41,359 research outputs found
Computing the optimal distributionally-robust strategy to commit to
The Stackelberg game model, where a leader commits to a strategy and the
follower best responds, has found widespread application, particularly to
security problems. In the security setting, the goal is for the leader to
compute an optimal strategy to commit to, in order to protect some asset. In
many of these applications, the parameters of the follower utility model are
not known with certainty. Distributionally-robust optimization addresses this
issue by allowing a distribution over possible model parameters, where this
distribution comes from a set of possible distributions. The goal is to
maximize the expected utility with respect to the worst-case distribution. We
initiate the study of distributionally-robust models for computing the optimal
strategy to commit to. We consider the case of normal-form games with
uncertainty about the follower utility model. Our main theoretical result is to
show that a distributionally-robust Stackelberg equilibrium always exists
across a wide array of uncertainty models. For the case of a finite set of
possible follower utility functions we present two algorithms to compute a
distributionally-robust strong Stackelberg equilibrium (DRSSE) using
mathematical programs. Next, in the general case where there is an infinite
number of possible follower utility functions and the uncertainty is
represented by a Wasserstein ball around a finitely-supported nominal
distribution, we give an incremental mixed-integer-programming-based algorithm
for computing the optimal distributionally-robust strategy. Experiments
substantiate the tractability of our algorithm on a classical Stackelberg game,
showing that our approach scales to medium-sized games
Stackelberg Equilibria in Normal-Form Games with Sequential Strategies
Ve Stackelbergových hrách se musí jeden z agentů přihlásit ke své strategii ještě před tím, než ostatní hráči spočítají své strategie. To jim dává možnost hrát svou nejlepší strategii proti prvnímu hráči. Standardní modely výpočtu optimální strategie prvního hráče v sekvenčních hrách jsou výpočetně náročné. V této práci se zaměříme na Stackelbergovy hry a jejich řešení ve hrách v normální formě se sekvenčními strategiemi, což je zjednodušená forma sekvenční hry, v níž žádný z hráčů nemá v průběhu hry žádné informace o akcích svých protihráčů.In Stackelberg games, one agent must commit to a strategy before the other agents compute their strategies, allowing them to always play the best response to first player's strategy. Standard models of computing optimal strategy of the first player in sequential games are challenging to compute. In this work, we will focus on Stackelberg games and their solution in normal-form games with sequential strategies, which is a simplified form of a sequential games, in which the players have no information about actions of their opponents throughout the game
The Transactional Conflict Problem
The transactional conflict problem arises in transactional systems whenever
two or more concurrent transactions clash on a data item.
While the standard solution to such conflicts is to immediately abort one of
the transactions, some practical systems consider the alternative of delaying
conflict resolution for a short interval, which may allow one of the
transactions to commit. The challenge in the transactional conflict problem is
to choose the optimal length of this delay interval so as to minimize the
overall running time penalty for the conflicting transactions. In this paper,
we propose a family of optimal online algorithms for the transactional conflict
problem.
Specifically, we consider variants of this problem which arise in different
implementations of transactional systems, namely "requestor wins" and
"requestor aborts" implementations: in the former, the recipient of a coherence
request is aborted, whereas in the latter, it is the requestor which has to
abort. Both strategies are implemented by real systems.
We show that the requestor aborts case can be reduced to a classic instance
of the ski rental problem, while the requestor wins case leads to a new version
of this classical problem, for which we derive optimal deterministic and
randomized algorithms.
Moreover, we prove that, under a simplified adversarial model, our algorithms
are constant-competitive with the offline optimum in terms of throughput.
We validate our algorithmic results empirically through a hardware simulation
of hardware transactional memory (HTM), showing that our algorithms can lead to
non-trivial performance improvements for classic concurrent data structures
Robust Stackelberg Equilibria in Extensive-Form Games and Extension to Limited Lookahead
Stackelberg equilibria have become increasingly important as a solution
concept in computational game theory, largely inspired by practical problems
such as security settings. In practice, however, there is typically uncertainty
regarding the model about the opponent. This paper is, to our knowledge, the
first to investigate Stackelberg equilibria under uncertainty in extensive-form
games, one of the broadest classes of game. We introduce robust Stackelberg
equilibria, where the uncertainty is about the opponent's payoffs, as well as
ones where the opponent has limited lookahead and the uncertainty is about the
opponent's node evaluation function. We develop a new mixed-integer program for
the deterministic limited-lookahead setting. We then extend the program to the
robust setting for Stackelberg equilibrium under unlimited and under limited
lookahead by the opponent. We show that for the specific case of interval
uncertainty about the opponent's payoffs (or about the opponent's node
evaluations in the case of limited lookahead), robust Stackelberg equilibria
can be computed with a mixed-integer program that is of the same asymptotic
size as that for the deterministic setting.Comment: Published at AAAI1
Imitative Follower Deception in Stackelberg Games
Information uncertainty is one of the major challenges facing applications of
game theory. In the context of Stackelberg games, various approaches have been
proposed to deal with the leader's incomplete knowledge about the follower's
payoffs, typically by gathering information from the leader's interaction with
the follower. Unfortunately, these approaches rely crucially on the assumption
that the follower will not strategically exploit this information asymmetry,
i.e., the follower behaves truthfully during the interaction according to their
actual payoffs. As we show in this paper, the follower may have strong
incentives to deceitfully imitate the behavior of a different follower type
and, in doing this, benefit significantly from inducing the leader into
choosing a highly suboptimal strategy. This raises a fundamental question: how
to design a leader strategy in the presence of a deceitful follower? To answer
this question, we put forward a basic model of Stackelberg games with
(imitative) follower deception and show that the leader is indeed able to
reduce the loss due to follower deception with carefully designed policies. We
then provide a systematic study of the problem of computing the optimal leader
policy and draw a relatively complete picture of the complexity landscape;
essentially matching positive and negative complexity results are provided for
natural variants of the model. Our intractability results are in sharp contrast
to the situation with no deception, where the leader's optimal strategy can be
computed in polynomial time, and thus illustrate the intrinsic difficulty of
handling follower deception. Through simulations we also examine the benefit of
considering follower deception in randomly generated games
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