Trust has neighbors

Each square is a player, and each player meets the eight around it. In every round of a meeting, both choose to cooperate or cheat. Cooperating together earns each of them 2. Cheating someone who cooperates earns the cheat 3 and costs the other 1. Cheating each other earns nothing.

After every round of meetings, each player looks around and copies whichever strategy scored best nearby, its own included.

Things to try

Let it run. Within a few seconds trust wins: Mirrors and Forgivers spread, and Takers end up in small pockets.

Set the rounds to 1, then start over. When every meeting is a one-off, cheating pays and Takers sweep a fresh grid. Now set the rounds back to 3, let trust win, and only then drop the rounds to 1. The grid stays as it is. A cooperator surrounded by cooperators earns more than most Takers on its border can, so trust that already has neighbors protects itself.

Tap a square to drop in a Taker. Among Mirrors it gets absorbed in one generation. Among Givers it spreads, because Givers never cheat back.

Turn mistakes up to 5% and watch the blue fade. Two Mirrors can feud forever over a single misread move, each repeating the other’s cheat. Forgivers let one cheat go and take over. Once the Takers are gone, plain Givers do well too, which is when a dropped-in Taker does the most damage.

Where this comes from

Nicky Case’s The Evolution of Trust (2017) showed strategies with memory competing in a tournament, where everyone meets everyone. This page asks what changes when players only meet their neighbors. Robert Axelrod ran the original strategy tournaments (The Evolution of Cooperation, 1984), and Martin Nowak and Robert May showed that cooperation can survive on a grid by clustering (“Evolutionary games and spatial chaos”, Nature, 1992). The colors and the strategy names are this page’s own.