Bayesian Games: Games with Incomplete Information (original) (raw)
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Bayesian Theory of Games: A Statistical Decision Theoretic Based Analysis of Strategic Interactions
2010
Bayesian rational prior equilibrium requires agent to make rational statistical predictions and decisions, starting with first order non informative prior and keeps updating with statistical decision theoretic and game theoretic reasoning until a convergence of conjectures is achieved. The main difference between the Bayesian theory of games and the current games theory are: I. It analyzes a larger set of games, including noisy games, games with unstable equilibrium and games with double or multiple sided incomplete information games which are not analyzed or hardly analyzed under the current games theory. II. For the set of games analyzed by the current games theory, it generates far fewer equilibria and normally generates only a unique equilibrium and therefore functions as an equilibrium selection and deletion criterion and, selects the most common sensible and statistically sound equilibrium among equilibria and eliminates insensible and statistically unsound equilibria. III. It...
SSRN Electronic Journal, 2012
This paper introduces a new game theoretic equilibrium which is based upon the Bayesian subjective view of probability, BEIC (Bayesian equilibrium iterative conjectures). It requires players to make predictions, starting from first order uninformative predictive distribution functions (or conjectures) and keep updating with statistical decision theoretic and game theoretic reasoning until a convergence of conjectures is achieved. Information known by the players such as the reaction functions are thereby incorporated into their higher order conjectures and help to determine the convergent conjectures and the equilibrium. In a BEIC, conjectures are consistent with the equilibrium or equilibriums they supported and so rationality is achieved for actions, strategies and conjectures. The BEIC approach is capable of analyzing a larger set of games than current Nash Equilibrium based games theory, including games with inaccurate observations, games with unstable equilibrium and games with double or multiple sided incomplete information games. On the other hand, for the set of games analyzed by the current games theory, it generates far lesser equilibriums and normally generates only a unique equilibrium. It treats games with complete and perfect information as special cases of games with incomplete information and noisy observation whereby the variance of the prior distribution function on type and the variance of the observation noise term tend to zero. Consequently, there is the issue of indeterminacy in statistical inference and decision making in these games as the equilibrium solution depends on which variances tends to zero first. It therefore identifies equilibriums in these games that have so far eluded the classical theory of games. Finally, it also resolves inconsistencies in equilibrium results by different solution concepts in current games theory such as that between Nash Equilibrium and iterative elimination of dominated strategies and that between Perfect Bayesian Equilibrium and backward induction (Subgame Perfect Equilibrium).
Bayesian Game Theorists and non-Bayesian Players
Bayesian game theorists claim to represent players as Bayes rational agents, maximising their expected utility given their beliefs about the choices of other players. I argue that this narrative is inconsistent with the formal structure of Bayesian game theory. This is because (i) the assumption of common belief in rationality is equivalent to equilibrium play, as in classical game theory, and (ii) the players' prior beliefs are a mere mathematical artefact and not actual beliefs hold by the players. Bayesian game theory is thus a Bayesian representation of the choice of players who are committed to play equilibrium strategy profiles.
Formulation of Bayesian Analysis for Games With Incomplete Information
International Journal of Game Theory, 1985
Abstract: A formal model is given of Harsanyi's infinite hierarchies of beliefs. It is shown that the model doses with some Bayesian game with incomplete information, and that any such game can be approximated by one with a finite number of states of world.
The Bayesian foundations of solution concepts of games
Journal of Economic Theory, 1988
We transform a noncooperative game into a Bayesian decision problem for each player where the uncertainty faced by a player is the strategy choices of the other players, the priors of other players on the choice of other players, the priors over priors, and so on. We provide a complete characterization between the extent of knowledge about the rationality of players and their ability to successively eliminate strategies which are not best responses. This paper therefore provides the informational foundations of iteratively undominated strategies and rationalizable strategic behavior
The Bayesian foundations of solution concepts of games* 1
Journal of Economic Theory, 1988
We transform a non co-operati ve game into a-Bayesian decision problem for each player where the uncertainty faced by a player is the strategy choices of the other players, the pr iors of other players on the choice of other players, the priors over priors and so on.We provide a complete characterization between the extent of knowledge about the rationality of players and their ability to successfulIy eliminate strategies which are not best responses. This paper therefore provides the informational foundations of iteratively unàominated strategies and rationalizable strategic behavior (Bernheim (1984) and Pearce (1984». Moreover, sufficient condi tions are also found for Nash equilibrium behavior. We also provide Aumann's (1985) results on correlated equilibria. *This pape r is a substantially expanded and revised version of "The Bayesian Foundations of Rationalizable Strategic Behavior and Nash Equilibrium Behavior." We wish to acknowledge the tremendous help and useful discussions we have had with Roger Myerson who first brought our attention to the Armbruster and Bege (1979) paper. Discussion with David Hirshleifer, José Alexandre Scheinkman and Hugo Sonnenschein have also helped to clarify our ideas.
Bayesian Games with Intentions
Electronic Proceedings in Theoretical Computer Science, 2016
We show that standard Bayesian games cannot represent the full spectrum of belief-dependent preferences. However, by introducing a fundamental distinction between intended and actual strategies, we remove this limitation. We define Bayesian games with intentions, generalizing both Bayesian games and psychological games [5], and prove that Nash equilibria in psychological games correspond to a special class of equilibria as defined in our setting.
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We report on an experiment designed to evaluate the empirical implications of Jordan's model of Bayesian learning in games of incomplete information. A finite example is constructed in which the model generates unique predictions of subjects' choices in nearly all periods. When the "true" game defined by players' private information was one with a unique equilibrium in pure strategies, the experimental subjects' play converged to the equilibrium, as Jordan's theory predicts, even when the subjects had not attained complete information about one another. But when there were two pure strategy equilibria, the theory's predictions were not consistent with observed behavior.
Dynamic Games with Incomplete Information
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We have now covered static and dynamic games of complete information and static games of incomplete information. The next step is to focus on dynamic games of incomplete information. When solving games of this type we will need to invoke Bayesrule because players later in the game will have additional information. The solution concept that we will use for games of this type will be the perfect Bayesian equilibrium (PBE). On the one hand, perfect Bayesian equilibrium re nes the Bayes-Nash equilibrium concept by ruling out noncredible threats. However, it also rules out some of the SPNE that rely on noncredible threatswhen there is imperfect information. So, perfect Bayesian equilibrium can be viewed as a stronger equilibrium concept than the previous ones. This basic game captures many types of card games, such as Bridge, Spades, and Poker, in which one player does not know what cards the other player(s) is holding. When playing games of this type people often use both the knowled...