Abstract
We employ the theory of Bayesian potential games to characterize pure-strategy equilibria of a Bayesian game with finite type structures, taking into account the cost/benefit features of agents. Building on a standard model of oligopolistic competition also applicable to environmental issues such as profit maximization in presence of an externality affecting all players, we rely on types to describe their heterogeneity. When the damage functions are additively separable, the potential provides necessary and sufficient conditions to ensure monotonicity of pure strategies.
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Notes
The technical similarities are shown in Monderer and Shapley (1996).
A partial order consists of a binary relation defined on a set indicating that, given two distinct elements in the set, one of them precedes the other. Such a relation is called a partial order to reflect the fact that not every pair of elements in the set need be related: in other words, there may exist a couple of elements such that none of them precedes the other. We will use a partial order on couples consisting of positive numbers and functions.
Given two sets \(X, Y,\) the notation \(X^Y\) indicates the set of functions from \(Y\) to \(X, X^Y =\left\{ f|f:Y\longrightarrow X\right\}\)
In the Examples in Sect. 4 such issue will be discussed after computing the equilibrium strategies.
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Acknowledgments
The authors would like to thank Raimondo Manca and an anonymous referee for very valuable comments and suggestions. The usual disclaimer applies.
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Palestini, A., Poggio, I. A Bayesian potential game to illustrate heterogeneity in cost/benefit characteristics. Int Rev Econ 62, 23–39 (2015). https://doi.org/10.1007/s12232-014-0221-9
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DOI: https://doi.org/10.1007/s12232-014-0221-9