Abstract
The “global game with strategic substitutes and complements” of Karp et al. (2007) is used to model the decision of where to fish. A complete information game is assumed, but the model is generalized to S>1 sites. In this game, a fisherman’s payoff depends on fish density in each site and the actions of other fishermen which can lead to congestion or agglomeration effects. Stable and unstable equilibria are characterized, as well as notions of equilibrium dominance. The model is applied to the Alaskan flatfish fishery by specifying a strategic interaction function (response to congestion) that is a non-linear function of the degree of congestion present in a given site. Results suggest that the interaction function may be non-monotonic in congestion.
Highlights
Understanding congestion externalities is important in many settings but is relevant to natural resource economics
Individuals possess complete information, so movers may realize that their former site exhibited congestion effects which were relieved upon their moving, increasing utility for stayers
As pointed out by Bayer and Timmins (2007), the share of agents selecting a site, is correlated with the error term, To circumvent this, they developed an instrumental variables approach for identifying congestion/agglomeration effects that leverages the exogenous data in the model as well as the spatial and, in our case, temporal variation to obtain instruments that are correlated with share but are uncorrelated with the error term, 21 The logic behind using the set of instruments they propose is that the desire to fish in a given location is determined by the location-specific information, and by the relative comparison of this information with the other potential locations one may fish
Summary
Understanding congestion externalities is important in many settings but is relevant to natural resource economics. Bayer and Timmins (2005) discuss existence of multiple equilibria when the interaction function is non-monotonic in congestion. The game presented here is effectively a sorting model of location choice, but the focus is actual characterization of the equilibria in the non-monotonic case This model serves as an intellectual framework for estimation of a random utility model with an interaction function that is non-monotonic in congestion. Individuals possess complete information (instrumentation to detect the location of fish and other vessels), so movers may realize that their former (equilibrium) site exhibited congestion effects which were relieved upon their moving, increasing utility for stayers. A stable equilibrium satisfies Definition 1 and does not provide incentives for groups of individuals to deviate (congestion effects); an unstable equilibrium does (agglomeration effects) Equilibria in this setting are best understood by examining the relationships between pairs of locations. The sufficient condition in Proposition 2 is probably more general than is necessary, since we could have defined some subset for each location over which a fixed point might exist, but having a general simplifies the exposition
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