## Abstract

One-sided matching mechanisms are fundamental for assigning a set of indivisible objects to a set of self-interested agents when monetary transfers are not allowed. Two widely-studied randomized mechanisms in multiagent settings are the Random Serial Dictatorship (RSD) and the Probabilistic Serial Rule (PS). Both mechanisms require only that agents specify ordinal preferences and have a number of desirable economic and computational properties. However, the induced outcomes of the mechanisms are often incomparable and thus there are challenges when it comes to deciding which mechanism to adopt in practice. In this paper, we first consider the space of general ordinal preferences and provide empirical results on the (in)comparability of RSD and PS. We analyze their respective economic properties under general and lexicographic preferences. We then instantiate utility functions with the goal of gaining insights on the manipulability, efficiency, and envyfreeness of the mechanisms under different risk-attitude models. Our results hold under various preference distribution models, which further confirm the broad use of RSD in most practical applications.

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## Notes

This problem is sometimes called the assignment problem or house allocation problem in the literature.

Given utility functions for the agents, where \(u_i(j)\) is the utility agent

*i*derives from being assigned object*j*, the (utilitarian) social welfare of an assignment*A*is \(\sum _i \sum _j A_{i,j}u_i(j)\).A recent experimental study on the incentive properties of PS shows that human subjects are less likely to manipulate the mechanism when misreporting is a Nash equilibrium. However, subjects’ tendency for misreporting is still significant even when it does not improve their assignments [25].

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## Acknowledgements

We are grateful for the valuable feedback we received from the anonymous reviewers. This work was partially supported by NSERC.

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## Appendices

### Appendix

### Appendix A: Numerical results

Table 7 shows the results of comparing RSD and PS under ordinal preferences for various combinations of agents and objects. Note that in most instances, RSD and PS do not induce the same random assignment.

### Appendix B: Descriptive statistics

### Appendix B.1: Descriptive statistics

### Appendix B.2: Descriptive statistics of the mechanisms grouped by risk attitudes

See Table 10.

### Appendix B.3: Descriptive statistics of the mechanisms grouped by market type

See Table 11.

### Appendix B.4: Pairwise comparison with both factors, market type and risk attitudes

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Hosseini, H., Larson, K. & Cohen, R. Investigating the characteristics of one-sided matching mechanisms under various preferences and risk attitudes.
*Auton Agent Multi-Agent Syst* **32, **534–567 (2018). https://doi.org/10.1007/s10458-018-9387-y

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DOI: https://doi.org/10.1007/s10458-018-9387-y

### Keywords

- One-sided matching
- Random Serial Dictatorship
- Probabilistic Serial Rule
- Strategyproofness
- Social welfare
- Fairness
- Risky attitudes