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Use the above normal form game as the stage game in a repeated game for each of the following questions. Ann chooses rows and Bob chooses columns.
(1) Find the individually rational and feasible set.
(2) Consider an infinitely repeated game in which both players discount the future using the discount rate δ with 0 < δ < 1.
(a) What is the smallest value of δ for which there is a SGPNE (using Nash revision strategies) in which (U,L) is played in every stage along the equilibrium path?
(b) Find the Nash revision strategies for Ann and Bob which form a SGPNE with the δ identified in part (a).
(c) Verify that the strategies found in part (b) do form a SGPNE.
(3) Now let δ = 1 and consider the repeated game in which the above stage game is played T = 10 times.
(a) In how many periods can a SGPNE support the play of (U,L)?
(b) Find a pair of strategies which form a SGPNE and support play of (U,L) in the number of periods indicated in part (a).
(c) Verify that the strategies you found in par (b) are in fact a SGPNE.