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This paper develops a method to flexibly adapt interpolation grids of value function approximations in the estimation of dynamic models using either NFXP (Rust, Econometrica: Journal of the Econom etric Society, 55, 999– 1 033, 1987) or MPEC (Su & Judd, Econometrica: Journal of the Econometric Society, 80, 2213–2230, 2012). Since MPEC requires the grid structure for the value function approximation to be hard-coded into the constraints, one cannot apply iterative node insertion for grid refinement; for NFXP, grid adaption by (iteratively) inserting new grid nodes will generally lead to discontinuous likelihood functions. Therefore, we show how to continuously adapt the grid by moving the nodes, a technique referred to as r-adaption. We demonstrate how to obtain optimal grids based on the balanced error principle, and implement this approach by including additional constraints to the likelihood maximization problem. The method is applied to two models: (i) the bus engine replacement model (Rust, 1987), modified to feature a continuous mileage state, and (ii) to a dynamic model of content consumption using original data from one of the world’s leading user-generated content networks in the domain of music.

International audience; We prove that, for the black hole search problem in networks of arbitrary but known topology, the pebble model of agent interaction is computationally as powerful as the whiteboard model; furthermore the complexity is exactly the same. More precisely, we prove that a team of two asynchronous agents, each endowed with a single identical pebble (that can be placed only on nodes, and with no more than one pebble per node), can locate the black hole in an arbitrary network of known topology; this can be done with Θ(nlog n) moves, where n is the number of nodes, even when the links are not FIFO. These results are obtained with a novel algorithmic technique, ping-pong, for agents using pebbles.