Harvard University - ECON 1051Problem Set 10 Solutions

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Problem Set 10 Solutions Attila Ambrus, Economics 1051, Spring 2011 Solutions prepared by Zhenyu Lai ([email protected]). Please email for any clariÖcations. 1. InÖnitely Repeated Hawk and Do... ve Game. Suppose that  = 0:99. Construct a SPE in the inÖnitely repeated version of the following game in which player 1ís normalized payo§ (1-)PDV 1 is larger than 5. For what other discount factors  is your construction a SPE? Dove Hawk Dove 3; 3 0; 8 Hawk 8; 0 1; 1 Solution. The most straightforward way to achieve a normalized payo§ of at least 5 is to alternate between payo§s of 3 (from (Dove, Dove)) and 8 (from (Hawk,Dove), (Dove, Hawk)). With this in mind, we construct the following grim trigger strategies. Player 1: Play Hawk in odd periods, Play Dove in even periods,  if nobody has deviated before Play Hawk in remaining periods, if somebody has deviated before Player 2: Play Dove, if nobody has deviated before Play Hawk in remaining periods, if somebody has deviated before First, we check if these strategies satisfy the condition that player 1ís normalized payo§s are at least 5 in equilibrium when  = 0:99 Normalized Payo§1 = (1 ) P DV1 = (1 ) 8 + 3 + 8 2 + 3 3 + ::: = (1 ) (8 + 3) 1 +  2 +  4 + :::
= (1 ) 8 + 3 1  2 = 8 + 3 1 +  = 8 + 3 (0:99) 1 + 0:99 > 5 Next, to check the range of  for which these strategies are an equilibrium, we check that neither player has an incentive to deviate. For each player, we check for deviations in each of two equivalence classes (odd periods and [Show More]

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