Mechanism design seeks to align individual incentives with desired outcomes, but mechanisms are often sensitive to small perturbations in agent preferences or external conditions. This paper introduces a novel approach to robust mechanism design by employing tropical geometric methods to analyze the structure induced by mechanisms, focusing specifically on dominant strategy incentive compatibility (DSIC). By representing constraints related to DSIC mechanisms using tropical geometry and studying the associated geometric and topological structures (such as critical loci) in the joint type space, we develop design principles that ensure mechanisms reside in regions conferring robustness. This framework provides quantitative measures of robustness and deepens the understanding of the interplay between geometry and robustness in mechanism design.

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Bramoullé et al. [3] provided identification conditions for linear social interaction models through network structures. Despite the importance of their results, the authors omitted detailed mathematical discussions. Moreover, they consider cases where many identical networks are observed simultaneously within the same dataset. In reality, multiple networks with different structures, such as families or classrooms, are repeatedly observed within the same dataset. The purpose of this paper is to fill in the mathematical gaps in their arguments and establish identification conditions for networks with different structures. In addition, we reveal the minimum network size as a necessary condition for identifying social effects. We also discuss the identification conditions of a network model with a network fixed effect.

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In this paper, a framework is devised to explore the implications of parameter heterogeneity in standard macro models. Instead of considering that a given characteristic of a population can be averaged out to form a single parameter value, it is assumed that, regarding the selected feature, the population spreads over a distribution, with individual agents occupying potentially different positions on it. Allowing for such a perspective opens the door for introducing intuitive parameter dynamics. As the distribution moves left or right, signaling an overall change in preferences or choices, the model’s variables will be impacted. The shifting distribution may lead to endogenous fluctuations on the trajectories of variables, under the form of periodic or a-periodic cycles. Two illustrations are set forth, for the standard Solow growth model and for a consumer’s problem of intertemporal preference. In these two cases, the shifting distribution is attached, respectively, to the savings rate and to the rate of time preference.

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This paper provides an overview of the theory of differential inclusions, and presents several results including the existence of solutions, extendability, the comparison principle, stability, and the theory of viability. Moreover, we explore their applications in economics. One application concerns the stability of equilibrium prices, whereas another involves results that characterizes solutions to continuous-time macroeconomic dynamic models.

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