$7\mathrm{.}3.$ ERICSSON VS$.$ NOKIA. Suppose that Ericsson and Nokia are the two primary com$-$ petitors in the market for $4$G handsets. Each firm must decide between two possible price levels: $$100$ and $$90.$ Production cost is $$40$ per handset. Firm demand is as fol$-$ lows: if both firms price at $$100,$ then Nokia sells $500$ and Ericsson $800$; if both firms price at $$90,$ then sales are $800$ and $900,$ respectively; if Nokia prices at $$100$ and Erics$-$ son at $$90,$ then Nokia's sales drop to $400,$ whereas Ericsson's increase to $1,100$; finally, if Nokia prices at $$90$ and Ericsson at $$100$ then Nokia sells $900$ and Ericsson $700.$

$($a$)$ Suppose firms choose prices simultaneously. Describe the game and solve it$.$