3,215 research outputs found
Multi-round Master-Worker Computing: a Repeated Game Approach
We consider a computing system where a master processor assigns tasks for
execution to worker processors through the Internet. We model the workers
decision of whether to comply (compute the task) or not (return a bogus result
to save the computation cost) as a mixed extension of a strategic game among
workers. That is, we assume that workers are rational in a game-theoretic
sense, and that they randomize their strategic choice. Workers are assigned
multiple tasks in subsequent rounds. We model the system as an infinitely
repeated game of the mixed extension of the strategic game. In each round, the
master decides stochastically whether to accept the answer of the majority or
verify the answers received, at some cost. Incentives and/or penalties are
applied to workers accordingly. Under the above framework, we study the
conditions in which the master can reliably obtain tasks results, exploiting
that the repeated games model captures the effect of long-term interaction.
That is, workers take into account that their behavior in one computation will
have an effect on the behavior of other workers in the future. Indeed, should a
worker be found to deviate from some agreed strategic choice, the remaining
workers would change their own strategy to penalize the deviator. Hence, being
rational, workers do not deviate. We identify analytically the parameter
conditions to induce a desired worker behavior, and we evaluate experi-
mentally the mechanisms derived from such conditions. We also compare the
performance of our mechanisms with a previously known multi-round mechanism
based on reinforcement learning.Comment: 21 pages, 3 figure
An Approximate Subgame-Perfect Equilibrium Computation Technique for Repeated Games
This paper presents a technique for approximating, up to any precision, the
set of subgame-perfect equilibria (SPE) in discounted repeated games. The
process starts with a single hypercube approximation of the set of SPE. Then
the initial hypercube is gradually partitioned on to a set of smaller adjacent
hypercubes, while those hypercubes that cannot contain any point belonging to
the set of SPE are simultaneously withdrawn.
Whether a given hypercube can contain an equilibrium point is verified by an
appropriate mathematical program. Three different formulations of the algorithm
for both approximately computing the set of SPE payoffs and extracting players'
strategies are then proposed: the first two that do not assume the presence of
an external coordination between players, and the third one that assumes a
certain level of coordination during game play for convexifying the set of
continuation payoffs after any repeated game history.
A special attention is paid to the question of extracting players' strategies
and their representability in form of finite automata, an important feature for
artificial agent systems.Comment: 26 pages, 13 figures, 1 tabl
Repeated Multimarket Contact with Private Monitoring: A Belief-Free Approach
This paper studies repeated games where two players play multiple duopolistic
games simultaneously (multimarket contact). A key assumption is that each
player receives a noisy and private signal about the other's actions (private
monitoring or observation errors). There has been no game-theoretic support
that multimarket contact facilitates collusion or not, in the sense that more
collusive equilibria in terms of per-market profits exist than those under a
benchmark case of one market. An equilibrium candidate under the benchmark case
is belief-free strategies. We are the first to construct a non-trivial class of
strategies that exhibits the effect of multimarket contact from the
perspectives of simplicity and mild punishment. Strategies must be simple
because firms in a cartel must coordinate each other with no communication.
Punishment must be mild to an extent that it does not hurt even the minimum
required profits in the cartel. We thus focus on two-state automaton strategies
such that the players are cooperative in at least one market even when he or
she punishes a traitor. Furthermore, we identify an additional condition
(partial indifference), under which the collusive equilibrium yields the
optimal payoff.Comment: Accepted for the 9th Intl. Symp. on Algorithmic Game Theory; An
extended version was accepted at the Thirty-Fourth AAAI Conference on
Artificial Intelligence (AAAI-20
Distributed Computing with Adaptive Heuristics
We use ideas from distributed computing to study dynamic environments in
which computational nodes, or decision makers, follow adaptive heuristics (Hart
2005), i.e., simple and unsophisticated rules of behavior, e.g., repeatedly
"best replying" to others' actions, and minimizing "regret", that have been
extensively studied in game theory and economics. We explore when convergence
of such simple dynamics to an equilibrium is guaranteed in asynchronous
computational environments, where nodes can act at any time. Our research
agenda, distributed computing with adaptive heuristics, lies on the borderline
of computer science (including distributed computing and learning) and game
theory (including game dynamics and adaptive heuristics). We exhibit a general
non-termination result for a broad class of heuristics with bounded
recall---that is, simple rules of behavior that depend only on recent history
of interaction between nodes. We consider implications of our result across a
wide variety of interesting and timely applications: game theory, circuit
design, social networks, routing and congestion control. We also study the
computational and communication complexity of asynchronous dynamics and present
some basic observations regarding the effects of asynchrony on no-regret
dynamics. We believe that our work opens a new avenue for research in both
distributed computing and game theory.Comment: 36 pages, four figures. Expands both technical results and discussion
of v1. Revised version will appear in the proceedings of Innovations in
Computer Science 201
Fashion, Cooperation, and Social Interactions
Fashion plays such a crucial rule in the evolution of culture and society
that it is regarded as a second nature to the human being. Also, its impact on
economy is quite nontrivial. On what is fashionable, interestingly, there are
two viewpoints that are both extremely widespread but almost opposite:
conformists think that what is popular is fashionable, while rebels believe
that being different is the essence. Fashion color is fashionable in the first
sense, and Lady Gaga in the second. We investigate a model where the population
consists of the afore-mentioned two groups of people that are located on social
networks (a spatial cellular automata network and small-world networks). This
model captures two fundamental kinds of social interactions (coordination and
anti-coordination) simultaneously, and also has its own interest to game
theory: it is a hybrid model of pure competition and pure cooperation. This is
true because when a conformist meets a rebel, they play the zero sum matching
pennies game, which is pure competition. When two conformists (rebels) meet,
they play the (anti-) coordination game, which is pure cooperation. Simulation
shows that simple social interactions greatly promote cooperation: in most
cases people can reach an extraordinarily high level of cooperation, through a
selfish, myopic, naive, and local interacting dynamic (the best response
dynamic). We find that degree of synchronization also plays a critical role,
but mostly on the negative side. Four indices, namely cooperation degree,
average satisfaction degree, equilibrium ratio and complete ratio, are defined
and applied to measure people's cooperation levels from various angles. Phase
transition, as well as emergence of many interesting geographic patterns in the
cellular automata network, is also observed.Comment: 21 pages, 12 figure
Cycles in adversarial regularized learning
Regularized learning is a fundamental technique in online optimization,
machine learning and many other fields of computer science. A natural question
that arises in these settings is how regularized learning algorithms behave
when faced against each other. We study a natural formulation of this problem
by coupling regularized learning dynamics in zero-sum games. We show that the
system's behavior is Poincar\'e recurrent, implying that almost every
trajectory revisits any (arbitrarily small) neighborhood of its starting point
infinitely often. This cycling behavior is robust to the agents' choice of
regularization mechanism (each agent could be using a different regularizer),
to positive-affine transformations of the agents' utilities, and it also
persists in the case of networked competition, i.e., for zero-sum polymatrix
games.Comment: 22 pages, 4 figure
A survey of random processes with reinforcement
The models surveyed include generalized P\'{o}lya urns, reinforced random
walks, interacting urn models, and continuous reinforced processes. Emphasis is
on methods and results, with sketches provided of some proofs. Applications are
discussed in statistics, biology, economics and a number of other areas.Comment: Published at http://dx.doi.org/10.1214/07-PS094 in the Probability
Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Applications of Repeated Games in Wireless Networks: A Survey
A repeated game is an effective tool to model interactions and conflicts for
players aiming to achieve their objectives in a long-term basis. Contrary to
static noncooperative games that model an interaction among players in only one
period, in repeated games, interactions of players repeat for multiple periods;
and thus the players become aware of other players' past behaviors and their
future benefits, and will adapt their behavior accordingly. In wireless
networks, conflicts among wireless nodes can lead to selfish behaviors,
resulting in poor network performances and detrimental individual payoffs. In
this paper, we survey the applications of repeated games in different wireless
networks. The main goal is to demonstrate the use of repeated games to
encourage wireless nodes to cooperate, thereby improving network performances
and avoiding network disruption due to selfish behaviors. Furthermore, various
problems in wireless networks and variations of repeated game models together
with the corresponding solutions are discussed in this survey. Finally, we
outline some open issues and future research directions.Comment: 32 pages, 15 figures, 5 tables, 168 reference
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