Implementation:Pyro ppl Pyro RSA Schelling

Property	Value
Implementation Type	Pattern Doc
Source File	examples/rsa/schelling.py
Module	examples.rsa
Pyro Features	pyro.sample, poutine.block, Search, HashingMarginal, recursive reasoning, Bernoulli distribution
Reference	Adapted from http://forestdb.org/models/schelling.html

Overview

This file implements the Schelling coordination game using Pyro's probabilistic programming primitives. Two agents (Alice and Bob) must independently choose between two locations to meet, without communicating. They coordinate by recursively reasoning about each other's choices.

The recursive reasoning structure:

• Bob at depth 0: Chooses based on prior preference alone
• Bob at depth > 0: Reasons about Alice's choice, who reasons about Bob at depth-1
• Alice: Always reasons about Bob at depth-1

Each agent has a shared prior preference (a weighted coin flip) for one location over the other. The recursive reasoning amplifies this preference: with a 60% prior preference and recursion depth 2, Bob's probability of choosing the preferred location increases significantly beyond 60%.

The key Pyro pattern demonstrated is using poutine.block() to prevent the inner model's sample sites from being visible to the outer model during nested inference.

Code Reference

def alice(preference, depth):
    alice_prior = location(preference)
    with poutine.block():
        bob_marginal = HashingMarginal(Search(bob).run(preference, depth - 1))
    return pyro.sample("bob_choice", bob_marginal, obs=alice_prior)

def bob(preference, depth):
    bob_prior = location(preference)
    if depth > 0:
        with poutine.block():
            alice_marginal = HashingMarginal(Search(alice).run(preference, depth))
        return pyro.sample("alice_choice", alice_marginal, obs=bob_prior)
    else:
        return bob_prior

def main(args):
    shared_preference = torch.tensor([args.preference])
    bob_decision = HashingMarginal(Search(bob).run(shared_preference, args.depth))

I/O Contract

Parameter	Type	Description
--preference	float	Shared prior preference for location 1 (default: 0.6)
--depth	int	Recursion depth for reasoning (default: 2)
-n / --num-samples	int	Monte Carlo samples for estimation (default: 10)

Output:

• Exact probability of Bob choosing the preferred location
• Empirical frequency estimate from sampling

Usage Examples

# Default: preference=0.6, depth=2
# python schelling.py

# Stronger preference with deeper reasoning
# python schelling.py --preference 0.7 --depth 4

# More samples for better empirical estimate
# python schelling.py -n 100

Related Pages

• Pyro_ppl_Pyro_SearchInference - Search inference utilities used by this model
• Pyro_ppl_Pyro_RSA_Generics - RSA model for generic statements
• Pyro_ppl_Pyro_RSA_Hyperbole - RSA model for hyperbole