Variable-Frame Level-n Theory

نویسندگان

  • Michael Bacharach
  • Dale O. Stahl
چکیده

This paper develops a boundedly rational version of variable frame theory (VFT) of Bacharach [B93] by merging the variable frame conceptual apparatus with the leveln theory (LNT) of Stahl and Wilson [SW95]. A fundamental feature of VFT is that a player’s options are determined by her ‘frame’: one ‘option’ is associated to each cell of a frame-induced partition of the actions. Coupled with the principles of payoff dominance (PD) and symmetry disqualification (SD), VFT resolves game-theoretic indeterminacy in pure coordination games, and the solution it defines explains the long puzzling ‘Schelling competence’, people’s ability to solve coordination problems by collectively alighting on a salient coordination point. The resolving power of VFT depends heavily on the refinement principles, PD and SD, which are not well supported in experiments. Further, in a theory which aspires to explain and predict real play, full rationality may be unduly strong. Both these points motivate this paper, in which we seek to apply the basic ideas of VFT to the boundedly rational LNT. In our variable frame level-n theory, VFLNT, we retain the LNT notion that a level-0 player has no model of her coplayers, and that she randomizes uniformly over her options, but we define her options with respect to her frame. Then, an extended principle of insufficient reason uniquely defines level-0 behaviour. This model of their behaviour yields limited Schelling competence. A level-1 player, unlike level-0s, is a rational Bayesian decision maker, and has a model of her coplayer. From this she determines a Bayes-optimal choice. In particular, she believes her coplayer to be level-0 (as in LNT). In our VFLNT, we further assume that a level-1 player has a frame f , and believes that her level-0 coplayer has a frame that is a subset of f . Level-2 players are very much like level-1 players except that they think their coplayer is either level-0 or level-1. Like rational VFT, the VFLNT predicts the Schelling competence, but for quite different reasons. The VFLNT explanation combines a non-rational tendency at level0 with rational capitalization on it by higher-level players. Thus, the resolution of coordination indeterminancies offered by rational VFT is more a product of the variable frame apparatus than of the rationality assumptions. While for many games, rational VFT and VFLNT have qualitatively similar behavioural predictions, there are empirically testable differences. We propose a method of empirically testing this VFLNT.

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عنوان ژورنال:
  • Games and Economic Behavior

دوره 32  شماره 

صفحات  -

تاریخ انتشار 2000