Preference Based Subjective Beliefs
- In Phase 1 (), subjects are randomly paired for 24 rounds and choose among four possible options involving a payoff pair—one for them, one for their matched partner—in a Random Dictator Game.
- In Phase 2 (), subjects are, again, randomly matched in pairs for 24 rounds and asked to choose among the same sets of payoff pairs. However, this time options correspond to contracts and yield a 2 × 2 effort game, which subjects then play at a second stage.
- subjects display—in both phases—some degree of heterogeneity in their decisions and, therefore, in their estimated preferences and beliefs;
- subjects’ preference parameters estimated in Phase 1 are significant determinants of Phase 2 first-order beliefs. Specifically, subject with higher guilt (envy) expect others to put less (more) effort, thus confirming our working conjecture.
2. Data and Methods
2.2. Choice Sets
- under the WING solution a player has a strict incentive to make effort only if the other does it as well;
- under the STING solution player 1’s payoff is sufficiently high to provide her with a strict incentive to make effort independently of what player 2 does, while player 2, as in the WING solution, has a strict incentive to make effort only if player 1 does it as well.
2.3.1. Dictator Game (24 Rounds)
- At the beginning of the round, a random assignment generates six pairs. Within each pair, another (independent and uniformly distributed) random device determines player position (i.e., the identity of the best paid player).
- Both players are informed about the round choice set, , and select their preferred option.
- Another independent draw fixes the identity of the Dictator. The Dictator’s choice, k, determines monetary payoffs for that pair and round: .
2.3.2. Effort Game (24 Rounds)
- The option selected by the (randomly selected) Dictator, k, yields a 2 × 2 effort game, (see Section 3 below).
- Subjects play and their strategy profile determines their financial rewards (1).
3.3. (Preference Dependent) Beliefs
- whenever , which is always the case for the contracts used in the experiment. ☐
4. Structural Estimations
Conflicts of Interest
Appendix A. Econometric Strategy
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See also Karni , for a similar view.
A similar conjecture is supported by the so-called social projection theory (take, e.g., Dawes , Krueger  and Kuhlman et al. ). See also the the analysis of the so-called false consensus bias proposed by Ross et al.  and Frey and Meier , by which actions—rather than preferences—influence beliefs.
The experiment was programmed and conducted with the software z-Tree (Fischbacher ). The interested reader can find in CABRA a more detailed account of the design of Phases 1 and 2, including the experimental instructions.
Participants gave their informed consent to participate in the experiment at the moment of signing up in the recruiting platform ORSEE (Greiner ).
A new set of instructions was distributed at the beginning of each phase. In this sense, subjects were not aware at all times about the rules of the phases that would come next.
A more detailed account of our estimation strategy can be found in the Appendix A.
No consistent version of social preferences can rationalize subjects with and , who can be then characterized as “noisy players”.
Frignani and Ponti  also apply the CABRA experimental design and analyze a situation in which make their option under the veil of ignorance, that is, before they are informed about the player position assignment.
|Myb||–0.071 ***||–0.001||–0.102 ***||–0.091 ***|
|Herb||0.022 ***||–0.014||0.034 ***||0.031 ***|
|Pl. 2 × STING||2.762 ***||0.550|
|2.444 ***||2.429 ***|
|–0.898 ***||–0.899 ***|
|–0.610 ***||–0.645 ***|
|cons.||0.482 ***||–0.029||1.016 ***||0.972 ***|
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Giaccherini, M.; Ponti, G. Preference Based Subjective Beliefs. Games 2018, 9, 50. https://doi.org/10.3390/g9030050
Giaccherini M, Ponti G. Preference Based Subjective Beliefs. Games. 2018; 9(3):50. https://doi.org/10.3390/g9030050Chicago/Turabian Style
Giaccherini, Matilde, and Giovanni Ponti. 2018. "Preference Based Subjective Beliefs" Games 9, no. 3: 50. https://doi.org/10.3390/g9030050