3 Bargaining Two players have to divide the amount of 4 according to the following protocol: both players submit their claim in a sealed envelope by writing down an integer from the set {0,1,2,3,4). If the sum of both submitted claims does not exceed 4, then both players receive their claim. If the sum of claims exceeds 4 and both players claim the same amount, then both receive 2. If the sum of claims exceeds 4 and both claims differ, then the lower claim will be payed out while the other player receives what is left. 1. Formulate this situation as a strategic form game that is, specify the set of players, the set of strategies and payoffs, for which you can sketch a payoff matrix). 2. Which strategies survive the elimination of strictly dominated strate gies (IEDS)? 3. Which strategies survive the elimination of weakly dominated strategies (IEDS)? 4. If you were playing this game, which strategy would you select and why? Give a concise answer 4 All Pay Auction Two players participate in an all-pay auction for an object worth 8. The rich player R has a budget of 4 while the poor player P only has a budget of 3. In the all-pay auction format, both players have to pay their bid irrespectively of winning the auction or not. Both players can only bid non negative integer values and neither can exceed their budget. If both players bid the same amount, then nobody wins the auction while both players still have to pay their bid. Bidding 0 is allowed 1. Formulate this situation as a strategic form game that is, specify the set of players, the set of strategies and payoffs, you can sketch a payoff matrix) 2. Which strategies survive the climination of strictly dominated strate gies (IEDS)