$($a$)$ Use the following normal$-$form game to answer the questions below.

Firm B

Firm A

Suppose the game is infinitely repeated, both firms agree to charge a high price, provided no

player has charged low price in the past. Suppose now the interest rate is $6\%,$ and the payoffs

for both players are $$x$ in the one$-$shot Nash equilibrium. What is the maximum value of $$x,$

such that collusion can be sustained?

$($b$)$ Short Message Service $($SMS$)$ has been a traditional text messaging service used by many

cellular phone owners for years. Usually, when you send a text message to friends who are

using the same mobile phone operator as you $($Intra$-$SMS$),$ it is free of charge. However, when

you send a text message to friends who are using a different mobile phone operator from you,

you have to pay for each text message.

Recently years, many cellular phone users switched to use instant messaging services instead

of SMS$.$ WhatsApp is one of the instant messaging application providers. After downloaded

the software to their cellular phones, consumers can enjoy free of charge instant messages

service and can send free messages to friends who are from any mobile phone operators.

Name the strategy adopted by WhatsApp. Briefly explain the rationale of this strategy.