Nash Equlibrium/Payoffs

Cole's decision is to lower price, because he is better off doing so regardless of Martin's decision. Let us take a look,

1) if Martin plays "lower price", Cole gets 70K from lowering price while only 40K from retain price

2) if Martin plays "retain price", Cole gets 100K from lowering price while only 80K from retain price

Hence Cole is always better choosing lower price. "lower price" is called dominant strategy, as it dominants "retain price" regardless of the opponent's action.

Similarly, you can verify that Martin is also always better choosing lower prices.

Hence Martin's dominant strategy is also lower price.

In this case, you have a Nash Equilibrium (Nash Eq. means that everyone chooses their best strategies and nobody can get more profit changing his/her strategy unilaterally) in which both players choose lower prices. The payoff of the Nash Eq. is 80K for Martin and 70K for Cole.

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