Question

Consider the following information for a simultaneous move game: Two discount stores (megastore and superstore) are interested in expanding their market share through advertising. The table below depicts the strategic outcomes (profits) of both stores with and without advertising.
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Superstore





Advertise

Don’t Advertise

Megastore

Advertise

$95, $80

$305, $55

Don’t Advertise

$65, $285

$165, $115

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80. ​The Nash equilibrium for the game is



a.

​For both stores to advertise



b.

​For megastore to advertise and for superstore not to advertise



c.

​For megastore not to advertise and for superstore to advertise



d.

​For both stores to not advertise

Answer 1

Answer:

a. For both companies to advertise

Explanation:

Using the dominant strategy we will first get their optimal profits and see which one is more beneficial or will generate more revenue than the other, where a dominant strategy is when a player takes the best option there is and never change their decision irrespective of the other players decision.  A dominant strategy equilibrium is then seen when both players get their optimal decision irregardless of the other and both meet and maximize their profits.

we will start by mega stores dominant strategy we see that if superstore does take the option of advertising then Megastore will be getting $95 of profit from also advertising but $65 it they do not advertise. So by the dominant strategy Megastore will take the option of advertising as it has more profits that dominate of $95.

Now we will see if Superstore does not take the advertising option we see that megastore will get $305 if they advertise but if they also follow superstore and do not advertise they will make $165 worth pf profits and both these amounts we see that Advertising to megastore has more profits than not advertising therefore Advertising is more dominant to Megastore than not advertising.

Now we will asses Superstore which is more dominant between advertising and not advertising therefore we check if Megastore does not advertise then superstore will make $285 if they take the adverting option then if they do not advertise they will profit $115.Superstore will take the option to advertise which will give them higher profit of $285. Now we see if Megastore takes the option of advertising then if superstore takes it too then they will profit $80 and if superstore refuses to advertise then their profit will be $55, for both options we see that superstore will surely take advertising as the highest paying option which is $80.

Therefore their nash equilibrium will be $80 for Superstore and $95 for Megastore where both companies will choose to advertise to maximize their profits and by dominant strategy.

Answer 2

Answer: a) For both stores to advertise.

Explanation: Superstore should advertise its products because the strategy provides a better payoff than the option of not advertising. The same situation exists for Megastore. Thus, the scenario when both companies advertise their products is a Nash equilibrium.