%
% Fill only lines marked with dots  
% 
%
%
\documentclass[10pt,a4paper,twoside]{article}
\usepackage{latexsym,amssymb}
\usepackage{amssymb,amsmath}
\usepackage{graphicx}
\usepackage{color}
\usepackage{fancyhdr}
\pagestyle{fancy}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  PLEASE, ONLY IN ENGLISH                                         %
%  PLEASE, ONLY ONE PAGE                                           %
%  PLEASE, USE LATEX2E                                             %
%                                                                  %
%  PLEASE, DO NOT DEFINE NEW COMMANDS                              %
%  USE NEWTHEOREMS BELOW, PLEASE, IF YOU WRITE THEOREMS AND SUCH   % %                                                                  %
%  PLEASE, CONTROL THE SIZE OF YOUR ABSTRACT BEFORE YOU SEND IT    %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\newtheorem{thm}{Theorem}
\newtheorem{defi}[thm]{Definition}
\newtheorem{axi}[thm]{Axiom}
\newtheorem{clm}[thm]{Claim}
\newtheorem{col}[thm]{Corollary}
\newtheorem{lem}[thm]{Lemma}
\newtheorem{con}[thm]{Conjecture}
\newtheorem{hyp}[thm]{Hypothesis}
\newtheorem{rem}[thm]{Remark}
\newcommand{\proof}{\noindent{\bf Proof:}\hspace{0.2cm}}
\setcounter{thm}{0}
\newcommand{\N}{{\mathbb N}}
\newcommand{\R}{{\mathbb R}}
\newcommand{\W}{W_0^{1,p}(\Omega)}
\newcommand{\eps}{{\varepsilon}}
\newcommand{\ds}{\displaystyle}

\newcommand{\F}{\mathcal F}
\newcommand{\E}{\mathscr E}
\newcommand{\J}{\mathscr{J}}
\newcommand{\Pl}{(\mathscr{P})}
\newcommand{\CC}{\mathbb C}
\newcommand{\into}{\int\limits_{\Omega}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\textwidth 15.0cm
\textheight 22.0cm
\oddsidemargin 0.4cm
\evensidemargin 0.4cm
\topmargin  0.0cm

\frenchspacing

\headwidth=\textwidth 	
\fancyhead[HCO]{9th Int. Conf. on Mathematics and Informatics,
	September 7-8, 2023, T\^argu Mure\c s, Romania}
\lhead{}\rhead{}
\fancyfoot{}
%


\begin{document}

\begin{center}{\Large\bf
Computing a Common Prior
}\end{center}
%
\begin{center}{\large\bf\noindent
Marianna E.-Nagy and Mikl\'os Pint\'er
}\\[2mm]
%%
Corvinus Center for Operations Research, Corvinus Institute of Advanced Studies, Corvinus University of Budapest
%%
\\[1mm]\texttt{
%%	
pmiklos@protonmail.com
%%
}\end{center}
%

\vspace*{7mm}
%
Morris (1994) and later Feinberg (2000) showed that a finite type space (information structure) attains a common prior if and only if there is no agreeable bet in it. 

We also consider finite type spaces and observe that deciding about the existence of a common prior is equivalent with considering the intersection of affine spaces each is spanned by the types of a player. This observation implies that we can apply the Fredholm alternative (Fredholm, 1903), and conclude that the computational complexity of computing a common prior or an agreeable bet is strongly polynomial. 
%
%
\begin{thebibliography}{9} 
% Please, use the following patterns
%
% for articles 
% \bibitem{1.} 
% delete the dots
 %... G. Sierksma, H. Hoogeveen, Seven criteria for integer sequences being graphic, \textit{J. Graph Theory}  \textbf{15,} 2 (1991) 223--231. 
%
%% for books
%\bibitem{2.} 
% delete the dots
%... C. Berge, \textit{Graphs and Hypergraphs}, North Holland, 1973. 
%%
\bibitem{1.}
Y. Feinberg, Characterizing Common Priors in the Form of Posteriors, \textit{Journal of Economic Theory} \textbf{91,}  (2000) 127--179.

\bibitem{2.}
I Fredholm, Sur une classe d'equations fonctionelles. \textit{Acta Mathematica} \textbf{27,} (1903) 365--390.

\bibitem{3.}
S. Morris, Trade with heterogeneous prior beliefs and asymmetric information, \textit{Econometrica} \textbf{62,} 6 (1994) 1327--1347.
\end{thebibliography}

%\end{thebibliography}
%

\end{document}


