def METHOD_NAME(game, tau, lam):
    """
    Compute the cognitive hierarchy prediction for 'game', with
    a Poisson distribution of types with mean 'tau', with precision of
    best responses 'lam'.
    """
    p = game.mixed_strategy_profile()
    if tau <= 0.0 or lam <= 0.0:
        return CognitiveHierarchyProfile(tau, lam, p)
    accum = float(scipy.stats.poisson(tau).pmf(0))
    for k in range(1, max(3, int(5*tau))):
        br = logit_br(game, p, lam=lam)
        prob = float(scipy.stats.poisson(tau).pmf(k))
        p = (1.0/(prob+accum)) * (prob*br + accum*p)
        accum += prob
    return CognitiveHierarchyProfile(tau, lam, p)