Suppose Noble is facing an investment opportunity to pay a fixed cost $80$ M within $1$ year to

acquire the gas field project $($with time$-0$ present value of cash inflows V$0=100$ M$)$ by t $=1.$ The

asset $($project$)$ value, V$,$ currently at $100$ M$,$ is expected $($with equal actual probability, q $=0\mathrm{.}5)$ at the

end of the year to either rise to V$+=200$ M $($double$)$ or fall to V$-=50$ M $($half$).$ This asset movement

is characterized with a standard deviation of project returns of $\backslash$sigma V $=69\mathrm{.}3\%.$ The annual risk$-$free

interest rate $($r$)$ over the period is $5\%.$ Suppose there is value erosion $($damage$)$ from random gas

discoveries analogous to a $4\%$ dividend$-$like payout $(\backslash$delta V $=0\mathrm{.}04)$ and Noble $($henceforth referred to

as firm A$)$ faces endogenous competition from a rival oil and gas firm $($firm B$).$

Suppose if Noble $($henceforth firm A$)$ makes a proprietary exploration & production

investment allowing it to capture $2/3$ of total industry production and value $($total market pie$)$ its main

competitor $($firm B$)$ will react in a reciprocating way that will cause a reduction in the value of the

total market pie by $$ due to a resulting price war. The $2$ x $2$ matrix representing the payoff values

for each player $($firm A$,$ firm B$)$ in the case of an up $(+)$ or down $(-)$ overall demand$($i$)$ The missing values A$?$ and B$?$ in the top $2$ x $2$ game $($up demand at t$=1)$;

$($ii$)$ Find any dominant strategies and the Nash equilibrium $($and put $*)$ in the top $2$ x $2$ game $($up

demand$)$; then do the same in the bottom game $($down demand$)$;

$($iii$)$ The current $($time$-0)$ value of the shared call option to invest for firm A $($CAS$).$ Do the same

for firm B $($CBS$)$;

$($iv$)$ If firm A must invest $-30$ M at t$=0($to get a shared option to invest at t$=1),$ what is the expanded

or strategic NPV$?$ Should the firm invest in this case? What is the lesson from this?

$($v$)$ How does the current shared option value for firm A $($CAS$)$ compare to the current value of a

proprietary option to invest if firm A faced no endogenous competition $($C$0$P$)$ but only faced a

$4\%$dividend$$ yield due to random gas discoveries by others? What would the expanded or

strategic NPV be $($assuming there was no endogenous competition$)?$ Should the firm invest

in this case?