Beliefs and (In)Stability in Normal-Form Games

Abstract

In this paper, we use experimental data to study players' stability in normal-form games where subjects have to report beliefs and to choose actions. Subjects saw each of 12 games four times in a regular or isomorphic form spread over two days without feedback. We document a high degree of stability within the same (strategically equivalent) game, although time and changes in the presentation of the game do lead to less stability. To look at stability across different games, we adopt the level−k theory, and show that stability of both beliefs and actions is significantly lower. Finally, we estimate a structural model in which players either apply a consistent level of reasoning across strategically different games, or reasoning levels change from game to game. Our results show that approximately 30% of subjects apply a consistent level of reasoning across the 12 games, but that they assign a low level of sophistication to their opponent. The remaining 70% apply different levels of reasoning to different games.

A hierarchy of mindreading strategies in joint action participation

“…Consistent with a number of authors, we have also observed evidence that participants are able to move from one level in the decision-making hierarchy to another (Bhatt & Camerer, 2005;Hyndman et al, 2013;Rand et al, 2012;Yoshida et al, 2010). Rand and colleagues suggest that participants who are prompted to think more carefully about their decisions may switch from intuitive cooperation to a more deliberative individualism.…”

“…Alternatively, an experimental design in which participants chose whether or not to reveal particular cues prior to each trial (e.g., the game's payoffs, a partner's previous decisions, and/or the partner's signal) would achieve a similar result. Finally, more work is required to determine how consistent participants are in their use of strategies, and when they are flexible (Bhatt & Camerer, 2005;Hyndman et al, 2013;Yoshida et al, 2010).…”

The dual accumulator model of strategic deliberation and decision making.

“…Stochastic choice. Empirical research on both strategic and nonstrategic decision making has documented both heterogeneity across subjects and intrinsic variability in the responses of individual decision makers: Not only do different individuals make different choices, but a given individual may also respond differently to a given game on different occasions, even without intervening feedback (Fragiadakis, Knoepfle, & Niederle, 2016;Hyndman, Terracol, & Vaksmann, 2015; see also Loomes, 2015 for a review of the empirical evidence about individual stochastic choice in the domain of risk).…”

“…2015; Hyndman et al, 2015;Cooper, Fatas, Morales, & Qi, 2016;Fragiadakis et al, 2016). 8 Some existing models generate stochastic choice predictions.…”

Experiments on Cognition, Communication, Coordination, and Cooperation in Relationships

“…Even so, most subjects' decision rules can be identified from search alone, which sometimes directly reveals a subject's rule's algorithm or distinguishes her/his intended guesses from errors (CGC, Table 7A, pp. 1758-1759).Costa-Gomes & Weizsäcker (2008) (see alsoHyndman et al 2013) reported experiments that elicited subjects' initial responses, including stated beliefs about others' decisions as well as own decisions, in a series of 14 asymmetric two-person 3×3 games. Subjects were rewarded for the correctness of their stated beliefs via a quadratic scoring rule, which is incentive compatible when the decision-maker is risk-neutral.…”