Searcher Competition in Block Building by Akaki Mamageishvili | Devcon SEA

hello everyone welcome to the presentation so today I will talk about Searcher competition in Block building so this is the paper title and it was coauthored with kristofh Schlegel and Dani from flash pods and Ben sudakov from eth and I'm a researcher at of chain labs so motivation was me and we we know that there are many forms of me extraction and I'm listing only the most popular ones here so there is this sexex Arbitrage background sandwiches and liquidation and in each form there are also many different spe specializations that you can take as a Searcher and here the main point is that there are many different types so Searchers are different in their specializations so it create some kind of heterogeneity among Searchers so we tried to model this uh with the tools of Game Theory and for that we need to identify who are the players and the main player is validator or a proposer that proposes the next blog and then there are these specialized arbitragers that in the ethereum setting are called Searchers and in current market there are also builders that aggregate Searchers and also men public manol transactions but we are ignoring um it for this uh simplified game because for us the fundamental players are Searchers and the proposer here we denote the set of Searchers by S that we can identify by their addresses then Searchers submit their bundles of transactions to include uh in the block and typically now they send it to um block Builder but in principle they could have sent it to a proposer then from these bundles there are some uh in these bundles there are some conflicts so you cannot build the block that is the union of all bundles so you can build many different blocks for a build block Searcher generates some value and validator or the proposer also generates a value so these are the uh smallest building blocks of our game so we are abstracting away from all part particular mechanisms how they interact and that includes Builders and we only try to understand who will get how much among these players depending on their bundles so for this we are using uh tools from Cooperative Game Theory and for that we need to define a value of a coalition and value of a coalition is the best block that the Searchers in this Coalition uh build okay if uh there is no uh proposer in the Coalition then the value is zero so proposer or validator can uh block any or veto any block so you need to agree uh with a proposer the The Searchers and this already gives a coalitional transferable utility game and in these games the most natural solution we think is the core and uh let me Define what is core it's very simple and intuitive uh the core solution gives uh payoffs to all players so that no uh Coalition of players prefer to deviate from the allocation and create their own block together because if if they can they will and so we need to specify the payments to all Searchers and the validator of the global game so there are nice properties that core has first of all it's uh always non empty you always have one solution in particular you can give all the value to the validator but of course there are this would be very unfair to Searchers and there are other core Solutions too often but not always so for example there are cores such that Searchers capture all the value and if we have uh additive value over the bundles then we actually have uh nice characterization of the core so to make it more interesting we look at the St stochastic setting where we have a number of opportunities denoted by m and number of searches denoted by n and each Searcher generates some value for each opportunity so we have this Matrix and by P we know the probability that each Searcher finds each opportunity okay then we have very nice um simple result that as soon as uh probability slightly high so it's larger than this to log n divided by n and there there are not too many opportunities so m is less than and then with high probability the validator captures everything and this can be in particular uh empirically checked in in the data so thank you for your attention happy to answer your questions yeah uh thank you very much so um I posted one question u i wonder I wonder if you know how many search providers are currently in ethereum ecosystem So currently today I don't know but uh it's in the order of hundreds hundreds yes okay and uh we have one more question how do you know that the core is non empty and this is usually requires strong assumptions so we know because if you give all the value to validator it satisfies all these inequalities that core requires it's very easy to check and strong assumption is that what you may refer as strong assumption is that validator validator can block any or veto any Coalition so that that has a veto power and that's what that's why core is nonempty and in particular we give exact uh example of a core uh okay uh thank you very much please give a round of applause to our speaker thank so