> ## Documentation Index
> Fetch the complete documentation index at: https://docs.fincept.in/llms.txt
> Use this file to discover all available pages before exploring further.

# Find Mixed Nash Equilibria

> Find all Nash equilibria (both pure and mixed strategy) using support enumeration algorithm. By Nash's theorem, every finite game has at least one Nash equilibrium (possibly in mixed strategies). Returns all equilibria with their strategy profiles. Computationally intensive for large games. Use when you need complete equilibrium characterization. [Tier: STANDARD, Credits: 2]



## OpenAPI

````yaml api-specs/economics.json post /quantlib/economics/games/mixed-nash
openapi: 3.1.0
info:
  title: FinceptQuantLib API - Economics
  description: >-
    Economics module endpoints for FinceptQuantLib API - general equilibrium,
    game theory, auctions, and utility functions
  version: 3.0.0
  contact:
    name: Fincept API Support
    url: https://fincept.in
servers:
  - url: https://api.fincept.in
    description: Fincept API Production Server
security:
  - APIKeyHeader: []
tags:
  - name: quantlib-economics
    description: >-
      Economics module - general equilibrium, game theory, auctions, and utility
      theory
    x-displayName: Economics
paths:
  /quantlib/economics/games/mixed-nash:
    post:
      tags:
        - quantlib-economics
      summary: Find Mixed Nash Equilibria
      description: >-
        Find all Nash equilibria (both pure and mixed strategy) using support
        enumeration algorithm. By Nash's theorem, every finite game has at least
        one Nash equilibrium (possibly in mixed strategies). Returns all
        equilibria with their strategy profiles. Computationally intensive for
        large games. Use when you need complete equilibrium characterization.
        [Tier: STANDARD, Credits: 2]
      operationId: mixed_nash_quantlib_economics_games_mixed_nash_post
      requestBody:
        content:
          application/json:
            schema:
              type: object
              required:
                - payoff_matrix_1
                - payoff_matrix_2
              properties:
                payoff_matrix_1:
                  type: array
                  description: Payoff matrix for Player 1
                  items:
                    type: array
                    items:
                      type: number
                  example:
                    - - 3
                      - 0
                    - - 0
                      - 3
                payoff_matrix_2:
                  type: array
                  description: Payoff matrix for Player 2
                  items:
                    type: array
                    items:
                      type: number
                  example:
                    - - 2
                      - 0
                    - - 0
                      - 2
            example:
              payoff_matrix_1:
                - - 3
                  - 0
                - - 0
                  - 3
              payoff_matrix_2:
                - - 2
                  - 0
                - - 0
                  - 2
        required: true
      responses:
        '200':
          description: Successful Response
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      nash_equilibria:
                        type: array
                        description: List of all Nash equilibria found
                        items:
                          type: object
                          properties:
                            strategy_1:
                              type: array
                              description: Player 1's equilibrium strategy
                              items:
                                type: number
                            strategy_2:
                              type: array
                              description: Player 2's equilibrium strategy
                              items:
                                type: number
                        example:
                          - strategy_1:
                              - 1
                              - 0
                            strategy_2:
                              - 1
                              - 0
                          - strategy_1:
                              - 0
                              - 1
                            strategy_2:
                              - 0
                              - 1
                          - strategy_1:
                              - 0.4
                              - 0.6
                            strategy_2:
                              - 0.6
                              - 0.4
                      count:
                        type: integer
                        description: Number of Nash equilibria found
                        example: 3
              example:
                success: true
                data:
                  nash_equilibria:
                    - strategy_1:
                        - 1
                        - 0
                      strategy_2:
                        - 1
                        - 0
                    - strategy_1:
                        - 0
                        - 1
                      strategy_2:
                        - 0
                        - 1
                    - strategy_1:
                        - 0.4
                        - 0.6
                      strategy_2:
                        - 0.6
                        - 0.4
                  count: 3
        '401':
          $ref: '#/components/responses/UnauthorizedError'
        '402':
          $ref: '#/components/responses/InsufficientTierError'
        '422':
          description: Validation Error
          content:
            application/json:
              schema:
                type: object
                properties:
                  detail:
                    type: array
                    items:
                      type: object
              example:
                detail:
                  - loc:
                      - body
                      - payoff_matrix_1
                    msg: field required
                    type: value_error.missing
      security:
        - APIKeyHeader: []
components:
  responses:
    UnauthorizedError:
      description: Authentication information is missing or invalid
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: string
                example: Invalid API key
    InsufficientTierError:
      description: API tier insufficient for this endpoint
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: string
                example: Endpoint requires Basic tier or higher
  securitySchemes:
    APIKeyHeader:
      type: apiKey
      in: header
      name: X-API-Key
      description: >-
        API key for authentication. Get your key at
        https://api.fincept.in/auth/register

````