Equilibria Existence in Bayesian Games: Climbing the Countable Borel Equivalence Relation Hierarchy

References

• [1] Blackwell D, Ryll-Nardzewski C (1963) Non-existence of everywhere proper conditional distributions. Ann. Math. Statist. 34(1):223–225.Crossref, Google Scholar
• [2] Brandenburger A, Dekel E (1987) Common knowledge with probability 1. J. Math. Econom. 16(3):237–245.Crossref, Google Scholar
• [3] Dougherty R, Jackson S, Kechris AS (1994) The structure of hyperfinite Borel equivalence relations. Trans. Amer. Math. Soc. 341(1):193–225.Crossref, Google Scholar
• [4] Harsányi JC (1967) Games with incomplete information played by Bayesian players, I–III: Part I. The basic model. Management Sci. 14(3):159–182.Link, Google Scholar
• [5] Hellman Z (2014) A game with no Bayesian approximate equilibria. J. Econom. Theory 153(September):138–151.Crossref, Google Scholar
• [6] Hellman Z, Levy YJ (2017) Bayesian games with a continuum of states. Theoret. Econom. 12:1089–1120.Crossref, Google Scholar
• [7] Hellman Z, Levy YJ (2019) Measurable selection for purely atomic games. Econometrica 87(2):593–629.Crossref, Google Scholar
• [8] Himmelberg C (1975) Measurable relations. Fundamenta Math. 87(1):53–72.Crossref, Google Scholar
• [9] Hjorth G (2012) Treeable equivalence relations. J. Math. Logic 12(1):1250003.Crossref, Google Scholar
• [10] Kearns MJ, Littman ML, Singh SP (2001) Graphical models for game theory. Breese JS, Koller D, eds. Proc. 17th Conf. Uncertainty Artificial Intelligence (Morgan Kaufmann, San Francisco), 253–260.Google Scholar
• [11] Kechris AS (1995) Classical Descriptive Set Theory, Graduate Texts in Mathematics, vol. 156 (Springer-Verlag, New York).Crossref, Google Scholar
• [12] Kechris AS, Miller BD (2004) Topics in Orbit Equivalence, Lecture Notes in Mathematics, vol. 1852 (Springer, Berlin).Crossref, Google Scholar
• [13] Lehrer E, Samet D (2011) Agreeing to agree. Theoret. Econom. 6(2):269–287.Crossref, Google Scholar
• [14] Levy Y (2013) A Cantor set of games with no shift-homogeneous equilibrium selection. Math. Oper. Res. 38(3):492–503.Link, Google Scholar
• [15] Milgrom PR, Weber RJ (1985) Distributional strategies for games with incomplete information. Math. Oper. Res. 10(4):619–632.Link, Google Scholar
• [16] Nielsen LT (1984) Common knowledge, communication, and convergence of beliefs. Math. Social Sci. 8(1):1–14.Crossref, Google Scholar
• [17] Peleg B (1969) Equilibrium points for games with infinitely many players. J. London Math. Soc. s1-44(1):292–294.Google Scholar
• [18] Selten R (1975) Reexamination of the perfectness concept for equilibrium points in extensive games. Internat. J. Game Theory 4(1):25–55.Crossref, Google Scholar
• [19] Simon RS (2000) The common prior assumption in belief spaces: An example. Technical report, Federmann Center for the Study of Rationality, Hebrew University of Jerusalem, Jerusalem.Google Scholar
• [20] Simon RS (2003) Games of incomplete information, ergodic theory, and the measurability of equilibria. Israel J. Math. 138(1):73–92.Crossref, Google Scholar
• [21] Simon RS, Tomkowicz G (2018) A Bayesian game without ε-equilibria. Israel J. Math. 227(1):215–231.Crossref, Google Scholar
• [22] Thomas S, Schneider S (2012) Countable Borel equivalence relations. Cummings J, Schimmerling E, eds. Appalachian Set Theory, 2006–2012 (Cambridge University Press, Cambridge, UK), 25–62.Crossref, Google Scholar
• [23] Zamir S (2009) Bayesian games: Games with incomplete information. Meyers RA, ed. Encyclopedia of Complexity and Systems Science (Springer, New York), 426–441.Google Scholar