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Journal Articles International Journal of Game Theory Year : 2003

Positive value of information in games

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Abstract

We exhibit a general class of interactive decision situations in which all the agents benefit from more information. This class includes as a special case the classical comparison of statistical experiments `a la Blackwell. More specifically, we consider pairs consisting of a game with incomplete information G and an information structure S such that the extended game (G,S) has a unique Pareto payoff profile u. We prove that u is a Nash payoff profile of (G,S), and that for any information structure T that is coarser than S, all Nash payoff profiles of (G,S) are dominated by u. We then prove that our condition is also necessary in the following sense: Given any convex compact polyhedron of payoff profiles, whose Pareto frontier is not a singleton, there exists an extended game (G,S) with that polyhedron as the convex hull of feasible payoffs, an information structure T coarser than S and a player i who strictly prefers a Nash equilibrium in (G,S) to any Nash equilibrium in (G,S).

Dates and versions

hal-00539798 , version 1 (25-11-2010)

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Marco Scarsini, Bruno Bassan, Olivier Gossner, Shmuel Zamir. Positive value of information in games. International Journal of Game Theory, 2003, Vol. 32, pp. 17-31. ⟨10.1007/s001820300142⟩. ⟨hal-00539798⟩
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