Random Payoff Matrix Game Generator

Description

Generate bounded two-player integer payoff matrices and a random initial profile, delegate all pure Nash equilibria and fixed-count row-then-column best responses with lowest-index tie breaking, and annotate repeated profiles; no mixed-equilibrium solver or convergence guarantee.

An optimization instance defines choices, constraints, and an objective. A feasible witness demonstrates that its stated constraints can be met; it establishes optimality only when the tool actually computes and verifies an optimum.

When to use this tool

Use this generator to create reproducible payoff matrix game cases from the supplied model or bank. Inspect the returned evidence before using cases in a test or exercise.

How to use the tool and how it works

Supply rowStrategies, columnStrategies, minimumPayoff, maximumPayoff, iterations in the field shapes below. Set seed when you need an explicit replay.
Run the tool and correct any input error. For generated controls, distinguish a successful fixture containing an invalid case from failure to generate the fixture.
Read rowPayoffs, columnPayoffs, initial, equilibria, trace, summary. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.

Draw independent row and column payoff matrices and a starting action profile. Delegate pure Nash equilibria and best-response dynamics, annotate each trace profile's equilibrium membership, and record the first repeated profile step.^[1]

Delegated operations used for this result: pure nash equilibria; best response dynamics. Their calculation or parsing conventions apply to the corresponding result fields.^{[2, 3]}

Input field	Meaning and units	Accepted input
rowStrategies	Row Strategies	Required. Safe integer; minimum 1; maximum 16.
columnStrategies	Column Strategies	Required. Safe integer; minimum 1; maximum 16.
minimumPayoff	Minimum Payoff	Required. Safe integer.
maximumPayoff	Maximum Payoff	Required. Safe integer.
iterations	Iterations	Required. Safe integer; minimum 1; maximum 128.
seed	Optional numeric seed; takes precedence over context randomness. Without either, use the fixed tool.io default seed.	Optional. Safe integer.

Output field	Interpretation	Returned shape
rowPayoffs	Row Payoffs	Required. Array of Array of Safe integer.; minimum items 1; maximum items 16.; minimum items 1; maximum items 16.
columnPayoffs	Column Payoffs	Required. Array of Array of Safe integer.; minimum items 1; maximum items 16.; minimum items 1; maximum items 16.
initial	Initial	Required. Object; no unknown keys.
initial.rowAction	Row Action	Required. Safe integer; minimum 0; maximum 15.
initial.columnAction	Column Action	Required. Safe integer; minimum 0; maximum 15.
equilibria	Equilibria	Required. Array of Object; no unknown keys.; maximum items 256.
equilibria[].rowStrategy	Row Strategy	Required. Safe integer; minimum 0; maximum 15.
equilibria[].columnStrategy	Column Strategy	Required. Safe integer; minimum 0; maximum 15.
equilibria[].rowPayoff	Row Payoff	Required. Safe integer.
equilibria[].columnPayoff	Column Payoff	Required. Safe integer.
trace	Trace	Required. Array of Object; no unknown keys.; minimum items 1; maximum items 128.
trace[].rowAction	Row Action	Required. Safe integer; minimum 0; maximum 15.
trace[].columnAction	Column Action	Required. Safe integer; minimum 0; maximum 15.
trace[].step	Step	Required. Safe integer; minimum 1; maximum 128.
trace[].isPureEquilibrium	Is Pure Equilibrium	Required. Boolean.
summary	Summary	Required. Object; no unknown keys.
summary.equilibriumCount	Equilibrium Count	Required. Safe integer; minimum 0; maximum 256.
summary.firstRepeatedProfileStep	First Repeated Profile Step	Required. Safe integer; minimum 1; maximum 128. or Null.
randomness	Replay metadata: source is seed or context; seed is the normalized 32-bit seed or null for a context source.	Required. Object; no unknown keys.
randomness.seed	Optional numeric replay seed; normalization and precedence are explained below.	Required. Safe integer. or Null.
randomness.source	Source	Required. Text; one of "context", "seed".

An explicit safe-integer seed takes precedence over injected context randomness and is normalized to an unsigned 32-bit integer. With no seed and no context source, replay uses the fixed tool.io default seed. A context source must return finite values from zero inclusive to one exclusive; its advancing state must be retained separately. randomness records the source and normalized seed, or null for context. These generators are not cryptographic random sources.

json

{
  "input": {
    "rowStrategies": 2,
    "columnStrategies": 2,
    "minimumPayoff": 0,
    "maximumPayoff": 4,
    "iterations": 3,
    "seed": 42
  },
  "output": {
    "rowPayoffs": [
      [
        3,
        2
      ],
      [
        4,
        3
      ]
    ],
    "columnPayoffs": [
      [
        0,
        2
      ],
      [
        1,
        3
      ]
    ],
    "initial": {
      "rowAction": 1,
      "columnAction": 0
    },
    "equilibria": [
      {
        "columnPayoff": 3,
        "columnStrategy": 1,
        "rowPayoff": 3,
        "rowStrategy": 1
      }
    ],
    "trace": [
      {
        "columnAction": 1,
        "rowAction": 1,
        "step": 1,
        "isPureEquilibrium": true
      },
      {
        "columnAction": 1,
        "rowAction": 1,
        "step": 2,
        "isPureEquilibrium": true
      },
      {
        "columnAction": 1,
        "rowAction": 1,
        "step": 3,
        "isPureEquilibrium": true
      }
    ],
    "summary": {
      "equilibriumCount": 1,
      "firstRepeatedProfileStep": 2
    },
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

A game can have no pure equilibrium and dynamics can cycle. This does not solve mixed equilibria, guarantee convergence, or represent real actors; strategy indexes are zero-based.
A replay requires the same complete input and implementation. Randomized construction does not guarantee uniform coverage of every feasible output; finite samples can repeat unless a distinct-selection rule is explicitly stated.
The field tables state structural bounds; cross-field constraints and bounded search or output budgets also apply. Unknown keys are rejected where the object contract disallows them. Input errors are distinct from null fields and deliberate invalid controls in a successful output.

Alternative or Complementary methods

For a supplied example, inspect the returned construction or delegated check directly. To evaluate a consumer, also test cases chosen for its own boundaries; a generated finite corpus does not establish exhaustive coverage.

References

Tool behavior and example: Random Payoff Matrix Game Generator — tool.io
Calculation or validation: game-theory/pure-nash-equilibria — tool.io
Calculation or validation: game-theory/best-response-dynamics — tool.io

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