> For the complete documentation index, see [llms.txt](https://docs.rwa.vip/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.rwa.vip/ii.-economic-theory-of-rwa-ecosystem/game-theory-in-the-rwa-ecosystem-protocol/prisoners-dilemma.md).

# Prisoner's Dilemma

<mark style="color:blue;">The</mark> <mark style="color:blue;"></mark><mark style="color:blue;">**Prisoner's Dilemma**</mark> is the first game theory students learn because it's simple and applicable to many strategic situations. Here's the story:

Two thieves plan to rob a store but are arrested for trespassing. The police suspect a robbery but lack evidence. They offer a deal: confess, and the suspects will face a lesser charge.

> You’re charged with trespassing, which means 1 month in prison. If you confess, I’ll drop the charge and release you. Your friend will face 12 months for attempted robbery. If you both confess, you’ll each serve 8 months.

The suspects are separated and told:

> *Both want to minimize their prison time. What should they do?*

Using a payoff matrix allows us to condense all information into an easy-to-analyze chart:

<figure><img src="/files/kWLNSuqB3eUvRC192Rou" alt=""><figcaption></figcaption></figure>

Player 1's available strategies are rows (Silent or Confess), with the corresponding payoffs as the first number in each cell. Player 2's available strategies are columns, with the corresponding payoffs as the second number in each cell.

* *Quiet: Silent*
* *Confess: Confess*
* *Blue numbers: Player 1's payoff*
* *Red numbers: Player 2's payoff*
* *-1: 1-month imprisonment*
* *-8: 8-month imprisonment*
* *-12: 12-month imprisonment*
* *0: Released without conviction*

### <mark style="color:blue;">Hypothesis & Conclusion</mark>

* *We assume both players aim to minimize their prison time.*
* *We assume there is only one interaction.*
* *We assume both players are selfish (i.e., they don't care about their friend's fate).*
* *We also assume players cannot interact and plan their responses in advance.*

These assumptions lead to a suboptimal outcome (confess, confess) with (-8, -8). If both remain silent, they would serve less time, but this is an unstable equilibrium. The only Nash equilibrium is (confess, confess), where no player wants to deviate from their strategy.

<mark style="color:blue;">**However, if they cooperated and stayed silent, they would achieve a better outcome. This highlights the dilemma:**</mark> cooperation benefits both, but individuals often act selfishly, prioritizing their own interests. This insight is key for both society and the RWA Ecosystem.


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