3 Bargaining Two players bargain over the devision of 10 according to the protocol dis- cussed in the lecture: players negotiate by making alternating offers starting with player 1. After an offer by one player, the other player can accept or reject. If accepted, then the proposed division is implemented and the game ends. I rejected, then the player who rejected can make another offer. If both players fail to agree until the deadline, then both players get nothing. Players are impatient and discount future payoffs by 61 2 52 = 0.95. 1. Suppose the deadline is after 3 periods, i.e. if players fails to agree after three rounds of negotiation then both players get nothing. Draw the game tree and characterise the SPNE (i.e. characterise the strategies and the resulting payoffs). Which player receives the higher payoff? 2. Now suppose the deadline is after 4 periods, i.e. if players fails to agree after four rounds of negotiation then both players get nothing. Draw the game tree and calculate the resulting payoffs in the unique SPNE. Which player receives a higher payoff in this case? 3. Calculate the payoffs in the SPNE after 41 rounds of bargaining. 4. Finally, suppose there is no deadline, i.e. players can bargain as long as they want. Characterise the SPNE (i.e. characterise the strategies and the resulting payoffs). Which player receives the higher payoff? 5. Interpret and explain the results 1)-4) with respect to rst mover and last mover advantage