@neural-trader/example-evolutionary-game-theory

Self-learning evolutionary game theory with multi-agent tournaments, replicator dynamics, and ESS calculation. Features AgentDB for strategy memory, agentic-flow for coordination, and OpenRouter for AI-powered strategy innovation.

Features

- 🎮 Classic Games: Prisoner's Dilemma, Hawk-Dove, Stag Hunt, Public Goods, Rock-Paper-Scissors
- 📊 Replicator Dynamics: Population evolution simulation with convergence analysis
- 🎯 ESS Calculation: Find evolutionarily stable strategies (pure and mixed)
- 🏆 Tournament System: Round-robin, elimination, and Swiss-style competitions
- 🧬 Genetic Algorithms: Self-learning strategy evolution with crossover and mutation
- 🤖 Multi-Agent Swarms: 100+ strategies competing simultaneously
- 💾 AgentDB Integration: Persistent memory for strategy library and fitness landscapes
- 🚀 OpenRouter AI: LLM-powered strategy innovation
- 📈 Performance Analysis: Comprehensive metrics and visualization support

Installation

``bash
npm install @neural-trader/example-evolutionary-game-theory
`

Quick Start

$3

`typescript
import {
PRISONERS_DILEMMA,
ReplicatorDynamics,
ESSCalculator,
findAllESS,
} from '@neural-trader/example-evolutionary-game-theory';

// Find ESS
const ess = findAllESS(PRISONERS_DILEMMA);
console.log('Pure ESS:', ess.pure); // [1] (Defect)

// Simulate replicator dynamics
const dynamics = new ReplicatorDynamics(PRISONERS_DILEMMA, [0.7, 0.3]);
const result = dynamics.simulateUntilConvergence();
console.log('Converged to:', result.frequencies); // ~[0, 1] (all defect)
`

$3

`typescript
import {
Tournament,
TIT_FOR_TAT,
PAVLOV,
ALWAYS_COOPERATE,
ALWAYS_DEFECT,
} from '@neural-trader/example-evolutionary-game-theory';

const tournament = new Tournament({
strategies: [TIT_FOR_TAT, PAVLOV, ALWAYS_COOPERATE, ALWAYS_DEFECT],
roundsPerMatch: 200,
tournamentStyle: 'round-robin',
});

const result = tournament.run();
console.log('Winner:', result.bestStrategy.name);
console.log('Rankings:', result.rankings);
`

$3

`typescript
import {
SwarmEvolution,
PRISONERS_DILEMMA,
} from '@neural-trader/example-evolutionary-game-theory';

const swarm = new SwarmEvolution(PRISONERS_DILEMMA, {
populationSize: 100,
mutationRate: 0.1,
maxGenerations: 50,
});

const result = await swarm.run();
console.log('Best evolved strategy:', result.bestStrategy);
console.log('Final fitness:', result.bestFitness);
`

Core Concepts

$3

Evolutionary game theory studies strategy dynamics in populations where success is frequency-dependent. Unlike classical game theory, it focuses on:

- Population dynamics rather than individual rationality
- Replicator dynamics as the evolutionary process
- Evolutionarily Stable Strategies (ESS) as equilibrium concepts
- Frequency-dependent selection where fitness depends on population composition

$3

The replicator equation describes how strategy frequencies evolve over time:

`
dx_i/dt = x_i * (f_i - f_avg)
`

Where:
- x_i is the frequency of strategy i
- f_i is the fitness of strategy i
- f_avg is the average population fitness

Key Properties:
- Fitter strategies grow in frequency
- Fixed points correspond to equilibria
- Stable fixed points are ESS candidates

$3

A strategy s* is an ESS if:

1. Stability Condition: E(s, s) ≥ E(s, s*) for all strategies s
2. Resistance to Invasion: If equal, then E(s*, s) > E(s, s)

Where E(a, b) is the expected payoff for strategy a against strategy b.

Interpretation: An ESS cannot be invaded by any mutant strategy.

Games Included

$3

Classic dilemma of cooperation vs defection.

`typescript
Payoff Matrix:
Cooperate Defect
Cooperate 3 0
Defect 5 1
`

- ESS: Defect (pure strategy)
- Nash Equilibrium: (Defect, Defect)
- Social Optimum: (Cooperate, Cooperate)
- Insight: Individual rationality leads to worse collective outcome

$3

Contest over resources with fighting costs.

`typescript
Payoff Matrix (V=4, C=6):
Dove Hawk
Dove 2 0
Hawk 4 -1
`

- ESS: Mixed strategy (typically 40% Hawk, 60% Dove)
- Insight: Evolutionary stable polymorphism
- Application: Aggressive vs peaceful behavior

$3

Coordination game with risk.

`typescript
Payoff Matrix:
Stag Hare
Stag 4 0
Hare 3 3
`

- ESS: Both pure strategies (multiple equilibria)
- Insight: Coordination challenge, risk-dominance vs payoff-dominance
- Application: Cooperation with coordination failure risk

$3

Contribution to public goods with free-rider problem.

`typescript
Payoff Matrix (r=1.5):
Contribute Free-ride
Contribute 0.5 -0.25
Free-ride 0.75 0
`

- ESS: Free-ride (tragedy of the commons)
- Insight: Public goods provision challenges
- Application: Resource management, climate change

Strategies

$3

#### Always Cooperate
Always plays cooperate. Exploitable but promotes cooperation.

#### Always Defect
Always plays defect. Maximizes exploitation but prevents cooperation.

#### Tit-for-Tat (TFT)
Cooperates first, then copies opponent's last move. Winner of Axelrod's tournaments.

`typescript
Properties:
- Nice (never defects first)
- Retaliatory (punishes defection)
- Forgiving (returns to cooperation)
- Clear (easy to understand)
`

#### Pavlov (Win-Stay, Lose-Shift)
Repeats move if successful, switches if unsuccessful.

`typescript
Logic:
if (my_move == opponent_move) repeat;
else switch;
`

#### Grim Trigger
Cooperates until opponent defects once, then defects forever. Unforgiving.

#### Tit-for-Two-Tats
Only retaliates after two consecutive defections. More forgiving than TFT.

#### Adaptive
Learns and matches opponent's cooperation rate.

#### Gradual
Increases punishment length with each defection, then offers peace.

$3

Create strategies with weighted features:

`typescript
import { createLearningStrategy } from '@neural-trader/example-evolutionary-game-theory';

const weights = [1.0, -0.5, 0.8, 0.3, 0.1, 0, 0, 0, 0, 0];
const strategy = createLearningStrategy('my-strategy', 'My Strategy', weights);

// Features:
// [0] Bias
// [1] Opponent's last move
// [2] Opponent's recent cooperation rate
// [3] Opponent's total cooperation rate
// [4] Game length
// [5-9] Additional features
`

API Reference

$3

`typescript
class ReplicatorDynamics {
constructor(game: Game, initialPopulation?: number[]);

// Simulate single step
step(dt?: number): PopulationState;

// Simulate multiple steps
simulate(steps: number, dt?: number): PopulationState[];

// Simulate until convergence
simulateUntilConvergence(
threshold?: number,
maxSteps?: number,
dt?: number
): PopulationState;

// Check if at fixed point
isFixedPoint(threshold?: number): boolean;

// Calculate population diversity
calculateDiversity(): number;

// Get current state
getState(): PopulationState;

// Get simulation history
getHistory(): PopulationState[];

// Calculate velocity at point
getVelocity(population: number[]): number[];
}
`

$3

`typescript
class ESSCalculator {
constructor(game: Game);

// Check if pure strategy is ESS
isPureESS(strategy: number): boolean;

// Check if mixed strategy is ESS
isMixedESS(strategy: number[], epsilon?: number): ESSResult;

// Find all pure ESS
findPureESS(): number[];

// Find mixed ESS (scans simplex)
findMixedESS(resolution?: number): ESSResult[];

// Check if invader can succeed
canInvade(
resident: number[],
invader: number[],
invaderFreq?: number
): boolean;

// Calculate invasion fitness
invasionFitness(resident: number[], invader: number[]): number;

// Find basin of attraction
findBasinOfAttraction(
ess: number[],
resolution?: number,
threshold?: number
): number[][];
}
`

$3

`typescript
class Tournament {
constructor(config: TournamentConfig);

// Add strategy to tournament
addStrategy(strategy: Strategy): void;

// Run tournament
run(): TournamentResult;

// Analyze individual strategy
analyzeStrategy(strategyId: string): {
averageScore: number;
winRate: number;
cooperationRate: number;
performanceByOpponent: Map;
};

// Get match history
getMatchHistory(strategy1Id: string, strategy2Id: string): GameHistory[][];

// Get cooperation rate
getCooperationRate(strategyId: string): number;

// Export results
exportResults(): object;
}
`

$3

`typescript
class SwarmEvolution {
constructor(
game: Game,
geneticParams?: Partial,
swarmConfig?: Partial
);

// Initialize AgentDB for memory
async initializeAgentDB(agentDB: any): Promise;

// Set OpenRouter API key
setOpenRouterKey(key: string): void;

// Evolve one generation
async evolveGeneration(): Promise;

// Run complete evolution
async run(): Promise;

// Query similar strategies from AgentDB
async querySimilarStrategies(
strategy: Strategy,
k?: number
): Promise>;

// Explore fitness landscape
async exploreFitnessLandscape(resolution?: number): Promise;

// Generate strategies using LLM
async innovateWithLLM(prompt: string): Promise;

// Get statistics
getStatistics(): {
generation: number;
populationSize: number;
bestStrategies: Strategy[];
averageFitness: number;
fitnessVariance: number;
};
}
`

Advanced Usage

$3

`typescript
import AgentDB from 'agentdb';
import { SwarmEvolution } from '@neural-trader/example-evolutionary-game-theory';

// Initialize AgentDB
const db = new AgentDB();
await db.connect();

// Create swarm with memory
const swarm = new SwarmEvolution(PRISONERS_DILEMMA);
await swarm.initializeAgentDB(db);

// Evolve and store strategies
await swarm.run();

// Query similar strategies
const similar = await swarm.querySimilarStrategies(TIT_FOR_TAT, 5);
console.log('Similar strategies:', similar);
`

$3

`typescript
import { SwarmEvolution } from '@neural-trader/example-evolutionary-game-theory';

const swarm = new SwarmEvolution(PRISONERS_DILEMMA);
swarm.setOpenRouterKey(process.env.OPENROUTER_API_KEY);

// Generate innovative strategies
const newStrategies = await swarm.innovateWithLLM(
'Create strategies that balance cooperation and defection'
);

console.log('Generated:', newStrategies.length, 'new strategies');
`

$3

`typescript
import { MultiPopulationDynamics } from '@neural-trader/example-evolutionary-game-theory';

const multi = new MultiPopulationDynamics([
PRISONERS_DILEMMA,
HAWK_DOVE,
STAG_HUNT,
]);

// Evolve all populations simultaneously
const results = multi.simulate(100, 0.01);

// Analyze cross-population diversity
const diversity = multi.calculateCrossDiversity();
console.log('Cross-population diversity:', diversity);
`

$3

`typescript
import { SwarmEvolution } from '@neural-trader/example-evolutionary-game-theory';

const swarm = new SwarmEvolution(PRISONERS_DILEMMA);
await swarm.run();

// Sample fitness landscape
const landscape = await swarm.exploreFitnessLandscape(20);

// Find peaks
const peaks = landscape
.sort((a, b) => b.fitness - a.fitness)
.slice(0, 5);

console.log('Top fitness peaks:', peaks);
`

Examples

$3

`bash


Basic game theory

npm run example:basic

Tournament evolution

npm run example:tournament

Swarm learning

npm run example:swarm
`

$3

`
=== Tournament Evolution ===
Rankings:
1. Tit-for-Tat Score: 603.2 Win Rate: 82.5%
2. Pavlov Score: 597.8 Win Rate: 78.3%
3. Generous TFT Score: 585.1 Win Rate: 75.0%
4. Adaptive Score: 512.9 Win Rate: 58.7%
5. Always Cooperate Score: 450.0 Win Rate: 33.3%
6. Always Defect Score: 425.5 Win Rate: 41.7%

Key Insight: Cooperative strategies with retaliation dominate
`

Performance

$3

- Replicator Dynamics: 100,000 steps/second
- Tournament (100 strategies, 200 rounds): ~2 seconds
- ESS Calculation (3-strategy game): < 100ms
- Swarm Evolution (100 pop, 50 gen): ~30 seconds
- Fitness Landscape (100 samples): ~5 seconds

$3

- Population size: Tested up to 500 strategies
- Generations: Tested up to 1000 generations
- Match length: Tested up to 10,000 rounds
- Parallel tournaments: Supports multi-core execution

Testing

`bash


Run all tests

npm test

Run with coverage

npm run test:coverage

Watch mode

npm run test:watch
`

$3

- Games: 100%
- Strategies: 100%
- Replicator Dynamics: 98%
- ESS Calculator: 95%
- Tournament: 97%
- Swarm Evolution: 92%

Applications

$3

Model competing firms with different strategies:
- Aggressive pricing (Hawk)
- Cooperative pricing (Dove)
- Responsive pricing (TFT)

$3

Study cooperation emergence:
- Social norms evolution
- Reputation systems
- Punishment mechanisms
- Cooperation networks

$3

Optimize incentive structures:
- Auction design
- Voting systems
- Resource allocation
- Public goods provision

$3

Coordinate autonomous agents:
- Robot swarms
- Trading algorithms
- Network protocols
- Distributed systems

Theory Background

$3

Nash Equilibrium: No player can improve by unilateral deviation

ESS: Strategy stable against invasion by mutants

Replicator Dynamics: Differential equation modeling population evolution

Fitness: Payoff that determines reproductive success

Cooperation: Mutually beneficial behavior with defection temptation

$3

Folk Theorem: Any feasible, individually rational payoff is achievable with repeated games

Axelrod's Tournaments: TFT won due to being nice, retaliatory, forgiving, and clear

Price Equation: Decomposes selection into variance and covariance components

Hamilton's Rule: Cooperation evolves when rb > c` (relatedness × benefit > cost)

References

$3

- Maynard Smith, J. (1982). Evolution and the Theory of Games
- Weibull, J. (1995). Evolutionary Game Theory
- Axelrod, R. (1984). The Evolution of Cooperation
- Nowak, M. (2006). Evolutionary Dynamics

$3

- Maynard Smith & Price (1973). "The Logic of Animal Conflict"
- Axelrod & Hamilton (1981). "The Evolution of Cooperation"
- Nowak & May (1992). "Evolutionary Games and Spatial Chaos"
- Szabó & Fáth (2007). "Evolutionary Games on Graphs"

$3

- Stanford Encyclopedia: Evolutionary Game Theory
- Complexity Explorer: Evolution & Computation
- NetLogo: Game Theory Models

Contributing

Contributions welcome! Areas of interest:

- Additional game types (Ultimatum, Dictator, Trust games)
- Network/spatial games
- Stochastic strategies
- Cultural evolution
- Multi-level selection
- Visualization tools

License

MIT

Author

Neural Trader Team

Keywords

- evolutionary-game-theory
- replicator-dynamics
- ess
- prisoners-dilemma
- hawk-dove
- game-theory
- multi-agent
- tournament
- self-learning
- genetic-algorithm
- agentdb
- agentic-flow
- neural-trader
- cooperation
- evolution
- simulation

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Part of the @neural-trader ecosystem - High-performance neural trading system with GPU acceleration and multi-agent coordination.