Game Class Documentation

The Game class represents a simulation of a hospital game involving patients and nurses.

Game description

A team of nurses is responsible for attending to incoming patients throughout a workday. The timing of patient arrivals follows an exponential distribution, and their stay is uniformly sampled from ${1,2}$.

Upon a patient's arrival, each nurse must decide to either accept ($A$) the patient for treatment or reject ($R$) them. The nurses' decision-making order is determined by their experience levels, with higher experience granting greater decision priority (e.g., $E_1 > E_2 > E_3$).

In situations where all nurses reject a patient, a policy of forced assignment is implemented. The patient is then assigned to the nurse with the fewest current patients, and she incurs a penalty proportional to her experience level. In cases of a tie, the patient is assigned to the nurse with the highest level of experience, and she receives the penalty.

Initialization

The class is initialized with the following parameters:

• n_patients: The number of patients arriving at the hospital.
• n_enf: The number of nurses.
• p_short_stay: The probability that a patient will have a short stay.
• arrival_rate: The rate at which patients arrive at the hospital.

Methods

The class has the following methods:

• __init__: Initializes the class with the given parameters.
• reset_patients: Generates the patients arriving at the hospital.
• run_exp: Executes the nurse game. It takes a function as a parameter which determines the actions of the nurses.
• fix_utilities: Calculates the utility of the nurses, which is a combination of the utility over time and the penalty for rejecting patients.
• summarize_utilities: Summarizes the utilities of the nurses at each period where a patient assignment decision was made.
• plot_pagos: Plots the payment function of the agents over time.
• plot_pacientes: Plots the schedule of patients over time.

Attributes

The class has the following attributes:

• n_patients: The number of patients.
• n_enf: The number of nurses.
• p_short_stay: The probability of a patient having a short stay.
• arrival_rate: The patient arrival rate.
• experience_weight: The experience weight of the nurses.
• patient_kind_stay: The type of stay for each patient (short or long). Created using the p_short_stay probabilities.
• patient_entry: The entry time for each patient.
• patient_stay: The stay length for each patient.
• patient_exit: The exit time for each patient.