[Paper Review] Decision Theory with Resource-Bounded Agents

Joseph Y. Halpern, Rafael Pass+1 more|arXiv (Cornell University)|Aug 17, 2013

Game Theory and Applications20 references4 citations

TL;DR

This paper proposes two frameworks for modeling resource-bounded agents in decision theory: one charging for computational complexity via Turing machines, and another modeling agents as finite automata with limited states. It shows that both approaches can rationalize well-known cognitive biases—like first-impression-matters effects and belief polarization—as optimal behavior under resource constraints, with automata-based strategies approaching optimal performance as state counts grow.

ABSTRACT

There have been two major lines of research aimed at capturing resource-bounded players in game theory. The first, initiated by Rubinstein, charges an agent for doing costly computation; the second, initiated by Neyman, does not charge for computation, but limits the computation that agents can do, typically by modeling agents as finite automata. We review recent work on applying both approaches in the context of decision theory. For the first approach, we take the objects of choice in a decision problem to be Turing machines, and charge players for the ``complexity'' of the Turing machine chosen (e.g., its running time). This approach can be used to explain well-known phenomena like first-impression-matters biases (i.e., people tend to put more weight on evidence they hear early on) and belief polarization (two people with different prior beliefs, hearing the same evidence, can end up with diametrically opposed conclusions) as the outcomes of quite rational decisions. For the second approach, we model people as finite automata, and provide a simple algorithm that, on a problem that captures a number of settings of interest, provably performs optimally as the number of states in the automaton increases.

Motivation & Objective

• To model decision-making agents with bounded computational resources, challenging the assumption of perfect rationality in classical decision theory.
• To explain systematic human behavioral biases—such as first-impression-matters and belief polarization—as rational responses under computational constraints.
• To develop simple, implementable strategies for bounded agents that approach optimal performance as resource limits increase.
• To compare two distinct approaches: complexity-based cost models for Turing machines and finite automaton models with state limits.
• To provide theoretical and experimental support for the effectiveness of finite automaton strategies in dynamic, uncertain environments.

Proposed method

• Models agents as choosing Turing machines, with utility dependent on both payoff and computational complexity (e.g., running time, state count).
• Introduces a cost model that charges for the complexity of the chosen algorithm, allowing rational trade-offs between payoff and computation.
• Models agents as finite automata with a fixed number of states, where transitions depend on incoming signals and internal state.
• Proposes a family of automata A[N, p_exp, Pos, Neg, r_u, r_d] parameterized by state count N, signal probabilities, and thresholds for positive/negative signals.
• Uses a dynamic decision problem where nature’s state changes stochastically, and agents must decide based on noisy signals over time.
• Proves that as N increases, the expected payoff of the automaton family approaches the theoretical optimum, even without an oracle.

Experimental results

Research questions

• RQ1 Can first-impression-matters biases be explained as rational behavior under computational cost?
• RQ2 Can belief polarization emerge rationally in agents with different priors but identical evidence, under resource constraints?
• RQ3 How well can a finite automaton with N states approximate optimal decision-making in a dynamic, uncertain environment?
• RQ4 What parameter settings in a finite automaton strategy yield near-optimal performance as N grows?
• RQ5 Can simple, low-complexity strategies perform well in real-world decision problems with limited computational resources?

Key findings

• The automaton family A[N, p_exp, Pos, Neg, r_u, r_d] achieves expected payoffs arbitrarily close to the theoretical optimum (x_G/2) as N increases, under mild conditions on π and P_exp.
• With π = 0.001, x_G = 1, and four signals, a 5-state automaton achieves an expected payoff over 0.4, significantly outperforming random or fixed strategies (which yield 0).
• Even a 2-state automaton achieves an expected payoff over 0.15 under the same conditions, demonstrating strong performance with minimal resources.
• The performance is robust: using the optimal p_exp for N=5 yields near-optimal results for N≥5, reducing the need for per-N optimization.
• Theoretical results show that for any decision setting, there exist parameters such that the automaton’s expected payoff converges to the optimal value as N→∞.
• Both complexity-charging and finite automaton models rationalize common cognitive biases as optimal responses to computational constraints, rather than irrationality.