Inspection Game
An inspection game is a two-player game in which an inspector chooses whether to monitor and an agent chooses whether to comply or cheat. Cheating pays only when unmonitored and monitoring is costly, so best responses cycle and there is no pure Nash equilibrium; the equilibrium is in mixed strategies.
Payoff matrix
| Row player (rows) / Column player (columns) | Work | Shirk |
|---|---|---|
| Trust | (4, 3) | (1, 4) |
| Monitor | (3, 2) | (2, 0) |
Payoffs are ordinal scores from the DecisionPlay engine's template for this game, 0 to 5, higher is better. They rank outcomes and are not dollar values. [MODELED]
Nash equilibria
- Mixed: Row player plays Trust 66.7%, Monitor 33.3%; Column player plays Work 50%, Shirk 50%. Expected payoffs (2.5, 2.67).
Computed by the DecisionPlay solver from the matrix above. [MODELED]
Where it shows up
Illustrative
- Tax auditing. A tax authority chooses whether to audit a return and a filer chooses whether to report honestly. Auditing everyone is costly, and cheating pays only if no audit follows.
- Fare checking on public transit. A transit agency chooses whether to check tickets and a rider chooses whether to pay. Checking has a cost, and not paying pays only when no check occurs.
Common misreadings
- The mixed equilibrium means people choose at random. It describes the frequencies at which each side's choices leave the other indifferent. Those frequencies can reflect how often a policy is applied or how a population divides, not a coin flip in each case.
- Preventing cheating requires monitoring every time. In the equilibrium, monitoring occurs only part of the time, at a rate that leaves cheating no more attractive than complying.
Try it
Map your own scenario or edit a payoff matrix in the solver.