Search arXivSearch

arXiv · 2104.08437

Verified Double Sided Auctions for Financial Markets

Abstract

Double sided auctions are widely used in financial markets to match demand and supply. Prior works on double sided auctions have focused primarily on single quantity trade requests. We extend various notions of double sided auctions to incorporate multiple quantity trade requests and provide fully formalized matching algorithms for double sided auctions with their correctness proofs. We establish new uniqueness theorems that enable automatic detection of violations in an exchange program by comparing its output with that of a verified program. All proofs are formalized in the Coq proof assistant without adding any axiom to the system. We extract verified OCaml and Haskell programs that can be used by the exchanges and the regulators of the financial markets. We demonstrate the practical applicability of our work by running the verified program on real market data from an exchange to automatically check for violations in the exchange algorithm.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Raja Natarajan, Suneel Sarswat, Abhishek Kr Singh. 2021-04-17. Verified Double Sided Auctions for Financial Markets. https://arxiv.org/abs/2104.08437

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Learning in Structured Stackelberg Games

We initiate the study of structured Stackelberg games, a novel form of strategic interaction between a leader and a follower where contextual information can be predictive of the follower's (unknown) type. Motivated by applications such as security games and AI safety, we show how this additional structure can help the leader learn a utility-maximizing policy in both the online and distributional settings. In the online setting, we first prove that standard learning-theoretic measures of complexity do not characterize the difficulty of the leader's learning task. Notably, we find that there exists a learning-theoretic measure of complexity, analogous to the Littlestone dimension in online classification, that tightly characterizes the leader's instance-optimal regret. We term this the Stackelberg-Littlestone dimension, and leverage it to provide a provably optimal online learning algorithm. In the distributional setting, we provide analogous results by showing that two new dimensions control the sample complexity upper- and lower-bound.

cs.GT

Equilibrium and Infeasibility: A new solution concept for games

Addressing infeasibility in non-cooperative games has become an important topic, as many problems across different applications face this issue. In this paper, we propose a new solution concept for generalized games with possibly infeasible individual constraints. A solution is defined as the limit of a sequence of generalized Nash equilibria induced by games with penalty terms relaxing the individual constraints. Existence is established for a broad range of games and we provide conditions allowing to characterize a $ψ$-penalized solution as a strategy profile maximizing every player's utility over all her penalty minimizing strategies. A variation of Divide-the-Dollar serves as an illustrative example. We further establish the compatibility with the GNE and the solution to the Nash bargaining.

cs.GT

Subgame-Perfect Nash Equilibria of Plurality Voting with Abstention: a PSPACE-Completeness Result for Restricted Ballots

We consider sequential Plurality elections in which each voter may abstain or vote for a single candidate. Each voter assigns utilities to all candidates; for each voter, this induces a (weak) order over the candidates. Ties are resolved uniformly at random, and voting has a small positive cost, so that a voter prefers to abstain when their vote cannot change the election outcome. We consider a variant of this model where, for each voter, we additionally specify a prefix of her ranking, so that she is only allowed to vote for a candidate from that prefix (or abstain). We prove that for this variant of the model, deciding whether a designated candidate is among the election winners in a subgame-perfect equilibrium of the associated extensive-form game is PSPACE-complete. This partially resolves an open problem from the work of Desmedt and Elkind [2010].

cs.GT