Abstract
Harsányi [4] showed that Bayesian games over finite games of payoff uncertainty with finite sets of belief types always admit Bayesian equilibria. That still left the question of whether Bayesian games over finite games of payoff uncertainty with infinitely many types are guaranteed to have equilibria. Simon [7] presented an example of a Bayesian game with no measurable Bayesian equilibria, even though the underlying game of payoff uncertainty is finite. We present a new and shorter proof of Simon's result using a simpler Bayesian game that moreover does not even have measurable approximate equilibria. That game in turn is used as the basis for constructing another Bayesian game which has no Bayesian equilibria at all, even in non-measurable strategies, in a construction complementary to one appearing in Friedenberg and Meier [1].
| Original language | English |
|---|---|
| Pages (from-to) | 138-151 |
| Number of pages | 14 |
| Journal | Journal of Economic Theory |
| Volume | 153 |
| Issue number | 1 |
| DOIs | |
| State | Published - Sep 2014 |
Bibliographical note
Funding Information:This research was supported in part by the European Research Council under the European Commission's Seventh Framework Program (FP7/2007–2013)/ERC grant agreement no. 249159 , and Israel Science Foundation grants 538/11 and 212/09 . I thank an anonymous referee and editor. Special thanks are due to Yehuda (John) Levy for suggesting that I study this topic and participating in many long conversations on it. I am also grateful to Sergiu Hart and Abraham Neyman for comments on improving the presentation and their general encouragement, and to Robert Simon for extensive email correspondence and personal communications.
Funding
This research was supported in part by the European Research Council under the European Commission's Seventh Framework Program (FP7/2007–2013)/ERC grant agreement no. 249159 , and Israel Science Foundation grants 538/11 and 212/09 . I thank an anonymous referee and editor. Special thanks are due to Yehuda (John) Levy for suggesting that I study this topic and participating in many long conversations on it. I am also grateful to Sergiu Hart and Abraham Neyman for comments on improving the presentation and their general encouragement, and to Robert Simon for extensive email correspondence and personal communications.
| Funders | Funder number |
|---|---|
| European Commission | |
| Seventh Framework Programme | 249159 |
| Israel Science Foundation | 212/09, 538/11 |
Keywords
- Approximate equilibria
- Bayesian games
- Existence of equilibria
- Incomplete information