Positive value of information in games

Bruno Bassan*, Olivier Gossner, Marco Scarsini, Shmuel Zamir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

40 Scopus citations

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 à la Blackwell. More specifically, we consider pairs consisting of a game with incomplete information G and an information structure script l sign such that the extended game Λ(G, script l sign) has a unique Pareto payoff profile u. We prove that u is a Nash payoff profile of Λ(G, script l sign), and that for any information structure script l sign that is coarser than script l sign, all Nash payoff profiles of Λ(G, script l sign) 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 Λ(G, script l sign) with that polyhedron as the convex hull of feasible payoffs, an information structure script l sign coarser than script l sign and a player i who strictly prefers a Nash equilibrium in Λ(G, script l sign) to any Nash equilibrium in Λ(G, script l sign).

Original languageEnglish
Pages (from-to)17-31
Number of pages15
JournalInternational Journal of Game Theory
Volume32
Issue number1
DOIs
StatePublished - Dec 2003

Keywords

  • Information structures
  • Pareto optima
  • Value of information

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