Question

Amy and Beth have to bargain about how to divide R250. Amy moves first, making an offer of some portion of the R250 to Beth. Beth then chooses to accept or reject the offered amount. If Beth accepts, the money is divided according to the proposal. If Beth rejects the offer, the amount is reduced by R50, so that there is R200 left, and then Beth gets a turn, making an offer to Amy. If Beth’s offer is accepted, the R200 is divided according to Beth’s proposal, but if rejected, the amount is again reduced by R50 and it is Amy's turn again to make an offer. This process continues, with the players taking turns to make offers and the other choosing accept or reject, and the amount being reduced each time an offer is rejected. If the amount reaches R0 before any offer is accepted, the game ends, with both players getting nothing. Assume common knowledge of rationality and that a player who is indifferent between accepting and rejecting will always choose reject. Also note that only integer Rand amount offers are allowed (i.e. no cents).

Use backwards induction to determine what offer Amy should make in the first round (when there is R250 to divide).

Answer 1

Player A Player A Player A Player B 125,125 Player B 125,125 Player B 125,125 100,100 Player A 100,100 Player A 100,100 Player A 50,50 75,75 75,75 Player B 75,75 Player B 25,25 50,50 Player A 50,50 0,0 Player A 25,25 100,100 125,125

Player A has a choice between dividing the amount in two equal parts and any other division where Player 1 receives more than player B. In any allocation other than (125,125), player B will reject player A's proposal and will be faced by the same choice but with lesser amount. This process continues till no money is left. Using backward induction, we found that player A should divide the amount in half.