Network Structures

2. Find all Nash equilibria for the game described by the following payoff matrix:

In the mixed-strategy equilibrium that you find, Player 1 plays strategy U more often than strategy D. One of your friends remarks that your answer must be wrong because clearly for Player 1 strategy D is more attractive than strategy U. This is because both U and D give Player 1 a payoff of 4 on the off-diagonal elements of the payoff matrix, but D gives Player 1 a payoff of 3 on the diagonal while U only gives Player 1 a payoff of 1 on the diagonal. Explain what is wrong with this reasoning.