Decision theory with resource-bounded agents.

Area of Science:

• Game Theory
• Decision Theory
• Cognitive Science

Background:

• Two main research lines address resource-bounded players in game theory: costly computation (Rubinstein) and limited computation via finite automata (Neyman).
• Recent work extends these approaches to decision theory.

Purpose of the Study:

• To review and apply two distinct approaches for modeling resource-bounded rationality in decision theory.
• To explain cognitive phenomena such as first-impression biases and belief polarization through rational decision-making under constraints.

Main Methods:

• The first approach models decision problems using Turing machines, with computational complexity (e.g., running time) as a cost.
• The second approach models agents as finite automata, analyzing algorithmic performance with increasing states.

Main Results:

• The Turing machine approach demonstrates how computational costs can rationalize phenomena like first-impression biases and belief polarization.
• The finite automata approach presents an algorithm that achieves provable optimality as the automaton's complexity (number of states) increases.

Conclusions:

• Resource-bounded rationality, modeled through computational costs or limitations, offers a framework for understanding seemingly irrational cognitive biases.
• Both costly computation and finite automata provide valuable insights into decision-making under constraints.