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# Nash Equlibrium/Payoffs

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4. The table below shows the payoffs two competing firms, Cole and Martin, face in the decision to reduce their price or retain their current price.
Cole

Lower Price Retain Price

Martin Lower
Price Cole 70K Martin 80K Cole 40K
Martin 100K
Retain
Price Cole 100K
Martin 50K Cole 80K
Martin 90K

a. What will Cole's decision be and why?
b. What will Martin's decision be and why?

https://brainmass.com/economics/principles-of-mathematical-economics/nash-equlibrium-payoffs-322934

## SOLUTION This solution is FREE courtesy of BrainMass!

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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