Open AccessSavage games
Author(s) -
Grant Simon,
Meneghel Idione,
Tourky Rabee
Publication year - 2016
Publication title -
theoretical economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.404
H-Index - 32
eISSN - 1555-7561
pISSN - 1933-6837
DOI - 10.3982/te2068
Subject(s) - mathematical economics , class (philosophy) , bayesian game , event (particle physics) , convexity , prior probability , independence (probability theory) , stochastic game , set (abstract data type) , matching (statistics) , game theory , computer science , repeated game , bayesian probability , mathematics , economics , artificial intelligence , statistics , physics , quantum mechanics , financial economics , programming language
We define and discuss Savage games, which are ordinal games of incomplete information set in L. J. Savage's framework of purely subjective uncertainty. Every Bayesian game is ordinally equivalent to a Savage game. However, Savage games are free of priors, probabilities, and payoffs. Players' information and subjective attitudes toward uncertainty are encoded in the state‐dependent preferences over state contingent action profiles. In the class of games we consider, player preferences satisfy versions of Savage's sure‐thing principle and small event continuity postulate. Savage games provide a tractable framework for studying attitudes toward uncertainty in a strategic setting. The work eschews any notion of objective randomization, convexity, monotonicity, or independence of beliefs. We provide a number of examples illustrating the usefulness of the framework, including novel results for a purely ordinal matching game that satisfies all of our assumptions and for games for which the preferences of the players admit representations from a wide class of decision‐theoretic models.