Samsung and Vizio must each decide which technology to utilize in building their

Question

Samsung and Vizio must each decide which technology to utilize in building their 2015 model ultra high definition television (HDTV) sets: either Alpha technology or Beta technology. Samsung has a technological advantage in using Alpha technology and Vizio has a technological advantage in using Beta technology. The payoff table below shows the profit outcomes for both firms in the various possible technology choice outcomes.

Vizio

Alpha

Beta

Samsung

Alpha

A

$7, $8

B

$10, $13

Beta

C

$9, $12

D

$13, $9

Payoffs in billions of dollars of profits.

Suppose the technology decision between Alpha and Beta will be made simultaneously. Answer the following questions:

a.   Samsung’s dominant strategy is _______________(Alpha, Beta, Neither: it has no dominant strategy).

b.   Vizio’s dominant strategy is _______________(Alpha, Beta, Neither: it has no dominant strategy).

c.   Explain why cell D is or is not strategically stable.

d.   As a simultaneous game, does this decision possess any Nash equilibrium cells? If so, which cell(s)? Explain why these cells are Nash.

Vizio

Alpha

Beta

Samsung

Alpha

A

$7, $8

B

$10, $13

Beta

C

$9, $12

D

$13, $9

Payoffs in billions of dollars of profits.

Explanation / Answer

Vizio

Samsung

Alpha

Beta

Alpha

($7, $8)

($10, $13)

Beta

($9, $12)

($13, $9)

A) The payoff matrix for this game is shown above. Samsung has a technological advantage in using Alpha technology and Vizio has a technological advantage in using Beta technology.

When Vizio invest in Alpha, Samsung earns a profit of $7 b by investing in Alpha and a profit of $9 b by investing in Beta. Thus it is profitable for Samsung to use Beta. Again, When Vizio invests in Beta, Samsung earns a profit of $13 b by investing in Alpha and a profit of $13 b by investing in Beta. Thus it has a dominant strategy in using Beta Technology.

B) When Samsung invest in Alpha, Vizio earns a profit of $8 b by investing in Alpha and a profit of $13 b by investing in Beta. Thus it is profitable for Vizio to use Beta. But When Samsung invests in Beta, Vizio earns a profit of $12 b by investing in Alpha and a profit of only $9 b by investing in Beta. Thus it has no dominant strategy.

C) Cell D has Samsung and Vizio both investing in Beta technology. This is straegically stable for Samsung but when Vizio has the information that Samsung will remain occupied with Beta, it has a better option to move or shift to Alpha since there it will earn a high payoff of $12 billion.

d) A firm’s best reply function maximizes its current payoff, given the strategy of the other firm. Using the best reply method, a player’s best reply is the strategy that pays him the maximum payoff, given the strategies chosen by the others.

There is one Nash equilibrium for this game: One when Samsung chooses Beta and Vizio chooses Alpha and Therefore the Nash equilibrium in this case is (Beta, Alpha)

Vizio

Samsung

Alpha

Beta

Alpha

($7, $8)

($10, $13)

Beta

($9, $12)

($13, $9)

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