NormalFormGame Struct Reference
A two-player normal form game with QRE equilibrium selection. More...
#include "game_distributions.hpp"
Inheritance diagram for NormalFormGame:
Public Member Functions | |
| template<typename... Vs> | |
| NormalFormGame (std::variant< Vs... > u_row, std::variant< Vs... > u_col, std::variant< Vs... > lambda) | |
| NormalFormGame (std::vector< std::vector< double >> u_row_, std::vector< std::vector< double >> u_col_, double lambda_=1.0, double damping_=0.5, double tolerance_=1e-2, size_t max_iter_=50000) | |
| const std::vector< double > & | action_probs (size_t player) const |
| The solved QRE mixed strategy for the requested player. | |
| double | expected_payoff (size_t player) const |
| Ex ante expected QRE payoff for the requested player. | |
| double | logprob (nfg_profile_t value) const |
| size_t | n_actions (size_t player) const |
| Number of actions for player 0 (row) or 1 (column) | |
| template<typename RNG > | |
| nfg_profile_t | sample (RNG &rng) |
| void | solve () |
| Solve the QRE fixed point. Uses lambda-continuation: starts at lam = min(lambda, 1) where the softmax response map is close to a contraction, then doubles lam up to the target, warm-starting each rung. This traces the principal QRE branch toward the NE as lambda grows, and markedly improves convergence at high precision. | |
| std::string | string () const |
 Public Member Functions inherited from Distribution< NormalFormGame, nfg_profile_t > | |
| double | logprob (nfg_profile_t value) |
| nfg_profile_t | sample (RNG &rng) |
| std::string | string () const |
Public Attributes | |
| bool | converged |
| false if the fixed-point iteration hit max_iter | |
| double | damping |
| fixed-point iteration damping factor in (0, 1] | |
| double | lambda |
| QRE precision (1/temperature) | |
| size_t | max_iter |
| std::vector< double > | sigma_col |
| std::vector< double > | sigma_row |
| solved QRE mixed strategies | |
| double | tolerance |
| std::vector< std::vector< double > > | u_col |
| u_col[a][b]: column player's payoff from joint action (a, b) | |
| std::vector< std::vector< double > > | u_row |
| u_row[a][b]: row player's payoff from joint action (a, b) | |
Detailed Description
A two-player normal form game with QRE equilibrium selection.
Solves the logit-QRE fixed point on construction:
sigma_row(a) prop exp(lambda * E_{b ~ sigma_col}[ u_row(a, b) ]) sigma_col(b) prop exp(lambda * E_{a ~ sigma_row}[ u_col(a, b) ])
The node value is a joint pure action profile drawn from p(a, b) = sigma_row(a) * sigma_col(b), so:
logprob((a, b)) = log sigma_row(a) + log sigma_col(b)
Special cases of the selection rule:
- lambda = 0 : uniform over joint actions (maximum entropy)
- lambda -> infty : Nash equilibrium selection (the QRE branch traced from the uniform distribution converges to a selected NE – for generic games, the risk-dominant one)
Unlike exact-NE selection, the QRE map is a smooth function of the payoff matrices, so likelihood-weighting and Metropolis inference over upstream payoff nodes behaves well (no piecewise-constant likelihoods).
The documentation for this struct was generated from the following file:
