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A simulation framework for measuring robustness of incentive mechanisms and its implementation in reputation systems

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Abstract

In game theoretical analysis of incentive mechanisms, all players are assumed to be rational. Since it is likely that mechanism participants in the real world may not be fully rational, such mechanisms may not work as effectively as in the idealized settings for which they were designed. Therefore, it is important to evaluate the robustness of incentive mechanisms against various types of agents with bounded rational behaviors. Such evaluations would provide us with the information needed to choose mechanisms with desired properties in real environments. In this article, we first propose a general robustness measure, inspired by research in evolutionary game theory, as the maximal percentage of invaders taking non-equilibrium strategies such that the agents sustain the desired equilibrium strategy. We then propose a simulation framework based on evolutionary dynamics to empirically evaluate the equilibrium robustness. The proposed simulation framework is validated by comparing the simulated results with the analytical predictions based on a modified simplex analysis approach. Finally, we implement the proposed simulation framework for evaluating the robustness of incentive mechanisms in reputation systems for electronic marketplaces. The results from the implementation show that the evaluated mechanisms have high robustness against a certain non-equilibrium strategy, but is vulnerable to another strategy, indicating the need for designing more robust incentive mechanisms for reputation management in e-marketplaces.

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Notes

  1. For ease of analysis, we assume a single equilibrium for a mechanism. Our analysis can be extended to handle multiple equilibria.

  2. When the game is symmetric and the positions of the \(n\) players are equivalent, a single population could represent all the players who interact with each other.

  3. We do not consider the case of \(\eta <1\) in Eq. (7) as in that case \(f_1<\frac{1}{N}\), which is a very small value for a large population size and hence equilibrium strategies are very likely to be robust against one or few invaders.

  4. There are two considerations for choosing an appropriate value for the parameter \(\epsilon \): (1) \(\epsilon \) should be no less than its measurable accuracy \(\frac{1}{T}\); (2) it is better to use a smaller value for \(\epsilon \).

  5. For a symmetric game played in a single population, it can be considered as two replicated populations.

  6. We assume that the strategy of bounded rational agents cannot evolve as they are not rational.

  7. The strategy of rational buyers can be various, and we assume that the rational buyers would not investigate the strategies not existing in the system.

  8. The main purpose of conducting the empirical evaluation is to verify whether the proposed simulation framework can output meaningful robustness evaluation results of different incentive mechanisms against different attacks. By considering those typical pure attacking strategies, we can (1) leverage the analytical results in the literature such as [14]; (2) perform qualitative analysis on the robustness of the incentive mechanisms. Then, we can easily check whether our simulation framework implemented in the empirical evaluation gives the same results.

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Authors and Affiliations

  1. School of Computer Engineering, Nanyang Technological University, Singapore, Singapore

    Yuan Liu, Jie Zhang & Bo An

  2. Department of Mathematical and Computer Sciences, The University of Tulsa, Tulsa, USA

    Sandip Sen

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  1. Yuan Liu
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  2. Jie Zhang
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Correspondence to Yuan Liu.

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Liu, Y., Zhang, J., An, B. et al. A simulation framework for measuring robustness of incentive mechanisms and its implementation in reputation systems. Auton Agent Multi-Agent Syst 30, 581–600 (2016). https://doi.org/10.1007/s10458-015-9296-2

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