example_5_3.jl

"""
Computing an equilibrium with SGM (Example 5.3, CLP, 2022)

Implementation of Example 5.3 from Carvalho, Lodi, and Pedroso (2022). For futher details,
    see:
    [*M. Carvalho, A. Lodi, J. P. Pedroso, "Computing equilibria for integer programming games". 2022. European Journal of Operational Research*](https://www.sciencedirect.com/science/article/pii/S0377221722002727)
    [*M. Carvalho, A. Lodi, J. P. Pedroso, "Computing Nash equilibria for integer programming games". 2020. arXiv:2012.07082*](https://arxiv.org/abs/2012.07082)

Notes
- SCIP can be replaced with other solvers, such as Gurobi or CPLEX.
"""

using IPG, SCIP

# ==== Player Definition ====
# Strategy spaces are defined through JuMP models
player1 = Player()
@variable(player1.X, x1, start=10.0)
@constraint(player1.X, x1 >= 0)

player2 = Player()
@variable(player2.X, x2, start=10.0)
@constraint(player2.X, x2 >= 0)

# Payoffs are defined using JuMP expressions
set_payoff!(player1, -x1^2 + x1*x2)
set_payoff!(player2, -x2^2 + x1*x2)

# ==== SGM Algorithm Subroutines ====
# The following are the default options for the SGM algorithm, so they can be omitted.
# See docstrings of each parameter for further details
IPG.initialize_strategies = IPG.initialize_strategies_feasibility
IPG.solve = IPG.solve_PNS
IPG.find_deviation = IPG.find_deviation_best_response

# It is also possible to pass custom subroutines. The following is a re-implementation of
# `IPG.get_player_order_random` for demonstration.
using Random
function get_player_random_order(players::Vector{Player}, iter::Integer, Σ_S::Vector{Profile{DiscreteMixedStrategy}}, payoff_improvements::Vector{Tuple{Player,Float64}})
    return shuffle(keys(players))
end
IPG.get_player_order = get_player_random_order

# ==== SGM ====
players = [player1, player2]
Σ, payoff_improvements = SGM(players, SCIP.Optimizer, max_iter=100, verbose=true);