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To understand the emergence of constitution, Myerson (2008) models a scernario that a political leader gathers supports from captains in order to defeat challengers whose arrival is modelled by a Poisson process.
I found using Poisson process seems to be simple and reasonable, but it is the only model I know that utilizes Poisson process.Are there any other well-known models utilizing Poisson process in a similar way? If not, what's drawback of Poisson process?
Most of the literature on "Strategic experimentation" (or Bandits) uses Poisson processes. Here players can use either a risky or safe arm and one of them generates a fixed stream of payoffs (usually the safe arm) the other one generates lump-sum payments whose arrival times are described by a Poisson process.
Some examples are:
Klein, Nicolas, and Sven Rady. "Negatively correlated bandits." The Review of Economic Studies (2011).
Keller, Godfrey, and Sven Rady. "Strategic experimentation with Poisson bandits." Theoretical Economics 5.2 (2010): 275-311.
Keller, Godfrey, Sven Rady, and Martin Cripps. "Strategic experimentation with exponential bandits." Econometrica 73.1 (2005): 39-68.
Klette and Kortum (2004) develop a parsimonious model of innovating firms rich enough to confront firm-level evidence. It captures the dynamics of individual heterogenous firms, describes the behavior of an industry with simultaneous entry and exit, and delivers ageneral equilibrium model of technological change. At the root of the model is a Poisson process for a firm’s innovations with anarrival rate a function of its current R&D and knowledge generated by its past R&D.
Klette and Kortum, "Innovating Firms and Aggregate Innovation", Journal of Political Economy (2004) Vol. 112, No. 5, pp. 986-1018.
