ELFT HÍRADÓ

[Tamás Kiss <kiss.tamas AT wigner.hu>]

*GAMENET*
<https://www.google.com/url?q=https%3A%2F%2Fgametheorynetwork.com&sa=D&sntz=1&usg=AFQjCNHV5rcbY5KQAUkY-ZNVOOKtxNyTgA>*
Training school on Borel Games*

*https://sites.google.com/view/borelgames2021tc/f%C5%91oldal
<https://sites.google.com/view/borelgames2021tc/f%C5%91oldal>*


*Date and Venue: *2021 August 2-4 on Zoom
<https://www.google.com/url?q=https%3A%2F%2Fzoom.us&sa=D&sntz=1&usg=AFQjCNG27r0sq6D3d8NnZVLk2mZvmFbDAw>
.


*Speakers: *Galit Ashkenazi-Golan
<https://www.google.com/url?q=https%3A%2F%2Fgalitashkenazi.wixsite.com%2Fwebsite-8&sa=D&sntz=1&usg=AFQjCNHqVAHiEu3wqpP3b2vh6DHZpVGz9Q>
(Tel-Aviv University), J
<https://www.google.com/url?q=https%3A%2F%2Fsites.google.com%2Fsite%2Fjanosflesch%2Fhome&sa=D&sntz=1&usg=AFQjCNF1RDwpVgehsxVXkq-YiYK-VFEsGw>
á
<https://www.google.com/url?q=https%3A%2F%2Fsites.google.com%2Fsite%2Fjanosflesch%2Fhome&sa=D&sntz=1&usg=AFQjCNF1RDwpVgehsxVXkq-YiYK-VFEsGw>nos
Flesch
<https://www.google.com/url?q=https%3A%2F%2Fsites.google.com%2Fsite%2Fjanosflesch%2Fhome&sa=D&sntz=1&usg=AFQjCNF1RDwpVgehsxVXkq-YiYK-VFEsGw>
(Maastricht University), Erez Nesharim
<http://www.google.com/url?q=http%3A%2F%2Fmath.huji.ac.il%2F~ereznesh%2F&sa=D&sntz=1&usg=AFQjCNH7cn5tvP-XM0zEISnXBELiNWn-gw>
(Hebrew University), Ron Peretz
<https://www.google.com/url?q=https%3A%2F%2Fronprtz.droppages.com&sa=D&sntz=1&usg=AFQjCNFFDZmoapRWrO4BGpTDnv_QFfJFvw>
(Bar Ilan University), Arkad
<https://www.google.com/url?q=https%3A%2F%2Farkpred.wixsite.com%2Farkpred&sa=D&sntz=1&usg=AFQjCNHwcXSysOCNfjPQ3zE9RwevLQYu3Q>
i
<https://www.google.com/url?q=https%3A%2F%2Farkpred.wixsite.com%2Farkpred&sa=D&sntz=1&usg=AFQjCNHwcXSysOCNfjPQ3zE9RwevLQYu3Q>
Predtetchinski
<https://www.google.com/url?q=https%3A%2F%2Farkpred.wixsite.com%2Farkpred&sa=D&sntz=1&usg=AFQjCNHwcXSysOCNfjPQ3zE9RwevLQYu3Q>
(Maastricht University), Eran Shmaya
<https://www.google.com/url?q=https%3A%2F%2Fwww.stonybrook.edu%2Fcommcms%2Feconomics%2Fpeople%2F_bios%2FSHMAYA.php&sa=D&sntz=1&usg=AFQjCNHU5JUxAbnM8uEQP4vfgz0mh_k7cg>
(Stony Brook University), Eilon Solan
<https://www.google.com/url?q=https%3A%2F%2Fsites.google.com%2Fsite%2Feilonsolanphd%2F&sa=D&sntz=1&usg=AFQjCNFzvzNDVlsXXbThiIpFwn9anHWj1w>
(Tel-Aviv University)


*Topic: *In even stages 0,2,4,... Player 1 selects a bit (0 or 1), and in
odd stages 1,3,5,... Player 2 selects a bit (0 or 1). This way the two
players select (the binary representation of) a number in the unit interval
x. Player 1 wins if x is in some given target set A, and Player 2 wins
otherwise. Does necessarily one of the players have a winning strategy,
namely, a strategy that guarantees that that player wins, regardless of the
choices of the other players? The game we just described is an
infinite-horizon extensive-form game. The determinacy of this game, namely,
the existence of a winning strategy to one of the players, is an extension
of the famous Zermelo's Theorem to this setup, and was fully answered in
1975 by Donald Martin
<https://www.google.com/url?q=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FDonald_A._Martin&sa=D&sntz=1&usg=AFQjCNE1OEVXCThIoNHCJRaoEb1B4iSc3A>
.

Borel games are two-player alternating-move games where the action sets of
each player after each history may be an arbitrary set, and the winning set
is a Borel set of plays. The determinacy of Borel games is a momentous
result. It has numerous applications in set theory, topology, logic,
computer science, and, of course, in game theory. In 1998 Martin extended
his determinacy result to two-player zero-sum simultaneous-move games with
both players have finite action sets. The two results were then unified and
extended by Eran Shmaya in 2011, who studied alternating-move games with
eventual perfect monitoring.

In this training school we intend to go over some of the determinacy
results and their applications. Our approach is didactic, and our ambition
is to guide the participants through the details of the results and the
proofs. We also present very recent papers with applications of Borel games
to game theory and analysis.


*Some readings: *This
<https://www.google.com/url?q=https%3A%2F%2Fgowers.wordpress.com%2F2013%2F08%2F23%2Fdeterminacy-of-borel-games-i%2F&sa=D&sntz=1&usg=AFQjCNHOsCk6AH-0ohDvYt_ZZ6kx6wHWQg>,
this
<https://www.google.com/url?q=https%3A%2F%2Fgowers.wordpress.com%2F2013%2F08%2F31%2Fdeterminacy-of-borel-games-ii%2F&sa=D&sntz=1&usg=AFQjCNGudormiywbcT2j702x9QS4AkCIFA>
and this
<https://www.google.com/url?q=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FBorel_determinacy_theorem&sa=D&sntz=1&usg=AFQjCNGLrRJdGtAHYlTbekdzepUYLO3nEQ>
.


*Welcome: *PhD students, MSc students, researchers, anybody who is
interested.


*Registration: *It is free but required: Please send an e-mail to
BorelGames2021TS
at protonmail dot com.


*Program: *Hours meant in CEST (Paris time).


*Day 1: Monday, August 2*

08:50: *Miklós Pintér*: Welcoming words

09:00-10:30: *Ron Peretz*
<https://www.google.com/url?q=https%3A%2F%2Fronprtz.droppages.com&sa=D&sntz=1&usg=AFQjCNFFDZmoapRWrO4BGpTDnv_QFfJFvw>:
Martin 75
<https://www.google.com/url?q=https%3A%2F%2Fwww.jstor.org%2Fstable%2F1971035%3Fseq%3D1&sa=D&sntz=1&usg=AFQjCNHAuXC18yyE3jHEtdlm5kA0_MpNcA>:
the seminal paper of Martin, proving that in alternating-move games with a
winning set are determined.

11:00-12:30: *Arkad*
<https://www.google.com/url?q=https%3A%2F%2Farkpred.wixsite.com%2Farkpred&sa=D&sntz=1&usg=AFQjCNHwcXSysOCNfjPQ3zE9RwevLQYu3Q>
*i*
<https://www.google.com/url?q=https%3A%2F%2Farkpred.wixsite.com%2Farkpred&sa=D&sntz=1&usg=AFQjCNHwcXSysOCNfjPQ3zE9RwevLQYu3Q>*
Predtetchinski*
<https://www.google.com/url?q=https%3A%2F%2Farkpred.wixsite.com%2Farkpred&sa=D&sntz=1&usg=AFQjCNHwcXSysOCNfjPQ3zE9RwevLQYu3Q>:
EFKNPP2020
<https://www.google.com/url?q=https%3A%2F%2Farxiv.org%2Fabs%2F2010.03327&sa=D&sntz=1&usg=AFQjCNFve3iS0KWVvGIeKDouJf2b7LQQ7g>:
games whose payoff function is the limsup functions.

13:30-15:00: *Erez Nesharim*
<http://www.google.com/url?q=http%3A%2F%2Fmath.huji.ac.il%2F~ereznesh%2F&sa=D&sntz=1&usg=AFQjCNH7cn5tvP-XM0zEISnXBELiNWn-gw>:
On Schmidt games and some applications in dynamics and number theory


*Day 2: Tuesday, August 3*

09:00-10:30: *J*
<https://www.google.com/url?q=https%3A%2F%2Fsites.google.com%2Fsite%2Fjanosflesch%2Fhome&sa=D&sntz=1&usg=AFQjCNF1RDwpVgehsxVXkq-YiYK-VFEsGw>
*á*
<https://www.google.com/url?q=https%3A%2F%2Fsites.google.com%2Fsite%2Fjanosflesch%2Fhome&sa=D&sntz=1&usg=AFQjCNF1RDwpVgehsxVXkq-YiYK-VFEsGw>*nos
Flesch*
<https://www.google.com/url?q=https%3A%2F%2Fsites.google.com%2Fsite%2Fjanosflesch%2Fhome&sa=D&sntz=1&usg=AFQjCNF1RDwpVgehsxVXkq-YiYK-VFEsGw>:
Mertens-Neyman 86: Equilibrium in multiplayer nonzero-sum alternating-move
games.

11:00-12:30: *Ron Peretz*
<https://www.google.com/url?q=https%3A%2F%2Fronprtz.droppages.com&sa=D&sntz=1&usg=AFQjCNFFDZmoapRWrO4BGpTDnv_QFfJFvw>:
Martin 98
<https://www.google.com/url?q=https%3A%2F%2Fwww.cambridge.org%2Fcore%2Fjournals%2Fjournal-of-symbolic-logic%2Farticle%2Fabs%2Fthe-determinacy-of-blackwell-games%2FD421AA799CD5935AF7B87FF9927FC2C1&sa=D&sntz=1&usg=AFQjCNGhLSPjn8aKOYuz8e9Vjxe15NwVHQ>:
Existence of the value in two-player zero-sum simultaneous-move games

13:30-15:00: *Eran*
<https://www.google.com/url?q=https%3A%2F%2Fwww.stonybrook.edu%2Fcommcms%2Feconomics%2Fpeople%2F_bios%2FSHMAYA.php&sa=D&sntz=1&usg=AFQjCNHU5JUxAbnM8uEQP4vfgz0mh_k7cg>
<https://www.google.com/url?q=https%3A%2F%2Fwww.stonybrook.edu%2Fcommcms%2Feconomics%2Fpeople%2F_bios%2FSHMAYA.php&sa=D&sntz=1&usg=AFQjCNHU5JUxAbnM8uEQP4vfgz0mh_k7cg>
*Shmaya*
<https://www.google.com/url?q=https%3A%2F%2Fwww.stonybrook.edu%2Fcommcms%2Feconomics%2Fpeople%2F_bios%2FSHMAYA.php&sa=D&sntz=1&usg=AFQjCNHU5JUxAbnM8uEQP4vfgz0mh_k7cg>:
Shmaya 11
<https://www.google.com/url?q=https%3A%2F%2Fwww.ams.org%2Fproc%2F2011-139-10%2FS0002-9939-2011-10987-0%2F&sa=D&sntz=1&usg=AFQjCNG_gqRRhG9DvhBbetOdwdNTyeKIZw>:
Determinacy of two-player alternating-move games with a winning set, when
information on the other player's move is obtained with delay.


*Day 3: Wednesday, August 4*

09:00-10:30: *Galit Ashkenazi-Golan*
<https://www.google.com/url?q=https%3A%2F%2Fgalitashkenazi.wixsite.com%2Fwebsite-8&sa=D&sntz=1&usg=AFQjCNHqVAHiEu3wqpP3b2vh6DHZpVGz9Q>:
AFPS 21: Regularity of the value and equilibrium in games with finitely
many players and tail-measurable payoffs.

11:00-12:30: *J*
<https://www.google.com/url?q=https%3A%2F%2Fsites.google.com%2Fsite%2Fjanosflesch%2Fhome&sa=D&sntz=1&usg=AFQjCNF1RDwpVgehsxVXkq-YiYK-VFEsGw>
*á*
<https://www.google.com/url?q=https%3A%2F%2Fsites.google.com%2Fsite%2Fjanosflesch%2Fhome&sa=D&sntz=1&usg=AFQjCNF1RDwpVgehsxVXkq-YiYK-VFEsGw>*nos
Flesch*
<https://www.google.com/url?q=https%3A%2F%2Fsites.google.com%2Fsite%2Fjanosflesch%2Fhome&sa=D&sntz=1&usg=AFQjCNF1RDwpVgehsxVXkq-YiYK-VFEsGw>:
AFPS 21
<https://www.google.com/url?q=https%3A%2F%2Farxiv.org%2Fabs%2F2106.03975&sa=D&sntz=1&usg=AFQjCNF3KgRBq3Wi2JmaNyBw-3bXqPwbww>:
Repeated games with countably many players and tail-measurable payoffs.

13:30-15:00: *Eilon*
<https://www.google.com/url?q=https%3A%2F%2Fsites.google.com%2Fsite%2Feilonsolanphd%2F&sa=D&sntz=1&usg=AFQjCNFzvzNDVlsXXbThiIpFwn9anHWj1w>
<https://www.google.com/url?q=https%3A%2F%2Fsites.google.com%2Fsite%2Feilonsolanphd%2F&sa=D&sntz=1&usg=AFQjCNFzvzNDVlsXXbThiIpFwn9anHWj1w>
*Solan*
<https://www.google.com/url?q=https%3A%2F%2Fsites.google.com%2Fsite%2Feilonsolanphd%2F&sa=D&sntz=1&usg=AFQjCNFzvzNDVlsXXbThiIpFwn9anHWj1w>:
AFPS 21: Big Match games/Absorbing games with tail-measurable payoffs.

15:00: *Mikl**ó**s Pint**é**r*: Ending words