!!!)_ The player going rst will start by taking off 1 leaving oppo nent in a losing position Multiples of a: l- 1 are losing positions. In the case where you lose when you pick up the last coin, the losing positions are 1+ multiples of (a: + 1). Most people won't start this game by using backwards induc- tion and will only use backwards induction close to the end of the game. So to win, you just have to start doing it before they do! In an exam answer you can bring in any research you have done on backwards induction that can be linked to this game (eg the papers in part a!!!)