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Why is mutual confession the Nash equilibrium in the prisoner’s dilemma?

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A colorful payoff matrix for a normal form game in game theory, showing strategy options-support, oppose, evade-for both party A and party B. Each cell contains cartoon figures representing each party's action and lists percentage payoffs for A and B. The bottom-right cell is labeled saddlepoint, highlighting the equilibrium. — game theory Table 1
The normal-form table illustrates the concept of a saddlepoint, or entry, in a payoff matrix at which the expected gain of each participant (row or column) has the highest guaranteed payoff.

In game theory, the prisoner’s dilemma results in mutual confession as the Nash equilibrium because it is the only outcome where neither player can improve their individual payoff by unilaterally changing their strategy.1

In this noncooperative game, each prisoner acts in their own self-interest to minimize their prison sentence. The logic follows these steps:21

If the opponent remains silent: A player receives a lighter sentence by confessing (going free) than by remaining silent (serving a short sentence).13
If the opponent confesses: A player still receives a lighter sentence by confessing (a serious sentence) than by remaining silent (a harsh sentence).13

Because confessing is the superior choice regardless of what the other player does, it is the dominant strategy for both individuals. Although mutual confession leads to a worse collective outcome than if both had remained silent, it remains the Nash equilibrium because any player who deviates from this strategy by choosing to remain silent would only face a longer prison term. Thus, no player has an incentive to switch strategies.31