WEBVTT
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Language: en

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hello<00:00:06.600><c> everyone</c><00:00:07.240><c> welcome</c><00:00:07.560><c> to</c><00:00:07.680><c> the</c>

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hello everyone welcome to the
 

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hello everyone welcome to the
presentation<00:00:08.960><c> so</c><00:00:09.160><c> today</c><00:00:09.440><c> I</c><00:00:09.519><c> will</c><00:00:09.719><c> talk</c><00:00:09.960><c> about</c>

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presentation so today I will talk about
 

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presentation so today I will talk about
Searcher<00:00:10.880><c> competition</c><00:00:11.320><c> in</c><00:00:11.599><c> Block</c><00:00:11.920><c> building</c>

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Searcher competition in Block building
 

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Searcher competition in Block building
so<00:00:12.599><c> this</c><00:00:12.719><c> is</c><00:00:12.880><c> the</c><00:00:13.120><c> paper</c><00:00:14.080><c> title</c><00:00:14.799><c> and</c><00:00:15.759><c> it</c><00:00:15.920><c> was</c>

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so this is the paper title and it was
 

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so this is the paper title and it was
coauthored<00:00:16.680><c> with</c><00:00:17.080><c> kristofh</c><00:00:17.480><c> Schlegel</c><00:00:17.880><c> and</c>

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coauthored with kristofh Schlegel and
 

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coauthored with kristofh Schlegel and
Dani<00:00:19.480><c> from</c><00:00:20.320><c> flash</c><00:00:20.760><c> pods</c><00:00:21.080><c> and</c><00:00:21.279><c> Ben</c><00:00:21.519><c> sudakov</c>

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Dani from flash pods and Ben sudakov
 

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Dani from flash pods and Ben sudakov
from

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from
 

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from
eth<00:00:24.439><c> and</c><00:00:24.640><c> I'm</c><00:00:24.800><c> a</c><00:00:25.640><c> researcher</c><00:00:26.199><c> at</c><00:00:26.400><c> of</c><00:00:26.560><c> chain</c>

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eth and I'm a researcher at of chain
 

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eth and I'm a researcher at of chain
labs

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so<00:00:30.439><c> motivation</c><00:00:31.320><c> was</c><00:00:31.720><c> me</c><00:00:32.680><c> and</c><00:00:32.880><c> we</c><00:00:33.040><c> we</c><00:00:33.160><c> know</c><00:00:33.320><c> that</c>

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so motivation was me and we we know that
 

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so motivation was me and we we know that
there<00:00:33.559><c> are</c><00:00:33.760><c> many</c><00:00:34.000><c> forms</c><00:00:34.360><c> of</c><00:00:34.960><c> me</c><00:00:35.440><c> extraction</c>

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there are many forms of me extraction
 

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there are many forms of me extraction
and<00:00:36.320><c> I'm</c><00:00:36.480><c> listing</c><00:00:37.160><c> only</c><00:00:37.399><c> the</c><00:00:37.559><c> most</c><00:00:37.840><c> popular</c>

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and I'm listing only the most popular
 

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and I'm listing only the most popular
ones<00:00:38.559><c> here</c><00:00:39.040><c> so</c><00:00:39.239><c> there</c><00:00:39.320><c> is</c><00:00:39.520><c> this</c><00:00:39.719><c> sexex</c>

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ones here so there is this sexex
 

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ones here so there is this sexex
Arbitrage<00:00:41.160><c> background</c><00:00:41.719><c> sandwiches</c><00:00:42.280><c> and</c>

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Arbitrage background sandwiches and
 

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Arbitrage background sandwiches and
liquidation<00:00:43.399><c> and</c><00:00:43.559><c> in</c><00:00:43.760><c> each</c><00:00:44.039><c> form</c><00:00:44.840><c> there</c><00:00:44.960><c> are</c>

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liquidation and in each form there are
 

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liquidation and in each form there are
also<00:00:46.079><c> many</c><00:00:46.320><c> different</c><00:00:46.680><c> spe</c><00:00:47.160><c> specializations</c>

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also many different spe specializations
 

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also many different spe specializations
that<00:00:48.160><c> you</c><00:00:48.280><c> can</c><00:00:48.480><c> take</c><00:00:48.719><c> as</c><00:00:48.840><c> a</c><00:00:49.280><c> Searcher</c><00:00:50.039><c> and</c><00:00:50.199><c> here</c>

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that you can take as a Searcher and here
 

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that you can take as a Searcher and here
the<00:00:50.520><c> main</c><00:00:50.760><c> point</c><00:00:51.039><c> is</c><00:00:51.239><c> that</c><00:00:51.480><c> there</c><00:00:51.600><c> are</c><00:00:52.079><c> many</c>

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the main point is that there are many
 

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the main point is that there are many
different<00:00:52.879><c> types</c><00:00:53.520><c> so</c><00:00:53.760><c> Searchers</c><00:00:54.760><c> are</c>

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different types so Searchers are
 

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different types so Searchers are
different<00:00:56.520><c> in</c><00:00:56.719><c> their</c>

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different in their
 

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different in their
specializations<00:00:59.320><c> so</c><00:00:59.519><c> it</c><00:00:59.960><c> create</c><00:01:00.199><c> some</c><00:01:00.359><c> kind</c>

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specializations so it create some kind
 

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specializations so it create some kind
of<00:01:00.920><c> heterogeneity</c><00:01:01.680><c> among</c><00:01:02.199><c> Searchers</c><00:01:03.199><c> so</c><00:01:03.359><c> we</c>

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of heterogeneity among Searchers so we
 

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of heterogeneity among Searchers so we
tried<00:01:03.840><c> to</c><00:01:04.559><c> model</c><00:01:05.000><c> this</c><00:01:05.560><c> uh</c><00:01:05.720><c> with</c><00:01:05.840><c> the</c><00:01:06.000><c> tools</c><00:01:06.200><c> of</c>

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tried to model this uh with the tools of
 

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tried to model this uh with the tools of
Game<00:01:06.680><c> Theory</c><00:01:07.320><c> and</c><00:01:07.439><c> for</c><00:01:07.720><c> that</c><00:01:07.880><c> we</c><00:01:08.000><c> need</c><00:01:08.159><c> to</c>

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Game Theory and for that we need to
 

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Game Theory and for that we need to
identify<00:01:08.920><c> who</c><00:01:09.040><c> are</c><00:01:09.200><c> the</c><00:01:09.360><c> players</c><00:01:10.320><c> and</c><00:01:10.520><c> the</c>

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identify who are the players and the
 

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identify who are the players and the
main<00:01:11.000><c> player</c><00:01:11.360><c> is</c><00:01:11.799><c> validator</c><00:01:12.560><c> or</c><00:01:12.720><c> a</c><00:01:13.000><c> proposer</c>

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main player is validator or a proposer
 

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main player is validator or a proposer
that<00:01:14.200><c> proposes</c><00:01:14.680><c> the</c><00:01:14.840><c> next</c><00:01:15.360><c> blog</c><00:01:16.040><c> and</c><00:01:16.200><c> then</c>

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that proposes the next blog and then
 

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that proposes the next blog and then
there<00:01:16.560><c> are</c><00:01:17.520><c> these</c><00:01:17.799><c> specialized</c><00:01:18.400><c> arbitragers</c>

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there are these specialized arbitragers
 

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there are these specialized arbitragers
that<00:01:19.320><c> in</c><00:01:19.520><c> the</c><00:01:20.240><c> ethereum</c><00:01:20.799><c> setting</c><00:01:21.159><c> are</c><00:01:21.360><c> called</c>

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that in the ethereum setting are called
 

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that in the ethereum setting are called
Searchers<00:01:23.320><c> and</c><00:01:23.520><c> in</c><00:01:24.079><c> current</c><00:01:24.759><c> market</c><00:01:25.560><c> there</c>

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Searchers and in current market there
 

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Searchers and in current market there
are<00:01:25.880><c> also</c><00:01:26.200><c> builders</c><00:01:26.720><c> that</c><00:01:26.920><c> aggregate</c>

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are also builders that aggregate
 

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are also builders that aggregate
Searchers<00:01:28.600><c> and</c><00:01:28.880><c> also</c><00:01:29.439><c> men</c>

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Searchers and also men
 

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Searchers and also men
public<00:01:30.880><c> manol</c><00:01:31.320><c> transactions</c><00:01:32.320><c> but</c><00:01:32.680><c> we</c><00:01:32.799><c> are</c>

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public manol transactions but we are
 

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public manol transactions but we are
ignoring<00:01:34.560><c> um</c><00:01:35.200><c> it</c><00:01:35.520><c> for</c><00:01:35.880><c> this</c><00:01:36.360><c> uh</c><00:01:36.799><c> simplified</c>

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ignoring um it for this uh simplified
 

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ignoring um it for this uh simplified
game<00:01:38.399><c> because</c><00:01:38.680><c> for</c><00:01:38.880><c> us</c><00:01:39.200><c> the</c><00:01:39.320><c> fundamental</c>

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game because for us the fundamental
 

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game because for us the fundamental
players<00:01:40.320><c> are</c><00:01:40.880><c> Searchers</c><00:01:41.799><c> and</c><00:01:42.000><c> the</c><00:01:42.960><c> proposer</c>

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players are Searchers and the proposer
 

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players are Searchers and the proposer
here<00:01:44.200><c> we</c><00:01:44.920><c> denote</c><00:01:45.920><c> the</c><00:01:46.079><c> set</c><00:01:46.240><c> of</c><00:01:46.360><c> Searchers</c><00:01:46.840><c> by</c><00:01:47.200><c> S</c>

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here we denote the set of Searchers by S
 

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here we denote the set of Searchers by S
that<00:01:47.719><c> we</c><00:01:47.840><c> can</c><00:01:48.079><c> identify</c><00:01:48.680><c> by</c><00:01:48.880><c> their</c><00:01:49.200><c> addresses</c>

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that we can identify by their addresses
 

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that we can identify by their addresses
then<00:01:50.719><c> Searchers</c><00:01:51.240><c> submit</c><00:01:51.640><c> their</c><00:01:52.240><c> bundles</c><00:01:53.240><c> of</c>

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then Searchers submit their bundles of
 

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then Searchers submit their bundles of
transactions<00:01:54.000><c> to</c><00:01:54.320><c> include</c><00:01:55.320><c> uh</c><00:01:55.439><c> in</c><00:01:55.560><c> the</c><00:01:55.719><c> block</c>

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transactions to include uh in the block
 

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transactions to include uh in the block
and<00:01:56.479><c> typically</c><00:01:56.880><c> now</c><00:01:57.159><c> they</c><00:01:57.320><c> send</c><00:01:57.560><c> it</c><00:01:57.680><c> to</c><00:01:58.560><c> um</c>

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and typically now they send it to um
 

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and typically now they send it to um
block<00:01:59.079><c> Builder</c><00:02:00.079><c> but</c><00:02:00.240><c> in</c><00:02:00.399><c> principle</c><00:02:00.799><c> they</c>

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block Builder but in principle they
 

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block Builder but in principle they
could<00:02:01.079><c> have</c><00:02:01.200><c> sent</c><00:02:01.439><c> it</c><00:02:01.560><c> to</c><00:02:01.759><c> a</c><00:02:02.439><c> proposer</c><00:02:03.439><c> then</c>

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could have sent it to a proposer then
 

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could have sent it to a proposer then
from<00:02:04.719><c> these</c><00:02:05.280><c> bundles</c><00:02:05.799><c> there</c><00:02:05.920><c> are</c><00:02:06.159><c> some</c><00:02:07.079><c> uh</c><00:02:07.200><c> in</c>

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from these bundles there are some uh in
 

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from these bundles there are some uh in
these<00:02:07.560><c> bundles</c><00:02:08.319><c> there</c><00:02:08.440><c> are</c><00:02:08.640><c> some</c><00:02:09.119><c> conflicts</c>

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these bundles there are some conflicts
 

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these bundles there are some conflicts
so<00:02:09.879><c> you</c><00:02:10.280><c> cannot</c><00:02:11.280><c> build</c><00:02:11.720><c> the</c><00:02:12.000><c> block</c><00:02:12.319><c> that</c><00:02:12.440><c> is</c>

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so you cannot build the block that is
 

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so you cannot build the block that is
the<00:02:12.680><c> union</c><00:02:13.000><c> of</c><00:02:13.160><c> all</c>

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the union of all
 

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the union of all
bundles<00:02:14.920><c> so</c><00:02:15.800><c> you</c><00:02:16.000><c> can</c><00:02:16.160><c> build</c><00:02:16.640><c> many</c><00:02:17.000><c> different</c>

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bundles so you can build many different
 

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bundles so you can build many different
blocks<00:02:19.160><c> for</c><00:02:19.640><c> a</c><00:02:20.200><c> build</c><00:02:20.560><c> block</c><00:02:20.879><c> Searcher</c>

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blocks for a build block Searcher
 

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blocks for a build block Searcher
generates<00:02:21.959><c> some</c><00:02:22.360><c> value</c><00:02:23.239><c> and</c><00:02:23.879><c> validator</c><00:02:24.360><c> or</c>

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generates some value and validator or
 

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generates some value and validator or
the<00:02:24.599><c> proposer</c><00:02:25.080><c> also</c><00:02:25.319><c> generates</c><00:02:25.840><c> a</c><00:02:26.599><c> value</c><00:02:27.599><c> so</c>

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the proposer also generates a value so
 

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the proposer also generates a value so
these<00:02:28.000><c> are</c><00:02:28.319><c> the</c><00:02:29.200><c> uh</c><00:02:30.040><c> smallest</c><00:02:30.440><c> building</c>

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these are the uh smallest building
 

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these are the uh smallest building
blocks<00:02:31.120><c> of</c><00:02:31.319><c> our</c><00:02:31.720><c> game</c><00:02:32.720><c> so</c><00:02:32.920><c> we</c><00:02:33.000><c> are</c><00:02:33.200><c> abstracting</c>

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blocks of our game so we are abstracting
 

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blocks of our game so we are abstracting
away<00:02:33.959><c> from</c><00:02:34.200><c> all</c><00:02:34.519><c> part</c><00:02:35.040><c> particular</c><00:02:35.959><c> mechanisms</c>

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away from all part particular mechanisms
 

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away from all part particular mechanisms
how<00:02:37.560><c> they</c><00:02:37.800><c> interact</c><00:02:38.480><c> and</c><00:02:38.640><c> that</c><00:02:38.840><c> includes</c>

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how they interact and that includes
 

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how they interact and that includes
Builders<00:02:40.200><c> and</c><00:02:40.360><c> we</c><00:02:40.519><c> only</c><00:02:41.440><c> try</c><00:02:41.680><c> to</c><00:02:42.239><c> understand</c>

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Builders and we only try to understand
 

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Builders and we only try to understand
who<00:02:43.239><c> will</c><00:02:43.519><c> get</c><00:02:43.800><c> how</c><00:02:44.040><c> much</c><00:02:44.800><c> among</c><00:02:45.120><c> these</c>

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who will get how much among these
 

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who will get how much among these
players<00:02:45.640><c> depending</c><00:02:46.080><c> on</c><00:02:46.319><c> their</c>

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players depending on their
 

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players depending on their
bundles<00:02:48.680><c> so</c><00:02:48.920><c> for</c><00:02:49.159><c> this</c><00:02:49.319><c> we</c><00:02:49.440><c> are</c><00:02:49.640><c> using</c><00:02:50.440><c> uh</c>

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bundles so for this we are using uh
 

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bundles so for this we are using uh
tools<00:02:51.000><c> from</c><00:02:51.239><c> Cooperative</c><00:02:51.800><c> Game</c><00:02:52.080><c> Theory</c><00:02:52.760><c> and</c>

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tools from Cooperative Game Theory and
 

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tools from Cooperative Game Theory and
for<00:02:53.120><c> that</c><00:02:53.280><c> we</c><00:02:53.400><c> need</c><00:02:53.560><c> to</c><00:02:54.000><c> define</c><00:02:54.440><c> a</c><00:02:54.760><c> value</c><00:02:55.080><c> of</c><00:02:55.280><c> a</c>

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for that we need to define a value of a
 

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for that we need to define a value of a
coalition<00:02:57.400><c> and</c><00:02:58.080><c> value</c><00:02:58.480><c> of</c><00:02:58.640><c> a</c><00:02:59.280><c> coalition</c><00:02:59.920><c> is</c>

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coalition and value of a coalition is
 

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coalition and value of a coalition is
the<00:03:00.959><c> best</c><00:03:01.680><c> block</c><00:03:02.440><c> that</c><00:03:02.959><c> the</c><00:03:03.120><c> Searchers</c><00:03:03.599><c> in</c>

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the best block that the Searchers in
 

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the best block that the Searchers in
this

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this
 

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this
Coalition<00:03:05.720><c> uh</c>

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Coalition uh
 

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Coalition uh
build<00:03:08.640><c> okay</c><00:03:08.879><c> if</c><00:03:09.599><c> uh</c><00:03:10.080><c> there</c><00:03:10.200><c> is</c><00:03:10.400><c> no</c><00:03:11.239><c> uh</c><00:03:11.680><c> proposer</c>

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build okay if uh there is no uh proposer
 

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build okay if uh there is no uh proposer
in<00:03:12.360><c> the</c><00:03:12.519><c> Coalition</c><00:03:12.959><c> then</c><00:03:13.080><c> the</c><00:03:13.239><c> value</c><00:03:13.519><c> is</c><00:03:13.680><c> zero</c>

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in the Coalition then the value is zero
 

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in the Coalition then the value is zero
so<00:03:15.360><c> proposer</c><00:03:15.959><c> or</c><00:03:16.120><c> validator</c><00:03:16.799><c> can</c><00:03:17.799><c> uh</c><00:03:18.120><c> block</c>

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so proposer or validator can uh block
 

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so proposer or validator can uh block
any<00:03:20.080><c> or</c><00:03:20.319><c> veto</c><00:03:20.799><c> any</c><00:03:21.319><c> block</c><00:03:21.720><c> so</c><00:03:21.879><c> you</c><00:03:22.000><c> need</c><00:03:22.360><c> to</c>

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any or veto any block so you need to
 

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any or veto any block so you need to
agree<00:03:23.720><c> uh</c><00:03:24.560><c> with</c><00:03:24.720><c> a</c><00:03:24.920><c> proposer</c><00:03:25.920><c> the</c><00:03:26.120><c> The</c>

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agree uh with a proposer the The
 

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agree uh with a proposer the The
Searchers<00:03:27.400><c> and</c><00:03:27.560><c> this</c><00:03:27.720><c> already</c><00:03:28.080><c> gives</c><00:03:28.280><c> a</c>

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Searchers and this already gives a
 

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Searchers and this already gives a
coalitional<00:03:29.760><c> transferable</c><00:03:30.360><c> utility</c><00:03:31.840><c> game</c>

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coalitional transferable utility game
 

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coalitional transferable utility game
and<00:03:32.959><c> in</c><00:03:33.120><c> these</c><00:03:33.319><c> games</c><00:03:33.599><c> the</c><00:03:33.799><c> most</c><00:03:34.120><c> natural</c>

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and in these games the most natural
 

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and in these games the most natural
solution<00:03:35.200><c> we</c><00:03:35.360><c> think</c><00:03:35.640><c> is</c><00:03:36.560><c> the</c>

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solution we think is the
 

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solution we think is the
core<00:03:38.879><c> and</c><00:03:39.480><c> uh</c><00:03:39.599><c> let</c><00:03:39.760><c> me</c><00:03:39.959><c> Define</c><00:03:40.360><c> what</c><00:03:40.480><c> is</c><00:03:40.799><c> core</c>

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core and uh let me Define what is core
 

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core and uh let me Define what is core
it's<00:03:42.080><c> very</c><00:03:42.319><c> simple</c><00:03:42.720><c> and</c><00:03:43.400><c> intuitive</c><00:03:44.400><c> uh</c><00:03:44.640><c> the</c>

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it's very simple and intuitive uh the
 

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it's very simple and intuitive uh the
core<00:03:45.159><c> solution</c><00:03:46.159><c> gives</c><00:03:46.799><c> uh</c><00:03:47.400><c> payoffs</c><00:03:47.840><c> to</c><00:03:48.000><c> all</c>

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core solution gives uh payoffs to all
 

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core solution gives uh payoffs to all
players<00:03:49.519><c> so</c><00:03:49.840><c> that</c><00:03:50.560><c> no</c><00:03:51.560><c> uh</c><00:03:51.720><c> Coalition</c><00:03:52.239><c> of</c>

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players so that no uh Coalition of
 

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players so that no uh Coalition of
players<00:03:53.120><c> prefer</c><00:03:53.560><c> to</c><00:03:54.239><c> deviate</c><00:03:54.760><c> from</c><00:03:54.959><c> the</c>

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players prefer to deviate from the
 

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players prefer to deviate from the
allocation<00:03:55.879><c> and</c><00:03:56.079><c> create</c><00:03:56.400><c> their</c><00:03:56.599><c> own</c><00:03:57.040><c> block</c>

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allocation and create their own block
 

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allocation and create their own block
together<00:03:59.159><c> because</c><00:03:59.519><c> if</c><00:03:59.879><c> if</c><00:04:00.040><c> they</c><00:04:00.159><c> can</c><00:04:00.439><c> they</c>

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together because if if they can they
 

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together because if if they can they
will<00:04:01.920><c> and</c><00:04:02.040><c> so</c><00:04:02.319><c> we</c><00:04:02.959><c> need</c><00:04:03.200><c> to</c><00:04:04.040><c> specify</c><00:04:04.720><c> the</c>

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will and so we need to specify the
 

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will and so we need to specify the
payments<00:04:05.720><c> to</c><00:04:06.680><c> all</c><00:04:07.000><c> Searchers</c><00:04:07.560><c> and</c><00:04:07.760><c> the</c>

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payments to all Searchers and the
 

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payments to all Searchers and the
validator<00:04:08.680><c> of</c><00:04:08.879><c> the</c><00:04:09.319><c> global</c>

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validator of the global
 

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validator of the global
game<00:04:11.720><c> so</c><00:04:11.959><c> there</c><00:04:12.079><c> are</c><00:04:12.959><c> nice</c><00:04:13.319><c> properties</c><00:04:13.840><c> that</c>

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game so there are nice properties that
 

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game so there are nice properties that
core<00:04:14.680><c> has</c><00:04:15.000><c> first</c><00:04:15.200><c> of</c><00:04:15.360><c> all</c><00:04:15.959><c> it's</c><00:04:16.959><c> uh</c><00:04:17.239><c> always</c><00:04:17.600><c> non</c>

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core has first of all it's uh always non
 

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core has first of all it's uh always non
empty<00:04:18.199><c> you</c><00:04:18.320><c> always</c><00:04:18.600><c> have</c><00:04:18.840><c> one</c><00:04:19.040><c> solution</c><00:04:19.759><c> in</c>

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empty you always have one solution in
 

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empty you always have one solution in
particular<00:04:20.400><c> you</c><00:04:20.560><c> can</c><00:04:20.799><c> give</c><00:04:20.959><c> all</c><00:04:21.120><c> the</c><00:04:21.280><c> value</c><00:04:21.519><c> to</c>

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particular you can give all the value to
 

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particular you can give all the value to
the

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the
 

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the
validator<00:04:23.400><c> but</c><00:04:23.639><c> of</c><00:04:23.880><c> course</c><00:04:24.160><c> there</c><00:04:24.280><c> are</c><00:04:25.120><c> this</c>

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validator but of course there are this
 

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validator but of course there are this
would<00:04:25.479><c> be</c><00:04:26.199><c> very</c><00:04:26.479><c> unfair</c><00:04:26.919><c> to</c><00:04:27.680><c> Searchers</c><00:04:28.680><c> and</c>

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would be very unfair to Searchers and
 

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would be very unfair to Searchers and
there<00:04:29.240><c> are</c><00:04:29.440><c> other</c><00:04:29.840><c> core</c><00:04:30.160><c> Solutions</c><00:04:30.680><c> too</c><00:04:31.199><c> often</c>

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there are other core Solutions too often
 

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there are other core Solutions too often
but<00:04:31.800><c> not</c><00:04:32.039><c> always</c><00:04:32.759><c> so</c><00:04:32.960><c> for</c><00:04:33.120><c> example</c><00:04:33.440><c> there</c><00:04:33.520><c> are</c>

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but not always so for example there are
 

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but not always so for example there are
cores<00:04:34.120><c> such</c><00:04:34.360><c> that</c><00:04:35.080><c> Searchers</c><00:04:35.680><c> capture</c><00:04:36.000><c> all</c>

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cores such that Searchers capture all
 

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cores such that Searchers capture all
the

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the
 

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the
value<00:04:38.039><c> and</c><00:04:38.280><c> if</c><00:04:38.680><c> we</c><00:04:38.919><c> have</c><00:04:39.759><c> uh</c><00:04:39.919><c> additive</c><00:04:40.720><c> value</c>

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value and if we have uh additive value
 

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value and if we have uh additive value
over<00:04:41.360><c> the</c><00:04:41.520><c> bundles</c><00:04:42.000><c> then</c><00:04:42.840><c> we</c><00:04:43.120><c> actually</c><00:04:43.520><c> have</c>

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over the bundles then we actually have
 

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over the bundles then we actually have
uh<00:04:44.639><c> nice</c><00:04:45.120><c> characterization</c><00:04:46.120><c> of</c><00:04:46.280><c> the</c>

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uh nice characterization of the
 

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uh nice characterization of the
core<00:04:48.080><c> so</c><00:04:48.240><c> to</c><00:04:48.440><c> make</c><00:04:48.600><c> it</c><00:04:48.759><c> more</c><00:04:49.000><c> interesting</c><00:04:49.479><c> we</c>

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core so to make it more interesting we
 

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core so to make it more interesting we
look<00:04:49.800><c> at</c><00:04:50.000><c> the</c><00:04:50.520><c> St</c><00:04:50.840><c> stochastic</c><00:04:51.680><c> setting</c><00:04:52.560><c> where</c>

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look at the St stochastic setting where
 

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look at the St stochastic setting where
we<00:04:52.960><c> have</c><00:04:53.240><c> a</c><00:04:53.400><c> number</c><00:04:53.800><c> of</c><00:04:54.560><c> opportunities</c>

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we have a number of opportunities
 

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we have a number of opportunities
denoted<00:04:56.039><c> by</c><00:04:56.199><c> m</c><00:04:56.520><c> and</c><00:04:56.680><c> number</c><00:04:56.880><c> of</c><00:04:57.000><c> searches</c>

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denoted by m and number of searches
 

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denoted by m and number of searches
denoted<00:04:57.880><c> by</c><00:04:58.039><c> n</c><00:04:58.880><c> and</c><00:04:59.800><c> each</c><00:05:00.320><c> Searcher</c><00:05:01.320><c> generates</c>

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denoted by n and each Searcher generates
 

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denoted by n and each Searcher generates
some<00:05:02.440><c> value</c><00:05:02.759><c> for</c><00:05:03.000><c> each</c><00:05:03.400><c> opportunity</c><00:05:03.960><c> so</c><00:05:04.160><c> we</c>

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some value for each opportunity so we
 

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some value for each opportunity so we
have<00:05:04.520><c> this</c><00:05:05.000><c> Matrix</c><00:05:06.000><c> and</c><00:05:06.360><c> by</c><00:05:07.199><c> P</c><00:05:07.520><c> we</c><00:05:07.800><c> know</c><00:05:07.960><c> the</c>

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have this Matrix and by P we know the
 

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have this Matrix and by P we know the
probability<00:05:09.520><c> that</c><00:05:09.800><c> each</c><00:05:10.160><c> Searcher</c><00:05:10.680><c> finds</c>

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probability that each Searcher finds
 

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probability that each Searcher finds
each<00:05:11.880><c> opportunity</c><00:05:12.880><c> okay</c><00:05:13.280><c> then</c><00:05:13.759><c> we</c><00:05:14.199><c> have</c><00:05:15.199><c> very</c>

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each opportunity okay then we have very
 

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each opportunity okay then we have very
nice

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nice
 

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nice
um<00:05:18.639><c> simple</c><00:05:19.280><c> result</c><00:05:19.680><c> that</c><00:05:19.960><c> as</c><00:05:20.080><c> soon</c><00:05:20.400><c> as</c><00:05:21.400><c> uh</c>

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um simple result that as soon as uh
 

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um simple result that as soon as uh
probability<00:05:22.520><c> slightly</c><00:05:23.039><c> high</c><00:05:23.440><c> so</c><00:05:23.680><c> it's</c><00:05:23.960><c> larger</c>

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probability slightly high so it's larger
 

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probability slightly high so it's larger
than<00:05:24.600><c> this</c><00:05:24.759><c> to</c><00:05:25.120><c> log</c><00:05:25.360><c> n</c><00:05:25.600><c> divided</c><00:05:26.080><c> by</c><00:05:26.560><c> n</c><00:05:27.039><c> and</c>

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than this to log n divided by n and
 

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than this to log n divided by n and
there<00:05:27.919><c> there</c><00:05:28.039><c> are</c><00:05:28.199><c> not</c><00:05:28.479><c> too</c><00:05:28.720><c> many</c>

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there there are not too many
 

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there there are not too many
opportunities<00:05:29.840><c> so</c><00:05:30.000><c> m</c><00:05:30.120><c> is</c><00:05:30.280><c> less</c><00:05:30.479><c> than</c><00:05:30.919><c> and</c><00:05:31.160><c> then</c>

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opportunities so m is less than and then
 

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opportunities so m is less than and then
with<00:05:31.479><c> high</c><00:05:31.720><c> probability</c><00:05:32.240><c> the</c><00:05:32.479><c> validator</c>

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with high probability the validator
 

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with high probability the validator
captures<00:05:33.560><c> everything</c><00:05:34.280><c> and</c><00:05:34.520><c> this</c><00:05:34.919><c> can</c><00:05:35.160><c> be</c><00:05:35.720><c> in</c>

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captures everything and this can be in
 

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captures everything and this can be in
particular<00:05:36.960><c> uh</c><00:05:37.120><c> empirically</c><00:05:38.000><c> checked</c><00:05:39.000><c> in</c><00:05:39.360><c> in</c>

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particular uh empirically checked in in
 

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particular uh empirically checked in in
the<00:05:40.680><c> data</c><00:05:41.680><c> so</c><00:05:42.160><c> thank</c><00:05:42.360><c> you</c><00:05:42.520><c> for</c><00:05:42.759><c> your</c><00:05:43.479><c> attention</c>

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the data so thank you for your attention
 

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the data so thank you for your attention
happy<00:05:44.680><c> to</c><00:05:44.840><c> answer</c><00:05:45.120><c> your</c>

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happy to answer your
 

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happy to answer your
questions<00:05:48.000><c> yeah</c><00:05:48.479><c> uh</c><00:05:48.680><c> thank</c><00:05:48.840><c> you</c><00:05:48.960><c> very</c><00:05:49.160><c> much</c><00:05:49.759><c> so</c>

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questions yeah uh thank you very much so
 

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questions yeah uh thank you very much so
um<00:05:50.720><c> I</c><00:05:50.880><c> posted</c><00:05:51.479><c> one</c><00:05:51.759><c> question</c><00:05:52.479><c> u</c><00:05:52.720><c> i</c><00:05:52.840><c> wonder</c><00:05:53.840><c> I</c>

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um I posted one question u i wonder I
 

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um I posted one question u i wonder I
wonder<00:05:54.240><c> if</c><00:05:54.360><c> you</c><00:05:54.639><c> know</c><00:05:54.880><c> how</c><00:05:55.039><c> many</c><00:05:55.319><c> search</c>

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wonder if you know how many search
 

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wonder if you know how many search
providers<00:05:56.120><c> are</c><00:05:56.280><c> currently</c><00:05:56.639><c> in</c><00:05:56.840><c> ethereum</c>

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providers are currently in ethereum
 

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providers are currently in ethereum
ecosystem<00:05:58.800><c> So</c><00:05:59.120><c> currently</c><00:05:59.960><c> today</c><00:06:00.400><c> I</c><00:06:00.479><c> don't</c>

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ecosystem So currently today I don't
 

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ecosystem So currently today I don't
know<00:06:01.639><c> but</c><00:06:02.160><c> uh</c><00:06:02.440><c> it's</c><00:06:02.639><c> in</c><00:06:02.960><c> the</c><00:06:03.759><c> order</c><00:06:04.120><c> of</c>

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know but uh it's in the order of
 

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know but uh it's in the order of
hundreds<00:06:05.479><c> hundreds</c><00:06:06.160><c> yes</c><00:06:06.759><c> okay</c><00:06:07.759><c> and</c><00:06:08.000><c> uh</c><00:06:08.160><c> we</c>

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hundreds hundreds yes okay and uh we
 

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hundreds hundreds yes okay and uh we
have<00:06:08.440><c> one</c><00:06:08.560><c> more</c><00:06:09.000><c> question</c><00:06:10.000><c> how</c><00:06:10.160><c> do</c><00:06:10.319><c> you</c><00:06:10.479><c> know</c>

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have one more question how do you know
 

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have one more question how do you know
that<00:06:11.280><c> the</c><00:06:11.440><c> core</c><00:06:11.800><c> is</c><00:06:12.000><c> non</c><00:06:12.319><c> empty</c><00:06:12.919><c> and</c><00:06:13.560><c> this</c><00:06:13.720><c> is</c>

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that the core is non empty and this is
 

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that the core is non empty and this is
usually<00:06:14.479><c> requires</c><00:06:15.120><c> strong</c>

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usually requires strong
 

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usually requires strong
assumptions<00:06:17.360><c> so</c><00:06:17.639><c> we</c><00:06:17.800><c> know</c><00:06:18.160><c> because</c><00:06:18.560><c> if</c><00:06:18.680><c> you</c>

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assumptions so we know because if you
 

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assumptions so we know because if you
give<00:06:19.120><c> all</c><00:06:19.280><c> the</c><00:06:19.479><c> value</c><00:06:19.800><c> to</c><00:06:20.000><c> validator</c><00:06:20.680><c> it</c>

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give all the value to validator it
 

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give all the value to validator it
satisfies<00:06:21.479><c> all</c><00:06:21.680><c> these</c><00:06:22.039><c> inequalities</c><00:06:22.759><c> that</c>

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satisfies all these inequalities that
 

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satisfies all these inequalities that
core

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core
 

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core
requires<00:06:24.880><c> it's</c><00:06:25.039><c> very</c><00:06:25.240><c> easy</c><00:06:25.440><c> to</c><00:06:25.639><c> check</c><00:06:26.479><c> and</c>

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requires it's very easy to check and
 

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requires it's very easy to check and
strong<00:06:27.720><c> assumption</c><00:06:28.240><c> is</c><00:06:28.479><c> that</c><00:06:29.880><c> what</c><00:06:30.039><c> you</c><00:06:30.120><c> may</c>

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strong assumption is that what you may
 

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strong assumption is that what you may
refer<00:06:30.639><c> as</c><00:06:30.960><c> strong</c><00:06:31.160><c> assumption</c><00:06:31.599><c> is</c><00:06:31.759><c> that</c>

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refer as strong assumption is that
 

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refer as strong assumption is that
validator<00:06:33.080><c> validator</c><00:06:33.680><c> can</c><00:06:33.880><c> block</c><00:06:34.520><c> any</c><00:06:34.800><c> or</c>

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validator validator can block any or
 

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validator validator can block any or
veto<00:06:35.840><c> any</c>

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veto any
 

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veto any
Coalition<00:06:38.319><c> so</c><00:06:39.080><c> that</c><00:06:39.479><c> that</c><00:06:39.639><c> has</c><00:06:39.759><c> a</c><00:06:39.960><c> veto</c><00:06:40.319><c> power</c>

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Coalition so that that has a veto power
 

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Coalition so that that has a veto power
and<00:06:40.960><c> that's</c><00:06:41.199><c> what</c><00:06:41.560><c> that's</c><00:06:41.759><c> why</c><00:06:42.000><c> core</c><00:06:42.240><c> is</c>

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and that's what that's why core is
 

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and that's what that's why core is
nonempty<00:06:44.199><c> and</c><00:06:44.360><c> in</c><00:06:44.479><c> particular</c><00:06:44.880><c> we</c><00:06:45.039><c> give</c><00:06:45.319><c> exact</c>

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nonempty and in particular we give exact
 

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nonempty and in particular we give exact
uh<00:06:48.280><c> example</c><00:06:49.280><c> of</c><00:06:49.440><c> a</c>

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uh example of a
 

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uh example of a
core<00:06:51.319><c> uh</c><00:06:51.639><c> okay</c><00:06:52.039><c> uh</c><00:06:52.199><c> thank</c><00:06:52.360><c> you</c><00:06:52.520><c> very</c><00:06:52.720><c> much</c>

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core uh okay uh thank you very much
 

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core uh okay uh thank you very much
please<00:06:53.800><c> give</c><00:06:53.960><c> a</c><00:06:54.120><c> round</c><00:06:54.319><c> of</c><00:06:54.479><c> applause</c><00:06:54.759><c> to</c><00:06:54.840><c> our</c>

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speaker<00:06:59.039><c> thank</c>

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speaker thank
 

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speaker thank
so