Assignment Problem: Two equally strong wrestlers take part in a wrestling match Sometime before the match, each of them must decide whether to take anabolic steroids to improve his performance. If one takes steroids and the other doesn't, the one who takes steroids will win. If both take steroids or none of them does, the match will end in a draw. Each wrestler is paid £400 for a win, £200 for a draw and 0 for losing. However, taking steroids also implies a loss of utility, because of possible adverse health effects and/or the risk of being detected and penalised. This loss of utility has a monetary equivalent of £100. In other words, if a wrestler takes steroids, his payoff in the match is the amount he is paid minus £100. If a wrestler does not take steroids, his payoff is simply the amount he is paid.
Write down the payoff matrix of this game and find the pure strategy Nash equilibrium (or equilibria)- Explain your answer.