The (2 n+1−2)-ray algorithm: A new simplicial algorithm to compute economic equilibria

A new variable dimension simplicial restart algorithm is introduced to compute economic equilibria. The number of rays along which the algorithm can leave the starting point differs from the thusfar known algorithms. More precisely, the new algorithm has one ray to each of the 2 ⁿ⁺¹−2 faces of then-dimensional price simplex, whereas the existing algorithms haven+1 rays either to each facet or to each vertex of the unit simplex. The path of points followed by the algorithm can be interpreted as a globally and universally convergent price adjustment process. The process is also economically meaningful and therefore it is a good alternative for the well-known Walras' tatonnement process. Computational results show that the algorithm is competitive with the most efficient simplicial algorithms developed thusfar. This work is part of theVF-program “Equilibrium and Disequilibrium in Demand and Supply”, which has been approved by the Netherlands Ministry of Education and Sciences.