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On the role of fairness and limited backward induction in sequential bargaining games

New behavioral models and analyses

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Abstract

Experiments show that in sequential bargaining games (\(\mathcal {SBG}\)), subjects usually deviate from game-theoretic predictions. Previous explanations have focused on considerations of fairness in the offers, and social utility functions have been formulated to model the data. However, a recent explanation by Ho and Su (Manag. Sci. 59(2), 452–469 2013) for observed deviations from game-theoretic predictions in sequential games such as the Centipede game is that players engage in limited backward induction. In this article, a suite of new and existing computational models that integrate different choice models with utility functions are comprehensively evaluated on \(\mathcal {SBG}\) data. These include DeBruyn and Bolton’s recursive quantal response with social utility functions, those based on Ho and Su’s dynamic level-k, and analogous extensions of the cognitive hierarchy with dynamic components. Our comprehensive analysis reveals that in extended \(\mathcal {SBG}\) with 5 rounds, models that capture violations of backward induction perform better than those that model fairness. However, we did not observe this result for \(\mathcal {SBG}\) with less rounds, and fairness of the offer remains a key consideration in these games. These findings contribute to the broader observation that non-social factors play a significant role in non-equilibrium play of sequential games.

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Correspondence to Prashant Doshi.

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Qu, X., Doshi, P. On the role of fairness and limited backward induction in sequential bargaining games. Ann Math Artif Intell 79, 205–227 (2017). https://doi.org/10.1007/s10472-015-9481-7

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