What is game theory?

Game theory is the mathematical study of strategic decisions, where the outcome for each decision maker depends on the choices of all. It matters because pricing, bidding, negotiation and competition all involve this kind of interdependence.

How it works

A situation is described by its players, the choices open to each and the payoffs that result from every combination of choices. Each player is assumed to pick the option that gives them the best payoff given what they expect from the others. The central question is what combination of choices is stable, which leads to ideas such as the Nash equilibrium.

Results depend on the structure. In one-time encounters, players may defect from cooperation, while in repeated encounters, the threat of future punishment can sustain cooperation. Whether moves are simultaneous or in sequence, and whether information is shared, also changes what is rational.

Example

Say two airlines each choose a low or high fare on one route. If both choose high, each earns 100. If one goes low and the other stays high, the low one earns 150 and the other 20. If both go low, each earns 60. Low is the better reply to either choice, so both go low and earn 60 each. If the two meet every month for years, matching a rival's cut for a few months can make high fares worth keeping. The payoffs are an illustration.

How to model it in Machinations

Create two Registers for each airline's fare, set by Levers, and a Pool for each airline's profit. Use state connections so that each airline's customer Source depends on both fares. To model repeated play, add a Register for the rival's last move that feeds the next decision. Play many times, change the payoffs, and chart the profit Pools to see which strategies hold up.