TY - JOUR
T1 - Positive value of information in games
AU - Bassan, Bruno
AU - Gossner, Olivier
AU - Scarsini, Marco
AU - Zamir, Shmuel
PY - 2003/12
Y1 - 2003/12
N2 - 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).
AB - 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).
KW - Information structures
KW - Pareto optima
KW - Value of information
UR - http://www.scopus.com/inward/record.url?scp=0346361781&partnerID=8YFLogxK
U2 - 10.1007/s001820300142
DO - 10.1007/s001820300142
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AN - SCOPUS:0346361781
SN - 0020-7276
VL - 32
SP - 17
EP - 31
JO - International Journal of Game Theory
JF - International Journal of Game Theory
IS - 1
ER -