Question

Between 2006 and 2008, Sony and Toshiba were in a format war in the market for

high-definition optical discs. Sony had developed Blu-ray discs whereas Toshiba

had developed the HD-DVD format. Both producers were manufacturing players

for their own format. However, unless Sony and Toshiba agreed on producing

only one particular format, consumers were holding off their purchases. They

feared, should they buy a player, that they risked having invested in the wrong

format, leaving them unable to play content on high-definition optical discs. Both

producers could choose either format in the production of players. Sony could

produce HD-DVD players; in that case, they would have to pay $20 Billion royalties

per year to Toshiba if they sell any players. Toshiba could produce Blu-ray players;

in that case, they would have to pay $20 Billion royalties per year to Sony if they

sell any players. Assume that, if Sony and Toshiba agree on one format, they

would have a profit of $100 Billion in players each per year before eventual royalty

payments.

(a) What are the components of a strategic game? Model the interaction be-

tween Sony and Toshiba as a strategic game, in which Sony's and Toshiba's

strategies are given by the format of the high-definition disc players they

produce and their preferences are given by their profits after paying for or

receiving royalties.

Answer 1

Components of a strategic form game are:

1. Number of players in the game

2. Strategy set available to each player

3. Payoffs corresponding to all conceivable strategies of the players

To model the interaction between Sony and Toshiba, consider the strategy-payoff matrix below:

	Toshiba Blue-Ray	Toshiba HD-DVD
Sony Blue-Ray	(120,80)	(0,0)
Sony HD-DVD	(-20,-20)	(80,120)

Now consider each cell in the strategic interaction between Sony and Toshiba.

Cell 1: If Sony produces Blue-Ray discs and Toshiba also produces Blue-Ray discs, both will end up earning a profit of 100 billion dollars, with Toshiba's profits reduced by the $20 billion it pays in royalties, and Sony's profits increased by the same amount.

Cell 2: If Sony produces Blue-Ray discs and Toshiba produces HD-DVD discs, both of them end up earning no profit, as the consumers hold off their purchases.

Cell 3: If Sony produces HD-DVD discs and Toshiba produces Blue-Ray discs, both of them end up earning no profit, which are further lessened by the royalties they have to pay for adopting the opponent's technology.

Cell 4: This is similar to cell 1. Both the firms agree on producing HD-DVD discs, leading to profits of 80 and 120 billion dollars.

Thus, one can model strategic interactions among the firms as a game involving a payoff matrix of the type discussed above. The Nash equilibrium of the game can then be solved for by looking at mutual best responses.