109 research outputs found
Computational Results for Extensive-Form Adversarial Team Games
We provide, to the best of our knowledge, the first computational study of
extensive-form adversarial team games. These games are sequential, zero-sum
games in which a team of players, sharing the same utility function, faces an
adversary. We define three different scenarios according to the communication
capabilities of the team. In the first, the teammates can communicate and
correlate their actions both before and during the play. In the second, they
can only communicate before the play. In the third, no communication is
possible at all. We define the most suitable solution concepts, and we study
the inefficiency caused by partial or null communication, showing that the
inefficiency can be arbitrarily large in the size of the game tree.
Furthermore, we study the computational complexity of the equilibrium-finding
problem in the three scenarios mentioned above, and we provide, for each of the
three scenarios, an exact algorithm. Finally, we empirically evaluate the
scalability of the algorithms in random games and the inefficiency caused by
partial or null communication
Team-Maxmin Equilibrium: Efficiency Bounds and Algorithms
The Team-maxmin equilibrium prescribes the optimal strategies for a team of
rational players sharing the same goal and without the capability of
correlating their strategies in strategic games against an adversary. This
solution concept can capture situations in which an agent controls multiple
resources-corresponding to the team members-that cannot communicate. It is
known that such equilibrium always exists and it is unique (unless degeneracy)
and these properties make it a credible solution concept to be used in
real-world applications, especially in security scenarios. Nevertheless, to the
best of our knowledge, the Team-maxmin equilibrium is almost completely
unexplored in the literature. In this paper, we investigate bounds of
(in)efficiency of the Team-maxmin equilibrium w.r.t. the Nash equilibria and
w.r.t. the Maxmin equilibrium when the team members can play correlated
strategies. Furthermore, we study a number of algorithms to find and/or
approximate an equilibrium, discussing their theoretical guarantees and
evaluating their performance by using a standard testbed of game instances
Persuading Voters: It's Easy to Whisper, It's Hard to Speak Loud
We focus on the following natural question: is it possible to influence the
outcome of a voting process through the strategic provision of information to
voters who update their beliefs rationally? We investigate whether it is
computationally tractable to design a signaling scheme maximizing the
probability with which the sender's preferred candidate is elected. We focus on
the model recently introduced by Arieli and Babichenko (2019) (i.e., without
inter-agent externalities), and consider, as explanatory examples, -voting
rule and plurality voting. There is a sharp contrast between the case in which
private signals are allowed and the more restrictive setting in which only
public signals are allowed. In the former, we show that an optimal signaling
scheme can be computed efficiently both under a -voting rule and plurality
voting. In establishing these results, we provide two general (i.e., applicable
to settings beyond voting) contributions. Specifically, we extend a well known
result by Dughmi and Xu (2017) to more general settings, and prove that, when
the sender's utility function is anonymous, computing an optimal signaling
scheme is fixed parameter tractable w.r.t. the number of receivers' actions. In
the public signaling case, we show that the sender's optimal expected return
cannot be approximated to within any factor under a -voting rule. This
negative result easily extends to plurality voting and problems where utility
functions are anonymous
Public Bayesian persuasion: being almost optimal and almost persuasive
We study algorithmic Bayesian persuasion problems in which the principal (a.k.a. the sender) has to persuade multiple agents (a.k.a. receivers) by using public communication channels. Specifically, our model follows the multi-receiver model with no inter-agent externalities introduced by Arieli and Babichenko (J Econ Theory 182:185–217, 2019). It is known that the problem of computing a sender-optimal public persuasive signaling scheme is not approximable even in simple settings. Therefore, prior works usually focus on determining restricted classes of the problem for which efficient approximation is possible. Typically, positive results in this space amounts to finding bi-criteria approximation algorithms yielding an almost optimal and almost persuasive solution in polynomial time. In this paper, we take a different perspective and study the persuasion problem in the general setting where the space of the states of nature, the action space of the receivers, and the utility function of the sender can be arbitrary. We fully characterize the computational complexity of computing a bi-criteria approximation of an optimal public signaling scheme in such settings. In particular, we show that, assuming the Exponential Time Hypothesis, solving this problem requires at least a quasi-polynomial number of steps even in instances with simple utility functions and binary action spaces such as an election with the k-voting rule. In doing so, we prove that a relaxed version of the MAXIMUM FEASIBLE SUBSYSTEM OF LINEAR INEQUALITIES problem requires at least quasi-polynomial time to be solved. Finally, we close the gap by providing a quasi-polynomial time bi-criteria approximation algorithm for arbitrary public persuasion problems that, under mild assumptions, yields a QPTAS
Signaling in Bayesian Network Congestion Games: the Subtle Power of Symmetry
Network congestion games are a well-understood model of multi-agent strategic
interactions. Despite their ubiquitous applications, it is not clear whether it
is possible to design information structures to ameliorate the overall
experience of the network users. We focus on Bayesian games with atomic
players, where network vagaries are modeled via a (random) state of nature
which determines the costs incurred by the players. A third-party entity---the
sender---can observe the realized state of the network and exploit this
additional information to send a signal to each player. A natural question is
the following: is it possible for an informed sender to reduce the overall
social cost via the strategic provision of information to players who update
their beliefs rationally? The paper focuses on the problem of computing optimal
ex ante persuasive signaling schemes, showing that symmetry is a crucial
property for its solution. Indeed, we show that an optimal ex ante persuasive
signaling scheme can be computed in polynomial time when players are symmetric
and have affine cost functions. Moreover, the problem becomes NP-hard when
players are asymmetric, even in non-Bayesian settings
No-Regret Learning Dynamics for Extensive-Form Correlated Equilibrium
The existence of simple, uncoupled no-regret dynamics that converge to
correlated equilibria in normal-form games is a celebrated result in the theory
of multi-agent systems. Specifically, it has been known for more than 20 years
that when all players seek to minimize their internal regret in a repeated
normal-form game, the empirical frequency of play converges to a normal-form
correlated equilibrium. Extensive-form (that is, tree-form) games generalize
normal-form games by modeling both sequential and simultaneous moves, as well
as private information. Because of the sequential nature and presence of
partial information in the game, extensive-form correlation has significantly
different properties than the normal-form counterpart, many of which are still
open research directions. Extensive-form correlated equilibrium (EFCE) has been
proposed as the natural extensive-form counterpart to normal-form correlated
equilibrium. However, it was currently unknown whether EFCE emerges as the
result of uncoupled agent dynamics. In this paper, we give the first uncoupled
no-regret dynamics that converge to the set of EFCEs in -player general-sum
extensive-form games with perfect recall. First, we introduce a notion of
trigger regret in extensive-form games, which extends that of internal regret
in normal-form games. When each player has low trigger regret, the empirical
frequency of play is close to an EFCE. Then, we give an efficient
no-trigger-regret algorithm. Our algorithm decomposes trigger regret into local
subproblems at each decision point for the player, and constructs a global
strategy of the player from the local solutions at each decision point
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