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Fairness in the multi-proposer-multi-responder ultimatum game
Hana Krakovská1,2, Rudolf Hanel1,2, Mark Broom3
1Institute of the Science of Complex Systems, Center for Medical Data Science, Medical University of Vienna, Vienna, Austria.
This study extends the Ultimatum Game to multiple proposers and responders, analyzing competitive interactions. It identifies potential "fair" thresholds for responder shares in multi-player scenarios.
Area of Science:
- Behavioral Economics
- Game Theory
- Social Psychology
Background:
- The standard Ultimatum Game involves two players, but real-world interactions are often more complex.
- Existing models do not fully capture the dynamics of group decision-making in economic games.
Purpose of the Study:
- To introduce and analyze the Multi-Proposer-Multi-Responder Ultimatum Game.
- To derive subgame-perfect Nash equilibria for this extended game.
- To offer insights into observed proposal and rejection behaviors in economic games.
Main Methods:
- Formulation of the Multi-Proposer-Multi-Responder Ultimatum Game.
- Derivation of subgame-perfect Nash equilibria for various player configurations.
- Analysis of asymptotic player numbers to estimate fair thresholds.
Main Results:
- The study derives non-trivial Nash equilibria for the multi-player game.
- Competition among proposers and responders is introduced and analyzed.
- Two potential "fair" thresholds for responder shares are estimated: 31.8% and 36.8%.
Conclusions:
- The Multi-Proposer-Multi-Responder Ultimatum Game provides a more realistic model for economic interactions.
- The derived equilibria can help explain experimental observations in simpler Ultimatum Games.
- The findings suggest specific share percentages that could be considered fair in group settings.
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