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Secure and efficient networks

Info

Drag nodes to move them. As Defender, click two nodes to add or remove a link while building.

Rules

The Defender builds a connected network. Each link creates 2 units of value and costs the amount shown above. Every node's value equals its number of links. Net value is network value minus connection costs, before any attack.

The Defender protects one node and the Attacker targets one node without seeing that protection. A protected target blocks the attack. Otherwise, the Attacker earns the target's value and the Defender loses twice that value (ρ = 2). Damage does not spread further through the network.

Each round is a new encounter on the same network. The Defender's payoff is network value minus connection costs and any damage. The computer chooses its move before you commit yours, using the encounter equilibrium. Hints are optional.

When you play as Attacker, the computer builds the best of the candidate network structures in the paper. Above 13 nodes, this is a candidate benchmark whose global optimality has not been verified.

Drag nodes to rearrange the graph. Click two nodes to add or remove a link while building. Keyboard selection works with Tab and Enter. Hover or focus on a node to see its value. Moving nodes changes only the layout. For larger networks, scroll the board.

Gameplay data Checking storage

Game settings, networks, protection choices, targets, outcomes and hints viewed are recorded to study how people design and protect networks. A random session identifier connects your rounds. No name or email is requested.

Oleh Stupak · Secure and efficient networks
Games and Economic Behavior · 2026

Choose your role
1

Choose 2–30 nodes. One node can be protected.

Change the cost to explore different network shapes.

Sandbox

Drag to move.

Hints

How to play

Choose your role, number of nodes and cost per link, then click Start. The computer plays the other side.

Play as Defender

Click pairs of nodes to build a connected network. Click Defend, choose one node to protect, then click Play. The computer secretly chooses its target.

Play as Attacker

The computer builds the network and secretly protects one node each round. Click your target, then click Attack. You can drag nodes to inspect the graph, but cannot change its links.

Scoring

A node’s value is its number of links. A protected target blocks the attack and earns the Attacker 0. Otherwise, the Attacker earns that value and the Defender loses twice that value. Damage goes no further.

Each link creates 2 units of value. Set its cost yourself or click Randomise cost to draw a new setting.
Defender payoff = network value − link costs − damage.

Hints stay above the graph. Changing a setting starts a fresh game; changing only cost keeps your Defender network.