The powerless yet relevant third: a three-player ultimatum/dictator game with earned funds and roles

ABSTRACT

We report the first experiment to pair a three-player ultimatum/dictator game with a real effort task. The inclusion of the real effort task shifts the standard for division from simple egalitarianism towards relative performance; even in treatments in which roles and funds are exogenous. Additionally, we find proposers overcompensate themselves relative to their effort, and this additional compensation comes at the expense of powerless (third) players. Individual characteristics predict the nature of a proposals. Lastly, we find that responders’ choice to accept is based on their own and the powerless third party’s compensation.

KEYWORDS:

• Equity
• bargaining
• experiment
• three-player game

JEL CLASSIFICATION:

• D63
• J31
• C91

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ In the literature this game is referred to as a three-person ultimatum game. However, given that there is a completely separate literature on three-person ultimatum games in which there is one proposer and two responders, we will refer to this game as an ultimatum/dictator game to avoid confusion.

² The experiment was actually played for two 5-period rounds. The groups were randomly assigned on the first and sixth periods. Roles were also determined in periods 1 and 6 and constant thereafter.

³ Players are randomly assigned to groups of three before the real effort task, then – in the treatments where performance on the task is used to determine roles – the top performer is assigned the role of proposer, the second best performer the role of responder, and the third the role of receiver.

⁴ The first p-value is from a t-test with the null hypothesis relative pay is equal to relative effort and the appropriate alternative hypotheses and the second p-value is from a non-parametric sign test with the same structure.