Game theory

Nash equilibrium and stable strategies

A Nash equilibrium is a strategy profile where no participant can improve their outcome by changing only their own strategy, given what everyone else is doing.

Start a decisionSee the mechanism

Nicolas mechanism signals

These concepts follow the mathematical contract used by the app.

Convex cost

cost = c * sum a_ij^2

Voice budget

sum a_ij^2 <= B

Outcome rule

shifted softmax over support

What equilibrium means

Nash equilibrium is about stability rather than goodness. A situation can be stable even if the collective outcome is inefficient or undesirable.

That distinction matters for governance because groups can get stuck in patterns nobody likes enough to defend as ideal.

Why incentives matter

Changing a decision rule changes what behavior is cheap, costly, visible, or strategic.

Mechanism design pays attention to those incentives rather than treating votes as neutral measurements.

How Nicolas relates

Nicolas does not claim to compute equilibria or guarantee equilibrium behavior.

It uses an explicit quadratic cost rule and delegation model so participants can inspect the incentives created by the decision process.

Use cases

Where this decision model helps

Mechanism design context

Understand why decision rules create incentives as well as tallies.

Strategic behavior

Ask how participants might respond to costs, delegation, and visible outputs.

Governance education

Use game theory concepts to discuss the limits of any voting rule.

FAQ

What is a Nash equilibrium?

It is a strategy profile where no participant can improve by changing only their own strategy while others keep theirs fixed.

Does Nicolas compute Nash equilibria?

No. Nicolas does not estimate hidden utilities or compute game-theoretic equilibria.

Why include Nash equilibrium near Nicolas?

It helps explain why incentives and stable behavior matter when designing collective decision mechanisms.

Keep reading

Continue with adjacent concepts and practical Nicolas workflows.

Mechanism designLearn how rules and incentives shape collective decisions.Prisoner's dilemmaSee a classic game where stable individual incentives can harm the group.