Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2501.16291

Sequential Decision Making in Stochastic Games with Incomplete Preferences over Temporal Objectives

Abhishek Ninad Kulkarni·Jie Fu·Ufuk Topcu
View original source ↗Read source document ↗Export metadata ↓

Abstract

Ensuring that AI systems make strategic decisions aligned with the specified preferences in adversarial sequential interactions is a critical challenge for developing trustworthy AI systems, especially when the environment is stochastic and players' incomplete preferences leave some outcomes unranked. We study the problem of synthesizing preference-satisfying strategies in two-player stochastic games on graphs where players have opposite (possibly incomplete) preferences over a set of temporal goals. We represent these goals using linear temporal logic over finite traces (LTLf), which enables modeling the nuances of human preferences where temporal goals need not be mutually exclusive and comparison between some goals may be unspecified. We introduce a solution concept of non-dominated almost-sure winning, which guarantees to achieve a most preferred outcome aligned with specified preferences while maintaining robustness against the adversarial behaviors of the opponent. Our results show that strategy profiles based on this concept are Nash equilibria in the game where players are risk-averse, thus providing a practical framework for evaluating and ensuring stable, preference-aligned outcomes in the game. Using a drone delivery example, we demonstrate that our contributions offer valuable insights not only for synthesizing rational behavior under incomplete preferences but also for designing games that motivate the desired behavior from the players in adversarial conditions.

Explore related subjects

cs.GTcs.FL

Keep this discovery

BibTeXRIS

Abhishek Ninad Kulkarni, Jie Fu, Ufuk Topcu. 2025-01-27. Sequential Decision Making in Stochastic Games with Incomplete Preferences over Temporal Objectives. https://arxiv.org/abs/2501.16291

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

KEEP EXPLORING

Related papers

arXiv2026

MMS Allocation for Chores with Online Agent Arrivals

We study the fair allocation of $m$ indivisible chores to $n$ agents with subadditive cost functions arriving online in an arbitrary order. Upon an agent's arrival, we are informed of her cost function and must irrevocably assign her a set of chores. We focus on the Maximin Share (MMS) fairness notion and aim to compute an allocation in which all items are assigned, and no agent incurs a cost more than $\alpha$ times her MMS. Without any prior information about the instance (other than $n$ and $m$), we design an algorithm with a competitive ratio of $O(\min\{n, k\log^{1+\epsilon}k, \log m\})$ for any constant $\epsilon > 0$, where $k$ denotes the number of cost function types. Our bound matches the best known offline approximation guarantees for MMS under subadditive costs and is nearly optimal with respect to all three parameters: we show that even for binary additive cost functions, no online algorithm can achieve a competitive ratio of $o(\min\{n, k\log k, \log m\})$. We then consider the setting in which the $k$ cost function types are known in advance (though the realized types of arriving agents are not). For additive cost functions, we provide an algorithm with a competitive ratio of $O(\min\{\log k, \log(kn)/\log\log(kn)\})$, and show that constant-competitive algorithms do not exist for general $k$, even for the binary additive setting. For binary additive functions when $k \le n$, we propose a $3$-competitive algorithm and establish a lower bound of $2$.

cs.GT↗
arXiv2026

Truncated Noisy Best-Response Algorithms: Toward Game Theoretic Learning with Safety Guarantees

We consider a game theoretic approach to solve multi-agent coordination problems with submodular maximization objectives. It is known for such problems that the Nash equilibria for the corresponding game are always within 50% of the optimal, but that the equilibria which achieve this worst-case bound are not stable. To exploit this instability, we propose a family of algorithms which we call Truncated Noisy Best-Response (TNBR) Algorithms. These algorithms are flexibly characterized by agents asynchronously and stochastically selecting actions from a neighbourhood of their best response payoffs. We compute bounds on the recurrent classes of TNBR algorithms' associated Markov chains. Our bounds fall into two categories: first, "Performance" bounds ensure that TNBR algorithms always have a high-value recurrent state; second, "Safety" bounds ensure that TNBR algorithms never have arbitrarily-bad recurrent states. Furthermore, these two types of bounds are linked by a waterbed-like effect: every game with a poor Safety guarantee necessarily has a favorable Performance guarantee.

cs.GT↗
arXiv2026

Existence of the Core in Approval-Based Committee Elections

We settle the main open question in the theory of approval-based multi-winner elections: we show that there always exists a committee in the core. The core is a stability and group fairness concept. The proof introduces a new voting rule that optimizes an entropy-like objective function over committees and payment systems. All local optima of this objective function lie in the core, which implies that a core committee can be found in polynomial time.

cs.GT↗