Classic Games

The foundational games of game theory, modeled in Tenet.

Prisoner's Dilemma

The most famous game in game theory. Two prisoners must decide whether to cooperate or defect.

Key insight: Both players defecting is the only Nash equilibrium, even though mutual cooperation would be better.

game PrisonersDilemma {
    players Prisoner1, Prisoner2
    strategies Cooperate, Defect
    
    payoff Prisoner1 {
        (Cooperate, Cooperate): 3  // Both stay quiet
        (Cooperate, Defect): 0     // I'm quiet, they rat
        (Defect, Cooperate): 5     // I rat, they're quiet
        (Defect, Defect): 1        // Both rat
    }
    
    payoff Prisoner2 {
        (Cooperate, Cooperate): 3
        (Defect, Cooperate): 0
        (Cooperate, Defect): 5
        (Defect, Defect): 1
    }
}

Nash Equilibrium: (Defect, Defect) with payoffs (1, 1)

Battle of the Sexes

A coordination game with two equilibria. Success requires coordination.

game BattleOfSexes {
    players Alice, Bob
    strategies Opera, Football
    
    payoff Alice {
        (Opera, Opera): 3       // Alice's preference
        (Opera, Football): 0
        (Football, Opera): 0
        (Football, Football): 2
    }
    
    payoff Bob {
        (Opera, Opera): 2
        (Opera, Football): 0
        (Football, Opera): 0
        (Football, Football): 3 // Bob's preference
    }
}

Nash Equilibria:

  • (Opera, Opera) with payoffs (3, 2)
  • (Football, Football) with payoffs (2, 3)

Matching Pennies

A zero-sum game with no pure strategy equilibrium.

game MatchingPennies {
    players Matcher, Mismatcher
    strategies Heads, Tails
    
    payoff Matcher {
        (Heads, Heads): 1
        (Heads, Tails): -1
        (Tails, Heads): -1
        (Tails, Tails): 1
    }
    
    payoff Mismatcher {
        (Heads, Heads): -1
        (Heads, Tails): 1
        (Tails, Heads): 1
        (Tails, Tails): -1
    }
}

Nash Equilibrium (Mixed): Both players randomize 50-50

Stag Hunt

A game about trust and social cooperation.

game StagHunt {
    players Hunter1, Hunter2
    strategies Stag, Hare
    
    payoff Hunter1 {
        (Stag, Stag): 4     // Successful cooperative hunt
        (Stag, Hare): 0     // Partner abandons, stag escapes
        (Hare, Stag): 3     // Safe small catch
        (Hare, Hare): 3     // Safe small catch
    }
    
    payoff Hunter2 {
        (Stag, Stag): 4
        (Hare, Stag): 0
        (Stag, Hare): 3
        (Hare, Hare): 3
    }
}

Nash Equilibria:

  • (Stag, Stag) — Pareto optimal
  • (Hare, Hare) — Risk dominant

Chicken (Hawk-Dove)

A game about brinkmanship and aggression.

game Chicken {
    players Driver1, Driver2
    strategies Swerve, Straight
    
    payoff Driver1 {
        (Swerve, Swerve): 0       // Tie
        (Swerve, Straight): -1    // I'm the chicken
        (Straight, Swerve): 1     // I win
        (Straight, Straight): -10 // Crash!
    }
    
    payoff Driver2 {
        (Swerve, Swerve): 0
        (Straight, Swerve): -1
        (Swerve, Straight): 1
        (Straight, Straight): -10
    }
}

Nash Equilibria:

  • (Swerve, Straight) — Driver2 wins
  • (Straight, Swerve) — Driver1 wins

Next Steps