Game Theory

3. Use the model setup in \"The economics of lending with join liability: theory and practice\" by Ghatak and Guinnane with Y" = 10, YL = 0,1" = 2,0 = 2, pa = 0.7 and pb = 0.3 to (i) calculate the expected payoffs of (a) a safe borrower partnering with a safe borrower, (b) a risky borrower partnering with a risky borrower, (c) a safe partner borrowing with a risky borrower, and (d) a risky borrower partnering with a safe borrower; (ii) use these to calculate the highest price a. risky borrower would pay to partner with safe borrower, and the lowest price a safe borrower would accept to partner with a risky borrower; (iii) use these price calculations to explain how joint liability can help resolve the adverse selection problem discussed in the paper. Street : 0= center of street R = 14 way down street Example of an outcome : Plat O ( left side ) P2 at O ( right side ) p3 at R The liegram shows regions of demand given this outcome :Pl gets 50% P2 get 14 of 50% = 12.5% P3 gets 3/4 of 50% = 37.5% Note : these are payoffs AFTER " nature " . Why did PV get 50% ! 12 get 12.5% ? - Nature chooses , so you need to do expected value : E ( PI) - 2 ( 50 ) + E ( 12.5) = 31.25% E ( P2 ) = 2 ( 50) + E ( 12.5) = 31.25%% So if more than are player shows up at a location , you need to calculate expected values . Then you can draw gamefree / normal Farms ; PI 2 O P3 - - R 2 R R P2 P2 O 31. 25, 31.25 37.5 Simultaneous Zoom in move game 31.25 , 31.25, 37.5 each outcome has 3 lexpected ) payotts .Once you have all outcomes you can set up 3 equations wl 3 unknowns make players indifferent between O and R