After spending billions in research and development, in 2006, Toshiba launched its HD-DVD player six times the resolution of DVDs it was designed to replace. Within months, SONY launched its Blu-ray player, offering similar features but in an incompatible format. The war was on. SONY and Toshiba engaged in fierce price competition, in some cases reducing prices for player below production costs. They also raced to sign exclusive contracts with major movie studios (Disney signing to Blu-ray and paramount to HD-DVD). Below is a game they play on whether to invest heavily or slacken, the payoff are given in each case

Toshiba

SONY Invest heavily slacken

Invest heavily 0,0 3,1

Slacken 1,3 2,2

Find the pure strategy Nash equilibrium.

Compute the mixed strategy Nash equilibrium and draw the best response functions.

Suppose the game is a sequential game with Sony moving first. What are Toshibas contingent strategies? Find the Nash equilibrium.