Download Seminar 2 Ex.1 In each year, simultaneously, Iraq and Kuwait

Seminar 2 Ex.1 In each year, simultaneously, Iraq and Kuwait decide whether to extract high (H) or low (L) amount of oil from a common field. Extracting high amount of oil from the common field hurts the other country. In addition, Iraq has the option of attacking Kuwait (W), which is costly for both countries. The stage game is as follows: (i) Find a subgame perfect Nash equilibrium in which each country extracts low (L) amount of oil every year on the equilibrium path. (ii) Find a subgame perfect Nash equilibrium in which Iraq extracts high (H) amount of oil and Kuwait extracts low (L) amount of oil every year on the equilibrium path. Ex. 2 Consider two agents {1;2} owning one dollar which they can use only after they divide it. Each player’s utility of getting x dollar at t is δtx for δ ∈(0;1). Given any n>0, consider the following n-­‐period symmetric, random bargaining model. Given any date t _∈ {0;1;….;n−1}, we toss a fair coin; if it comes Head (which comes with probability 1/2), we select player 1; if it comes Tail, we select player 2. The selected player makes an offer (x;y) ∈ [0; 1]2 such that x+y ≤ 1. Knowing what has been offered, the other player accepts or rejects the offer. If the offer (x,y) is accepted, the game ends, yielding payoff vector (δtx ; δty ). If the offer is rejected, we proceed to the next date, when the same procedure is repeated, except for t = n − 1, after which the game ends, yielding (0,0). The coin tosses at different dates are stochastically independent. And everything described up to here is common knowledge. (i) Compute the subgame perfect equilibrium for n=1. What is the value of playing this game for a player? (ii) Compute the subgame perfect equilibrium for n=2. Ex. 3 Consider a two-­‐player game in which the payoffs, which depend on µ, and actions are as in the following table: If µ=0 If µ=1 where Pr(µ=0)=Pr(µ=1)=1/2. Only Player 2 knows whether µ=0 or µ=1. (i) Write this as a Bayesian game. (ii) Find a Bayesian Nash equilibrium of this game. Ex. 4 Find the perfect Bayesian Nash Equilibrium of the following game