The sensitivity of Bayesian implementation to agents' beliefs about others suggests the use of more robust notions of implementation such as ex post implementation, which requires that each agent's strategy be optimal for every possible realization of the types of other agents. We show that the only deterministic social choice functions that are ex post implementable in generic mechanism design frameworks with multidimensional signals, interdependent valuations, and transferable utilities are constant functions. In other words, deterministic ex post implementation requires that the same alternative must be chosen irrespective of agents' signals. The proof shows that ex post implementability of a nontrivial deterministic social choice function implies that certain rates of information substitution coincide for all agents. This condition amounts to a system of differential equations that are not satisfied by generic valuation functions.

This paper proposes a tractable model of Bayesian learning on large random networks where agents choose whether to adopt an innovation. We study the impact of the network structure on learning dynamics and product diffusion. In directed networks, all direct and indirect links contribute to agents' learning. In comparison, learning and welfare are lower in undirected networks and networks with cliques. In a rich class of networks, behavior is described by a small number of differential equations, making the model useful for empirical work.

We analyze a large, anonymous labour market in which firms motivate their workers via relational contracts. The market is frictionless and features on-the-job search, in that all acceptable vacancies are immediately filled and the employed compete with the unemployed for vacancies. While firms and workers are ex ante identical, the unique equilibrium exhibits a continuous distribution of contracts in which high wage firms have higher retention rates, more motivated workers and higher productivity. The model thus generates dispersion in wages, productivity and human resource strategies, and gives rise to endogenous job ladders. An exogenous increase in on-the-job search increases the quantity of jobs but decreases their quality; with sufficient on-the-job search there is full employment, and wage dispersion rather than unemployment motivates workers.

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