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We provide a complete characterization of stationary and nonstationary deterministic equilibria in search models of liquidity with indivisible assets. Two formulations are considered: the usual one with random search and bargaining; and a less common but arguably better one with directed search and posting. Also, we consider general meeting technologies. This is interesting because some results are easy with the particular technologies in previous studies but not in general. As is known, these models have equilibria where endogenous variables change over time as self‐fulfilling prophecies. More surprisingly, we prove there are no equilibria where they cycle in the long run.