Interim Bayesian Nash Equilibrium on Universal Type Spaces for Supermodular Games

2007 ◽  
Author(s):  
Timothy Van Zandt
Keyword(s):  
Nash Equilibrium ◽  
Supermodular Games ◽  
Bayesian Nash Equilibrium ◽  
Type Spaces

Bayesian Nash Equilibrium in Electricity Spot Markets: An Affine-Plane Approximation Approach

2021 ◽  
pp. 1-1
Author(s):  
Pranjal Pragya Verma ◽  
Mohammad Hesamzadeh ◽  
Ross Baldick ◽  
Darryl Biggar ◽  
K. Shanti Swarup ◽  
...  
Keyword(s):  
Nash Equilibrium ◽  
Affine Plane ◽  
Spot Markets ◽  
Approximation Approach ◽  
Bayesian Nash Equilibrium ◽  
Electricity Spot Markets

Generalized Belief Operator and Robustness in Binary‐Action Supermodular Games

Econometrica ◽  
2020 ◽  
Vol 88 (2) ◽  
pp. 693-726 ◽  
Author(s):  
Daisuke Oyama ◽  
Satoru Takahashi
Keyword(s):  
Incomplete Information ◽  
High Probability ◽  
Equilibrium Selection ◽  
Common Belief ◽  
Supermodular Games ◽  
Prior Beliefs ◽  
Global Game ◽  
Game Equilibrium ◽  
Type Spaces ◽  
Action Profile

This paper studies the robustness of an equilibrium to incomplete information in binary‐action supermodular games. Using a generalized version of belief operator, we explore the restrictions that prior beliefs impose on higher order beliefs. In particular, we obtain a nontrivial lower bound on the probability of a common belief event, uniform over type spaces, when the underlying game has a monotone potential. Conversely, when the game has no monotone potential, we construct a type space with an arbitrarily high probability event in which players never have common belief about that event. As an implication of these results, we show for generic binary‐action supermodular games that an action profile is robust to incomplete information if and only if it is a monotone potential maximizer. Our study offers new methodology and insight to the analysis of global game equilibrium selection.

LEARNING IN BAYESIAN GAMES BY BOUNDED RATIONAL PLAYERS II: NONMYOPIA

1998 ◽  
Vol 2 (2) ◽  
pp. 141-155 ◽  
Author(s):  
Konstantinos Serfes ◽  
Nicholas C. Yannelis
Keyword(s):  
Nash Equilibrium ◽  
Arbitrary Number ◽  
Bayesian Learning ◽  
Full Information ◽  
Bayesian Games ◽  
Response Strategies ◽  
Bayesian Nash Equilibrium ◽  
Current Period ◽  
Best Response ◽  
Rational Players

We generalize results of earlier work on learning in Bayesian games by allowing players to make decisions in a nonmyopic fashion. In particular, we address the issue of nonmyopic Bayesian learning with an arbitrary number of bounded rational players, i.e., players who choose approximate best-response strategies for the entire horizon (rather than the current period). We show that, by repetition, nonmyopic bounded rational players can reach a limit full-information nonmyopic Bayesian Nash equilibrium (NBNE) strategy. The converse is also proved: Given a limit full-information NBNE strategy, one can find a sequence of nonmyopic bounded rational plays that converges to that strategy.

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