I was solving for a stable equilibrium in a game. I calculated expected payoff of one of the players which came out to be the function $$E= -4pq + 0.1p + 0.2q + 0.7$$ where p is probability of an action by one player and q is the probability of the action by opponent. Now, opponent is trying to minimize this payoff. How to go about it ? I am stuck in the maths part of the problem now.
2026-05-04 19:20:02.1777922402
Verifying minimum of a function when second derivative is 0
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HINT: Keeping $p$ constant, the given equation $E=-4pq+0.1 p+0.2 q+0.7$ represents a straight line (of form $\color{blue}{y=mx+c}$) which does not have any local minimum or maximum.
But the straight line has global minimum at $(-\infty, -\infty)$