From Wikipedia on Prisoner's dilemma:

Two suspects are arrested by the police.

The police have insufficient evidence for a conviction, and, having separated the prisoners, visit each of them to offer the same deal.

If one testifies for the prosecution against the other (defects) and the other remains silent (cooperates), the defector goes free and the silent accomplice receives the full 10-year sentence.

If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge.

If each betrays the other, each receives a five-year sentence.

Each prisoner must choose to betray the other or to remain silent.

Each one is assured that the other would not know about the betrayal before the end of the investigation.

How should the prisoners act?

Read the details at wiki if you want. Here's the punch line:

No matter what the other player does, one player will always gain a greater payoff by playing defect. Since in any situation playing defect is more beneficial than cooperating, all rational players will play defect, all things being equal.

Now how does this apply to monogamy?

You have two people living an a less-than-perfect sexual relationship.

Both partners are physically capable of cheating, whether they've done it or not.

If one has sex outside the relationship (cheats) and the other remains faithful (true), the cheater gets free sex and the "faithful" one gets the extra dangers of an unfaithful partner (paternity fraud, pregnancy, STDs)

If both remain faithful, both partners are sentenced to only annoyances for the duration of the relatiosnhip

If each betrays the other, each suffers distrust, endangers theselves and others with STDs, and risks pregnancy.

Each prisoner must choose to betray the other or to remain faithful. Here, repeatedly. there are new temptations monthly if not daily.

Each one is assured that the other would not know about the betrayal before the end of the relatiosnhip.
Strictly speaking, true I assume. Once you know your partner is cheating, the relationship is over. there are zombie relationships and ones that are renewed after forgiveness of fidelity, but those are different relatiosnships from the pre-infidelity commitments.

How should the partners act?

But My title wasn't 'prisoner's dilemma and infidelity.' It was prisoner's dilemma and paternity fraud.

Here, the tools of a man are different from those of a woman (human sexuality101).

Basically, a man cannot commit paternity fraud on a woman.
She has the tools to identify the father, and if a man thinks he's a father, he's usually got a pretty good idea which woman it is that looks like she's about to have a baby.

Otoh, a soon-to-be-father doesn't look much different from the perpetual virgin, give or take a few stereoptical jabs at their appearances.

If a woman can cuckold him, she wins at least one extra roll in the hay + child support.

Is the woman who remains faithful the unreasonable woman?