(Bargaining) Two players A and B bargain to split a pot of money. They can bargain up

to three rounds. You do not need to explicitly consider discounting.

In Round 1,the total amount of money to be split is $10. Player A makes offer (a₁, b₁) to player B.

If B accepts A's offer, bargaining ends and they split the money according to the offer. If B rejects A's offer then they bargain in Round 2.

In Round 2, the pot of money shrinks to $8. Player B makes offer (a₂, b₂) to player A.

If A accepts B's offer, bargaining ends and they split the money according to the offer. If A rejects B's offer then they bargain in Round 3.

In Round 3, the pot of money shrinks to $5. Player A makes offer (a₃, b₃) to player B.

If B accepts A's offer, bargaining ends and they split the money according to the offer.

If B rejects A's offer then game also ends and both players's payoffs will be zero.

Assume that eachplayer always chooses toacceptan offer when the player is indifferent between Accept and Reject.

Find the subgame perfect equilibrium. Specifically, starting from the last round describe the optimal strategy to accept and reject offers

and the optimal offer to makein each round. In the equilibrium, when is an offer accepted and how much payoff will each player receive?