Depth of Reasoning and Higher Order Beliefs

Abstract

As demonstrated by the email game of Rubinstein (1989)

Measuring Level-K Reasoning, Satisficing, and Human Error in Game-Play Data

“…Our results speak that were such behavior in force in high-level chess at standard time controls, then we would see a fuzzier, noisier correlation with significantly lower overall depth values-such as we do see for time-pressure moves. Thus we regard our large field data as supporting the reality of non-equilibrium behavior under the conviction of the estimation reached at a "plateau" of the thinking process, and further, Strzalecki's contention [9] that the level-k choices are largely "independent of the tail assumptions on the higher order beliefs. "…”

“…The latter areas include concepts of behaviors that deviate from rationality and theoretically optimal (equilibrium) strategies. Studies applying these approaches have involved staged competitions with human subjects dedicated to the study; we mention in particular the "Iowa gambling study" [1], [2], the "Colonel Blotto game" [3], the "11-20 money request game" [4], [5], the "beauty contest" game as implemented by [6], and others in [7], [8], [9]. Their concepts include k-level reasoning [10], [11], which involves estimating the depth of interaction with one's opponent(s), satisficing introduced by [12], which means "settling" for a known outcome without looking deeper for a better one, and other forms of human (or agent) fallibility based either on insufficient resources for managing complexity (bounded rationality) or on lapses of attention or effort.…”

Beliefs and endogenous cognitive levels: An experimental study

“…We show that subjects may behave differently depending on their 2 The idea that one's behavior depends on both his own cognitive level as well as his expectations on the cognitive levels of others is explored theoretically by Strzalecki (2010) who studies the Email Game and shows that coordination can be achieved in a finite number of steps.…”

“…Our results suggest that the latter type of level 0 represent a larger fraction of those players. 15 About 82.6% of the subjects in the Decreasing group choose numbers between 31 and 34 in the (7c, 0g) configuration, which indicates that these people are at least level 1. 16 The fact that this behavior is representative of close to half of the population may help explain why only little support has been found when experiments are designed to assess the stability of the level-k model across games, see Georganas, Heally and Weber (2011).…”

BDI Logics for BDI Architectures: Old Problems, New Perspectives

“…Their fundamental role in human intelligence was highlighted in experiments such as false belief tasks [11]. In Game Theory, higher-order beliefs are at the heart of the definition of notion of equilibrium as each agent has to assume that the other agents are rational [41,59,71].…”