57 research outputs found
Equilibrium Analysis of Customer Attraction Games
We introduce a game model called "customer attraction game" to demonstrate
the competition among online content providers. In this model, customers
exhibit interest in various topics. Each content provider selects one topic and
benefits from the attracted customers. We investigate both symmetric and
asymmetric settings involving agents and customers. In the symmetric setting,
the existence of pure Nash equilibrium (PNE) is guaranteed, but finding a PNE
is PLS-complete. To address this, we propose a fully polynomial time
approximation scheme to identify an approximate PNE. Moreover, the tight Price
of Anarchy (PoA) is established. In the asymmetric setting, we show the
nonexistence of PNE in certain instances and establish that determining its
existence is NP-hard. Nevertheless, we prove the existence of an approximate
PNE. Additionally, when agents select topics sequentially, we demonstrate that
finding a subgame-perfect equilibrium is PSPACE-hard. Furthermore, we present
the sequential PoA for the two-agent setting
Competition among Parallel Contests
We investigate the model of multiple contests held in parallel, where each
contestant selects one contest to join and each contest designer decides the
prize structure to compete for the participation of contestants. We first
analyze the strategic behaviors of contestants and completely characterize the
symmetric Bayesian Nash equilibrium. As for the strategies of contest
designers, when other designers' strategies are known, we show that computing
the best response is NP-hard and propose a fully polynomial time approximation
scheme (FPTAS) to output the -approximate best response. When other
designers' strategies are unknown, we provide a worst case analysis on one
designer's strategy. We give an upper bound on the utility of any strategy and
propose a method to construct a strategy whose utility can guarantee a constant
ratio of this upper bound in the worst case.Comment: Accepted by the 18th Conference on Web and Internet Economics (WINE
2022
On Tightness of the Tsaknakis-Spirakis Algorithm for Approximate Nash Equilibrium
Finding the minimum approximate ratio for Nash equilibrium of bi-matrix games
has derived a series of studies, started with 3/4, followed by 1/2, 0.38 and
0.36, finally the best approximate ratio of 0.3393 by Tsaknakis and Spirakis
(TS algorithm for short). Efforts to improve the results remain not successful
in the past 14 years. This work makes the first progress to show that the bound
of 0.3393 is indeed tight for the TS algorithm. Next, we characterize all
possible tight game instances for the TS algorithm. It allows us to conduct
extensive experiments to study the nature of the TS algorithm and to compare it
with other algorithms. We find that this lower bound is not smoothed for the TS
algorithm in that any perturbation on the initial point may deviate away from
this tight bound approximate solution. Other approximate algorithms such as
Fictitious Play and Regret Matching also find better approximate solutions.
However, the new distributed algorithm for approximate Nash equilibrium by
Czumaj et al. performs consistently at the same bound of 0.3393. This proves
our lower bound instances generated against the TS algorithm can serve as a
benchmark in design and analysis of approximate Nash equilibrium algorithms
On the complexity of computing Markov perfect equilibrium in general-sum stochastic games
Similar to the role of Markov decision processes in reinforcement learning, Markov games (also called stochastic games) lay down the foundation for the study of multi-agent reinforcement learning and sequential agent interactions. We introduce approximate Markov perfect equilibrium as a solution to the computational problem of finite-state stochastic games repeated in the infinite horizon and prove its PPAD-completeness. This solution concept preserves the Markov perfect property and opens up the possibility for the success of multi-agent reinforcement learning algorithms on static two-player games to be extended to multi-agent dynamic games, expanding the reign of the PPAD-complete class
MEV Makes Everyone Happy under Greedy Sequencing Rule
Trading through decentralized exchanges (DEXs) has become crucial in today's
blockchain ecosystem, enabling users to swap tokens efficiently and
automatically. However, the capacity of miners to strategically order
transactions has led to exploitative practices (e.g., front-running attacks,
sandwich attacks) and gain substantial Maximal Extractable Value (MEV) for
their own advantage. To mitigate such manipulation, Ferreira and Parkes
recently proposed a greedy sequencing rule such that the execution price of
transactions in a block moves back and forth around the starting price.
Utilizing this sequencing rule makes it impossible for miners to conduct
sandwich attacks, consequently mitigating the MEV problem.
However, no sequencing rule can prevent miners from obtaining risk-free
profits. This paper systemically studies the computation of a miner's optimal
strategy for maximizing MEV under the greedy sequencing rule, where the utility
of miners is measured by the overall value of their token holdings. Our results
unveil a dichotomy between the no trading fee scenario, which can be optimally
strategized in polynomial time, and the scenario with a constant fraction of
trading fee, where finding the optimal strategy is proven NP-hard. The latter
represents a significant challenge for miners seeking optimal MEV.
Following the computation results, we further show a remarkable phenomenon:
Miner's optimal MEV also benefits users. Precisely, in the scenarios without
trading fees, when miners adopt the optimal strategy given by our algorithm,
all users' transactions will be executed, and each user will receive equivalent
or surpass profits compared to their expectations. This outcome provides
further support for the study and design of sequencing rules in decentralized
exchanges.Comment: 14 Pages, ACM CCS Workshop on Decentralized Finance and Security
(DeFi'23
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