# Hw07a_2008 - UNC-Wilmington Department of Economics and Finance Homework 7 Solutions Simultaneous and Repeated Games 1 ECN 321 Dr Chris Dumas

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UNC-Wilmington ECN 321 Department of Economics and Finance Dr. Chris Dumas Homework 7 Solutions Simultaneous and Repeated Games 1) Target will choose to Advertise, because Advertise is a dominant strategy for Target. Wal Mart will also choose to Advertise, because Advertise is a dominant strategy for Wal Mart. Therefore, because all players have dominant strategies, there is a dominant strategy equilibrium, and it is "Target plays Advertise, Walmart plays Advertise." 2) Gacy's does not have a dominant strategy. Mimbel's does not have a dominant strategy. Because at least one player does not have a dominant strategy (in fact, in this example neither player has a dominant strategy), there is no dominant strategy equilibrium in the game. Furthermore, because none of the players has a dominant strategy, there is not an iterated dominant strategy equilibrium in the game. When there are no dominant strategy equilibria or iterated dominant strategy equilibria, we look for Nash equilibria. To find Nash equilibria, we consider each cell in the payoff matrix in turn. For each cell in the payoff matrix, we ask ourselves, "Self, would any of the players like to change his/her strategy given the strategy being played by the other players in this cell." If none of the players would want to change his/her strategy, then that cell of the payoff matrix is a Nash equilibrium. If one or more of the players would want to change his/her strategy, then that cell is not a Nash equilibrium. By this method, we find that the only cell in the payoff matrix that is a Nash equilibrium is "City Center, City Center." When there is a single Nash equilibrium in a game, that cell gives the solution to the game. For example, in this game, because "City Center, City Center" is the Nash equilibrium, we predict that "Gacy's plays City Center, Mimbel's plays City Center" will be the outcome of the situation facing Gacy's and Mimbel's. 3) Students Study Not Study Teacher s Grade Hard 8 , 4 6 , 2 Grade Easy 10 , 8 4 , 10 Students do not have a dominant strategy. Teachers do not have a dominant strategy. Hence, there are no dominant strategy equilibria nor iterated dominant strategy equilibria.

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## This note was uploaded on 10/22/2009 for the course ECN 321 taught by Professor Dumas during the Fall '08 term at University of North Carolina Wilmington.

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Hw07a_2008 - UNC-Wilmington Department of Economics and Finance Homework 7 Solutions Simultaneous and Repeated Games 1 ECN 321 Dr Chris Dumas

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