8 research outputs found
Defensive Resource Allocation in Social Networks
In this work, we are interested on the analysis of competing marketing
campaigns between an incumbent who dominates the market and a challenger who
wants to enter the market. We are interested in (a) the simultaneous decision
of how many resources to allocate to their potential customers to advertise
their products for both marketing campaigns, and (b) the optimal allocation on
the situation in which the incumbent knows the entrance of the challenger and
thus can predict its response. Applying results from game theory, we
characterize these optimal strategic resource allocations for the voter model
of social networks.Comment: arXiv admin note: text overlap with arXiv:1402.538
Path Planning Problems with Side Observations-When Colonels Play Hide-and-Seek
Resource allocation games such as the famous Colonel Blotto (CB) and
Hide-and-Seek (HS) games are often used to model a large variety of practical
problems, but only in their one-shot versions. Indeed, due to their extremely
large strategy space, it remains an open question how one can efficiently learn
in these games. In this work, we show that the online CB and HS games can be
cast as path planning problems with side-observations (SOPPP): at each stage, a
learner chooses a path on a directed acyclic graph and suffers the sum of
losses that are adversarially assigned to the corresponding edges; and she then
receives semi-bandit feedback with side-observations (i.e., she observes the
losses on the chosen edges plus some others). We propose a novel algorithm,
EXP3-OE, the first-of-its-kind with guaranteed efficient running time for SOPPP
without requiring any auxiliary oracle. We provide an expected-regret bound of
EXP3-OE in SOPPP matching the order of the best benchmark in the literature.
Moreover, we introduce additional assumptions on the observability model under
which we can further improve the regret bounds of EXP3-OE. We illustrate the
benefit of using EXP3-OE in SOPPP by applying it to the online CB and HS games.Comment: Previously, this work appeared as arXiv:1911.09023 which was
mistakenly submitted as a new article (has been submitted to be withdrawn).
This is a preprint of the work published in Proceedings of the 34th AAAI
Conference on Artificial Intelligence (AAAI
Advertising Competitions in Social Networks
In the present work, we study the advertising competition of several marketing campaigns who need to determine how many resources to allocate to potential customers to advertise their products through direct marketing while taking into account that competing marketing campaigns are trying to do the same. Potential customers rank marketing campaigns according to the offers, promotions or discounts made to them. Taking into account the intrinsic value of potential customers as well as the peer influence that they exert over other potential customers we consider the network value as a measure of their importance in the market and we find an analytical expression for it.We analyze the marketing campaigns competition from a game theory point of view, finding a closed form expression of the symmetric equilibrium offer strategy for the marketing campaigns from which no campaign has any incentive to deviate. We also present several scenarios, such as Winner-takes-all and Borda, but not the only possible ones for which our results allow us to retrieve in a simple way the corresponding equilibrium strategy
Colonel Blotto and Hide-and-Seek Games as Path Planning Problems with Side Observations
Resource allocation games such as the famous Colonel Blotto (CB) and Hide-and-Seek (HS) games are often used to model a large variety of practical problems, but only in their one-shot versions. Indeed, due to their extremely large strategy space, it remains an open question how one can efficiently learn in these games. In this work, we show that the online CB and HS games can be cast as path planning problems with side-observations (SOPPP): at each stage, a learner chooses a path on a directed acyclic graph and suffers the sum of losses that are adversarially assigned to the corresponding edges; and she then receives semi-bandit feedback with side-observations (i.e., she observes the losses on the chosen edges plus some others). Then, we propose a novel algorithm, EXP3-OE, the first-of-its-kind with guaranteed efficient running time for SOPPP without requiring any auxiliary oracle. We provide an expected-regret bound of EXP3-OE in SOPPP matching the order of the best benchmark in the literature. Moreover, we introduce additional assumptions on the observability model under which we can further improve the regret bounds of EXP3-OE. We illustrate the benefit of using EXP3-OE in SOPPP by applying it to the online CB and HS games
Path Planning Problems with Side Observations---When Colonels Play Hide-and-Seek
International audienceResource allocation games such as the famous Colonel Blotto (CB) and Hide-and-Seek (HS) games are often used to model a large variety of practical problems, but only in their oneshot versions. Indeed, due to their extremely large strategy space, it remains an open question how one can efficiently learn in these games. In this work, we show that the online CB and HS games can be cast as path planning problems with side-observations (SOPPP): at each stage, a learner chooses a path on a directed acyclic graph and suffers the sum of losses that are adversarially assigned to the corresponding edges; and she then receives semi-bandit feedback with sideobservations (i.e., she observes the losses on the chosen edges plus some others). We propose a novel algorithm, EXP3-OE, the first-of-its-kind with guaranteed efficient running time for SOPPP without requiring any auxiliary oracle. We provide an expected-regret bound of EXP3-OE in SOPPP matching the order of the best benchmark in the literature. Moreover, we introduce additional assumptions on the observability model under which we can further improve the regret bounds of EXP3-OE. We illustrate the benefit of using EXP3-OE in SOPPP by applying it to the online CB and HS games
Approximate Equilibria in Non-constant-sum Colonel Blotto and Lottery Blotto Games with Large Numbers of Battlefields
In the Colonel Blotto game, two players with a fixed budget simultaneously allocate their resources across n battlefields to maximize the aggregate value gained from the battlefields where they have the higher allocation. Despite its long-standing history and important applicability, the Colonel Blotto game still lacks a complete Nash equilibrium characterization in its most general form-the non-constant-sum version with asymmetric players and heterogeneous battlefields. In this work, we propose a simply-constructed class of strategies-the independently uniform strategies-and we prove them to be approximate equilibria of the non-constant-sum Colonel Blotto game; moreover, we also characterize the approximation error according to the game's parameters. We also introduce an extension called the Lottery Blotto game, with stochastic winner-determination rules allowing more flexibility in modeling practical contexts. We prove that the proposed strategies are also approximate equilibria of the Lottery Blotto game