A generalized cognitive hierarchy model of games

• Published in: Games and economic behavior Vol. 99; pp. 257 - 274
• Main Authors: Chong, Juin-Kuan, Ho, Teck-Hua, Camerer, Colin
• Format: Journal Article
• Language: English
• Published: Duluth Elsevier Inc 01.09.2016; Academic Press
• Subjects: Behavior; Behavioral game theory; Bias; Cognitive hierarchy; Economics; Equilibrium; Games; Generalized cognitive hierarchy; Level-k model; Level-m model; Non-equilibrium structural models; Studies; Generalized cognitive hierarchy; D03; Level-k model; Non-equilibrium structural models; Level-m model; Cognitive hierarchy; Behavioral game theory; C91; D83; C72
• ISSN: 0899-8256; 1090-2473
• DOI: 10.1016/j.geb.2016.08.007

Subjects in simple games frequently exhibit non-equilibrium behaviors. Cognitive hierarchy (CH) and level k (LK) are two prevailing structural models that capture such behaviors well. This paper proposes a generalized CH (GCH) model that nests a variant of the LK model, called LM. GCH differs from CH in two ways. First, each lower level's actual frequency is exponentially weighted with α to form level-k's belief on relative proportions; α captures stereotype bias. CH assumes no stereotype bias (α=1) and LM assumes extreme bias (α=∞). Second, GCH replaces random choice with minimum aversion for level 0. Level 0s are more likely to choose strategies that never yield the minimum payoff for any of the opponent's strategies. GCH captures behaviors better than CH and LK in fifty-five n×m games from four datasets. Robustness tests using three new games further validate GCHs descriptive strength over CH and LK. •The GCH model generalizes the structural model of strategic thinking with two behavioral regularities, minimum aversion and stereotype bias.•Non-strategic players are averse to strategies that yield a minimum payoff for some opponent's strategies.•Strategic players with stereotype bias wrongly perceive the more frequently occurring levels as the only lower thinking level players.•Strategic players in level k models exhibit extreme stereotype bias which concentrates on one level below themselves.