Thread by @hansmriess

I'm excited to share our new paper w/ @mungowitz and @m_zavlanos introducing a decentralized mechanism for pricing and exchanging alternatives constrained by transaction costs: a thread 🧵 1/n

Our decentralized model is based on max-plus (linear) algebra, a branch of tropical 🌴 geometry. The recipe is simple: times <- plus, plus <- max. Max-plus algebra reinvents linear algebra with varying degrees of success, e.g. eigenvalues, linear systems, regression... 2/n

We use max-plus algebra to model the effective value of alternatives (e.g. goods, even opinions 🤔), taking transaction costs with neighbors in a trade network into account. This results in the data of a max-plus matrix-weighted graph. 3/n

(For the mathematician in the room, this data is REALLY a cellular sheaf over the trading network valued in the category of semimodules over the max-plus semiring. But if you don’t know what any of this means, it’s okay, it’s not even in the paper!) 4/n

The mathematical contribution of our paper is a characterization of the time-invariant solutions of a heat equation involving a weighted Tarski Laplacian. We also study the algebraic properties of the solution sets and the convergence behavior of the dynamical system. 5/n

Our contribution to the economics literature is theoretical evidence that differences in a) competitive equilibrium, b) bargaining, or c) cost-benefit analysis are due to differences in the way that transaction costs are incorporated into the decision-making process. 6/n

We also presented numerical simulations of the synchronization algorithm (we call it…RRAggU 🍝), demonstrating promising convergence behavior and providing support for the theoretical framework developed in the paper. 7/n

I'm grateful for the contributions of my co-authors @mungowitz and @m_zavlanos. We hope that our paper inspires further research in games, mechanism design, trade/auctions & applied sheaf theory. Check out our paper here: arxiv.org/pdf/2304.00210… #EconTwitter #MathTwitter 8/8