What is Nash equilibrium?

A Nash equilibrium is a set of choices in which no single player can do better by switching their own choice while the others stay put. It matters because it predicts where a strategic situation tends to settle, even when the result is worse for everybody.

How it works

Each player decides based on what they expect the others to do. In equilibrium those expectations are correct and every choice is the best reply to the others. If one player moves away, they lose or gain nothing, so there is no reason to move.

An equilibrium need not be the best outcome. In the prisoner's dilemma, both players choosing to betray is an equilibrium, even though both would be better off cooperating. A situation can also have several equilibria or none in pure choices. To find one, check each option and ask whether any player would switch given the rest.

Example

Say two shops on the same street can each set a price of 10 or 8. If both charge 10, each earns 100. If one cuts to 8 while the other stays at 10, the cutter earns 150 and the other 40. If both charge 8, each earns 80. Whatever the other does, cutting to 8 pays more, so both cut and each earns 80. Neither can improve alone, so it is an equilibrium, even though 100 each was available. The payoffs are illustrative.

How to model it in Machinations

Create two Registers for the shops' prices, each set by a Lever with choices of 10 or 8, and a Source for each shop's customers whose rate depends on both prices through state connections. Use a Pool for each shop's profit. Play all four combinations and chart the profit Pools. Then change one price at a time to check whether either shop gains by moving away from a given pair.