Non-differentiability of Payoff Functions and Non-uniqueness of Nash Equilibria
نویسنده
چکیده
Given non-degenerate intervals X of R and an increasing ordered mapping Φ : X × · · · ×X → R , games in strategic form between N players with the X as action sets with the following three properties are studied: the set of Nash equilibria E is convex, Φ is constant on E and in each Nash equilibrium at least one payoff function is not partially differentiable w.r.t. its own action. The results are illustrated for a special class of aggregative games that include the formal transboundary pollution games with global transboundary pollution. Keywords—Aggregative game, convex analysis, formal transboundary pollution game, non-differentiable payoff functions, uniqueness of Nash equilibria.
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