Gurddy MCP Server

""" Minimax Problem Examples using Gurddy This module demonstrates various minimax optimization problems: 1. Zero-sum game theory (Rock-Paper-Scissors, Matching Pennies) 2. Portfolio optimization (minimize maximum loss) 3. Robust optimization (worst-case scenario planning) 4. Competitive facility location 5. Security games (attacker-defender scenarios) """ import sys import os sys.path.insert(0, os.path.join(os.path.dirname(__file__), '..', '..')) from gurddy.solver.minimax_solver import MinimaxSolver def print_section(title): """Print formatted section header""" print("\n" + "=" * 70) print(f" {title}") print("=" * 70) def example_rock_paper_scissors(): """ Classic Rock-Paper-Scissors game. Payoff matrix (row player perspective): - Rock beats Scissors (+1), loses to Paper (-1), ties with Rock (0) """ print_section("Example 1: Rock-Paper-Scissors Game") # Payoff matrix: rows = [Rock, Paper, Scissors], cols = [Rock, Paper, Scissors] payoff_matrix = [ [0, -1, 1], # Rock vs [Rock, Paper, Scissors] [1, 0, -1], # Paper vs [Rock, Paper, Scissors] [-1, 1, 0] # Scissors vs [Rock, Paper, Scissors] ] solver = MinimaxSolver(None) # Solve for row player (maximizer) result_row = solver.solve_game_matrix(payoff_matrix, player="row") print("\nRow Player (Maximizer) Strategy:") print(f" Rock: {result_row['strategy'][0]:.4f}") print(f" Paper: {result_row['strategy'][1]:.4f}") print(f" Scissors: {result_row['strategy'][2]:.4f}") print(f" Game Value: {result_row['value']:.4f}") # Solve for column player (minimizer) result_col = solver.solve_game_matrix(payoff_matrix, player="col") print("\nColumn Player (Minimizer) Strategy:") print(f" Rock: {result_col['strategy'][0]:.4f}") print(f" Paper: {result_col['strategy'][1]:.4f}") print(f" Scissors: {result_col['strategy'][2]:.4f}") print(f" Game Value: {result_col['value']:.4f}") print("\n✓ Optimal strategy: Play each move with equal probability (1/3)") print("✓ Game value is 0 (fair game)") def example_matching_pennies(): """ Matching Pennies: Two players simultaneously choose Heads or Tails. If they match, Player 1 wins. If they don't match, Player 2 wins. """ print_section("Example 2: Matching Pennies Game") # Payoff matrix: rows = [Heads, Tails], cols = [Heads, Tails] payoff_matrix = [ [1, -1], # Player 1 Heads vs [Heads, Tails] [-1, 1] # Player 1 Tails vs [Heads, Tails] ] solver = MinimaxSolver(None) result_row = solver.solve_game_matrix(payoff_matrix, player="row") print("\nPlayer 1 (Matcher) Strategy:") print(f" Heads: {result_row['strategy'][0]:.4f}") print(f" Tails: {result_row['strategy'][1]:.4f}") print(f" Expected Payoff: {result_row['value']:.4f}") result_col = solver.solve_game_matrix(payoff_matrix, player="col") print("\nPlayer 2 (Mismatcher) Strategy:") print(f" Heads: {result_col['strategy'][0]:.4f}") print(f" Tails: {result_col['strategy'][1]:.4f}") print(f" Expected Payoff: {result_col['value']:.4f}") print("\n✓ Both players should randomize 50-50") print("✓ Game value is 0 (fair game)") def example_portfolio_optimization(): """ Portfolio optimization: Minimize maximum loss across different market scenarios. Investor allocates budget across 3 assets. """ print_section("Example 3: Robust Portfolio Optimization") print("\nProblem: Allocate $100 across 3 assets to minimize worst-case loss") print("Assets: Stock A, Stock B, Bond C") print("\nScenarios (loss per dollar invested):") print(" Bull Market: A=-0.2, B=-0.1, C=0.05 (stocks gain, bonds lose)") print(" Bear Market: A=0.3, B=0.2, C=-0.02 (stocks lose, bonds gain)") print(" Stable: A=0.05, B=0.03, C=-0.01 (small movements)") # Scenarios: loss coefficients for each asset scenarios = [ {"A": -0.2, "B": -0.1, "C": 0.05}, # Bull market (negative = gain) {"A": 0.3, "B": 0.2, "C": -0.02}, # Bear market {"A": 0.05, "B": 0.03, "C": -0.01} # Stable market ] solver = MinimaxSolver(None) result = solver.solve_minimax_decision(scenarios, ["A", "B", "C"], budget=100) print("\nOptimal Allocation (minimize maximum loss):") print(f" Stock A: ${result['decision']['A']:.2f}") print(f" Stock B: ${result['decision']['B']:.2f}") print(f" Bond C: ${result['decision']['C']:.2f}") print(f" Total: ${sum(result['decision'].values()):.2f}") print(f"\nWorst-case loss: ${result['max_loss']:.2f}") # Calculate loss in each scenario print("\nLoss in each scenario:") for i, scenario in enumerate(scenarios): loss = sum(scenario[asset] * result['decision'][asset] for asset in ["A", "B", "C"]) scenario_names = ["Bull Market", "Bear Market", "Stable Market"] print(f" {scenario_names[i]}: ${loss:.2f}") print("\n✓ Minimax strategy balances risk across all scenarios") def example_production_planning(): """ Production planning: Maximize minimum profit across uncertain demand scenarios. """ print_section("Example 4: Robust Production Planning") print("\nProblem: Produce 2 products to maximize worst-case profit") print("Products: Widget X, Gadget Y") print("\nDemand Scenarios (profit per unit):") print(" High Demand: X=$50, Y=$40") print(" Medium Demand: X=$30, Y=$35") print(" Low Demand: X=$20, Y=$25") # Scenarios: profit coefficients (negative because we're maximizing) scenarios = [ {"X": -50, "Y": -40}, # High demand (negative for maximin) {"X": -30, "Y": -35}, # Medium demand {"X": -20, "Y": -25} # Low demand ] solver = MinimaxSolver(None) result = solver.solve_maximin_decision(scenarios, ["X", "Y"], budget=100) print("\nOptimal Production (maximize minimum profit):") print(f" Widget X: {result['decision']['X']:.2f} units") print(f" Gadget Y: {result['decision']['Y']:.2f} units") # Calculate actual profits (negate because scenarios use negative values) profits = [] for scenario in scenarios: profit = -sum(scenario[product] * result['decision'][product] for product in ["X", "Y"]) profits.append(profit) min_profit = min(profits) print(f"\nGuaranteed minimum profit: ${min_profit:.2f}") # Calculate profit in each scenario print("\nProfit in each scenario:") scenario_names = ["High Demand", "Medium Demand", "Low Demand"] for i, profit in enumerate(profits): print(f" {scenario_names[i]}: ${profit:.2f}") print("\n✓ Maximin strategy ensures minimum profit guarantee") def example_battle_of_sexes(): """ Battle of the Sexes: Coordination game with conflicting preferences. Couple wants to spend evening together but prefer different activities. """ print_section("Example 5: Battle of the Sexes Game") print("\nScenario: Couple choosing between Opera and Football") print("Both prefer being together over being apart") print("But have different preferences for activities") # Payoff matrix (Player 1's payoff): rows = [Opera, Football], cols = [Opera, Football] payoff_matrix = [ [2, 0], # Player 1 chooses Opera: (both Opera=2, split=0) [0, 1] # Player 1 chooses Football: (split=0, both Football=1) ] solver = MinimaxSolver(None) result_row = solver.solve_game_matrix(payoff_matrix, player="row") print("\nPlayer 1 (prefers Opera) Mixed Strategy:") print(f" Opera: {result_row['strategy'][0]:.4f}") print(f" Football: {result_row['strategy'][1]:.4f}") print(f" Expected Payoff: {result_row['value']:.4f}") result_col = solver.solve_game_matrix(payoff_matrix, player="col") print("\nPlayer 2 (prefers Football) Mixed Strategy:") print(f" Opera: {result_col['strategy'][0]:.4f}") print(f" Football: {result_col['strategy'][1]:.4f}") print(f" Expected Payoff: {result_col['value']:.4f}") print("\n✓ Mixed strategy equilibrium exists but pure coordination is better") print("✓ This game has multiple Nash equilibria") def example_security_game(): """ Security game: Defender allocates resources, attacker chooses target. """ print_section("Example 6: Security Resource Allocation") print("\nScenario: Protect 3 targets from attack") print("Defender has limited resources, attacker chooses one target") print("\nPayoff matrix (defender's loss if target attacked):") print(" Target 1 (High Value): Unprotected=-10, Protected=-2") print(" Target 2 (Medium Value): Unprotected=-6, Protected=-1") print(" Target 3 (Low Value): Unprotected=-3, Protected=-0.5") # Simplified: Defender chooses protection level, Attacker chooses target # Payoff = defender's loss (negative values) # Rows = defender strategies, Cols = attacker targets payoff_matrix = [ [-10, -6, -3], # No protection [-2, -6, -3], # Protect Target 1 [-10, -1, -3], # Protect Target 2 [-10, -6, -0.5], # Protect Target 3 [-2, -1, -3], # Protect Targets 1&2 [-2, -6, -0.5], # Protect Targets 1&3 [-10, -1, -0.5] # Protect Targets 2&3 ] solver = MinimaxSolver(None) result_row = solver.solve_game_matrix(payoff_matrix, player="row") print("\nDefender's Optimal Mixed Strategy:") strategies = ["None", "T1", "T2", "T3", "T1&T2", "T1&T3", "T2&T3"] for i, prob in enumerate(result_row['strategy']): if prob > 0.01: # Only show strategies with significant probability print(f" Protect {strategies[i]}: {prob:.4f}") print(f"\nExpected Loss: {result_row['value']:.2f}") result_col = solver.solve_game_matrix(payoff_matrix, player="col") print("\nAttacker's Optimal Mixed Strategy:") targets = ["Target 1 (High)", "Target 2 (Med)", "Target 3 (Low)"] for i, prob in enumerate(result_col['strategy']): if prob > 0.01: print(f" Attack {targets[i]}: {prob:.4f}") print(f"\nExpected Loss: {result_col['value']:.2f}") print("\n✓ Defender randomizes to make attacker indifferent") print("✓ Attacker targets based on protection probability") def example_advertising_competition(): """ Advertising competition: Two companies compete for market share. """ print_section("Example 7: Advertising Budget Competition") print("\nScenario: Two companies allocate advertising budget") print("Market share depends on relative spending") print("\nPayoff matrix (Company A's market share gain):") print(" Rows: Company A strategies [Low, Medium, High]") print(" Cols: Company B strategies [Low, Medium, High]") # Payoff matrix: Company A's market share change payoff_matrix = [ [0, -5, -10], # A: Low budget [5, 0, -3], # A: Medium budget [10, 3, 0] # A: High budget ] solver = MinimaxSolver(None) result_row = solver.solve_game_matrix(payoff_matrix, player="row") print("\nCompany A's Optimal Strategy:") budgets = ["Low Budget", "Medium Budget", "High Budget"] for i, prob in enumerate(result_row['strategy']): print(f" {budgets[i]}: {prob:.4f}") print(f" Expected Market Share Gain: {result_row['value']:.2f}%") result_col = solver.solve_game_matrix(payoff_matrix, player="col") print("\nCompany B's Optimal Strategy:") for i, prob in enumerate(result_col['strategy']): print(f" {budgets[i]}: {prob:.4f}") print(f" Expected Market Share Loss: {result_col['value']:.2f}%") print("\n✓ Companies balance budget allocation to maximize/minimize market share") def main(): """Run all minimax examples""" print("\n" + "=" * 70) print(" GURDDY MINIMAX SOLVER - COMPREHENSIVE EXAMPLES") print("=" * 70) print("\nMinimax optimization finds optimal strategies in adversarial") print("and uncertain environments by minimizing worst-case outcomes.") # Game theory examples example_rock_paper_scissors() example_matching_pennies() example_battle_of_sexes() # Decision theory examples example_portfolio_optimization() example_production_planning() # Applied examples example_security_game() example_advertising_competition() print("\n" + "=" * 70) print(" ALL MINIMAX EXAMPLES COMPLETED") print("=" * 70) print("\nKey Takeaways:") print(" • Minimax finds optimal strategies in competitive scenarios") print(" • Mixed strategies often outperform pure strategies") print(" • Robust optimization handles uncertainty effectively") print(" • Game theory provides insights for strategic decision-making") print("\n") if __name__ == "__main__": main()