An infinite-horizon, alternating-offer bargaining game. Below we explore a modified version of the game, in search of subgame perfect equilib- rium (SPE). Players 1 and 2 alternate in making offers to each other. In odd periods (t= 1,3,), a cake of sizev >0 is available and player 1 makes an offer (x1,x2)R2+withx1+x2v. In even periods (t= 2,4,), a cake of sizew >0 is available and player 2 makes an offer (x1,x2)R2+withx1+x2w. In any period, if an offer is accepted, the cake available in that period is divided accordingly; otherwise, bargaining proceeds to the next period. Future payoffs are discounted at rate(0,1). Assume that min{w/v,w/v}> .

(a) Show that the game has a unique SPE outcome.

(b) Provide an example of SPE strategy profiles that gives the outcome in part (a). (Caution:It is enough to provide a strategy profile, without showing that it is an SPE.)

(c) How is your argument in part (a) affected if the assumption min{w/v,w/v}> is dropped?