Reference no: EM132207523
Question: You (Y ) have a job offer by Microsoft that pays a wage of r. But you have also a job offer from Facebook (F) and are in the process of negotiating your wage w. You cannot work for both Microsoft and Facebook.
The negotiation process uses alternating offer bargaining. You offer at datest = 0,2,4,... and Facebook offers at dates t = 1,3,.... When you make an offer w, Facebook can either accept the offer and hire you at wage w (ending the bargaining), or reject the offer and the negotiation continues. When Facebook makes an offer w, you can either accept the offer w and start working at Facebook for wage w and ending the negotiation, or reject the offer w and take Microsoft offer r, working for Microsoft at wage r and ending the game, or reject the offer w, and then the negotiation continues.
If the game continues to date T ≤ ∞ then the game ends with zero payoff s for both players. If You take Microsoft's offer at t < T , then your payoff is δtr and the payoff of Facebook is 0, where δ ∈ (0,1). If You start working for Facebook att < T for wage w , then Your payoff is δtw and Facebook's payoff is δt(π - w) , where
(π/2) < r < π.
(a) Compute the subgame perfect equilibrium for T = 4.
(b) Suppose now that T = ∞ . Conjecture a subgame-perfect equilibrium and check that the conjectured strategy profile is indeed a subgame-perfect equilibrium.
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