A Game-Theoretic Analysis of the Off-Switch Game

The off-switch game is a game theoretic model of a highly intelligent robot interacting with a human. In the original paper by Hadfield-Menell et al. (2016), the analysis is not fully game-theoretic as the human is modelled as an irrational player, and the robot's best action is only calculated under unrealistic normality and soft-max assumptions. In this paper, we make the analysis fully game theoretic, by modelling the human as a rational player with a random utility function. As a consequence, we are able to easily calculate the robot's best action for arbitrary belief and irrationality assumptions

Environmental negotiations as dynamic games : Why so selfish ?

We study a trade-off between economic and environmental indicators using a two-stage optimal control setting where the player can switch to a cleaner technology, that is environmentally “efficient”, but economically less productive. We provide an analytical characterization of the solution paths for the case where the considered utility functions are increasing and strictly concave with respect to consumption and decreasing linearly with respect to the pollution stock. In this context, an isolated player will either immediately start using the environmentally efficient technology, or for ever continue applying the old and “dirty” technology. In a two-player (say, two neighbor countries) dynamic game where the pollution results from a sum of two consumptions, we prove existence of a Nash (open-loop) equilibrium, in which each player chooses the technology selfish i.e., without considering the choice made by the other player. A Stackelberg game solution displays the same properties. Under cooperation, the country reluctant to adopt the technology as an equilibrium solution, chooses to switch to the cleaner technology provided it benefits from some “transfer” from the environmentally efficient partnerO41, Q56, Q58

Strategic Experimentation with Exponential Bandits

This paper studies a game of strategic experimentation with two-armed bandits whose risky arm might yield a payoff only after some exponentially distributed random time. Because of free-riding, there is an inefficiently low level of experimentation in any equilibrium where the players use stationary Markovian strategies with posterior beliefs as the state variable. After characterizing the unique symmetric Markovian equilibrium of the game, which is in mixed strategies, we construct a variety of pure-strategy equilibria. There is no equilibrium where all players use simple cut-off strategies. Equilibria where players switch finitely often between the roles of experimenter and free-rider all lead to the same pattern of information acquisition; the efficiency of these equilibria depends on the way players share the burden of experimentation among them. In equilibria where players switch roles infinitely often, they can acquire an approximately efficient amount of information, but the rate at which it is acquired still remains inefficient; moreover, the expected payoff of an experimenter exhibits the novel feature that it rises as players become more pessimistic. Finally, over the range of beliefs where players use both arms a positive fraction of the time, the symmetric equilibrium is dominated by any asymmetric one in terms of aggregate payoffs

Strategic Experimentation with Exponential Bandits

This paper studies a game of strategic experimentation with two-armed bandits whose risky arm might yield a payoff only after some exponentially distributed random time. Because of free-riding, there is an inefficiently low level of experimentation in any equilibrium where the players use stationary Markovian strategies with posterior beliefs as the state variable. After characterizing the unique symmetric Markovian equilibrium of the game, which is in mixed strategies, we construct a variety of pure-strategy equilibria. There is no equilibrium where all players use simple cut-off strategies. Equilibria where players switch finitely often between the roles of experimenter and free-rider all lead to the same pattern of information acquisition; the efficiency of these equilibria depends on the way players share the burden of experimentation among them. In equilibria where players switch roles infinitely often, they can acquire an approximately efficient amount of information, but the rate at which it is acquired still remains inefficient; moreover, the expected payoff of an experimenter exhibits the novel feature that it rises as players become more pessimistic. Finally, over the range of beliefs where players use both arms a positive fraction of the time, the symmetric equilibrium is dominated by any asymmetric one in terms of aggregate payoffs.Strategic Experimentation ; Two-Armed Bandit ; Exponential Distribution ; Bayesian Learning ; Markov Perfect Equilibrium ; Public Goods

The coalitional switch-off game of service providers

International audienceThis paper studies a significant problem in green networking called switching off base stations in case of cooperating service providers by means of stochastic geometric and coalitional game tools. The coalitional game herein considered is played by service providers who cooperate in switching off base stations. When they cooperate, any mobile is associated to the nearest BS of any service provider. Given a Poisson point process deployment model of nodes over an area and switching off base stations with some probability, it is proved that the distribution of signal to interference plus noise ratio remains unchanged while the transmission power is increased up to preserving the quality of service. The coalitional game behavior of a typical player is called to be \emph{hedonic} if the gain of any player depends solely on the members of the coalition to which the player belongs, thus, the coalitions form as a result of the preferences of the players over their possible coalitions' set. We utilize the Nash-stable core for determining the coalitions of service provider

The possibility of impossible stairways and greener grass

In classical game theory, players have finitely many actions and evaluate outcomes of mixed strategies using a von Neumann-Morgenstern utility function. Allowing a larger, but countable, player set introduces a host of phenomena that are impossible in finite games. Firstly, in coordination games, all players have the same preferences: switching to a weakly dominant action makes everyone at least as well off as before. Nevertheless, there are coordination games where the best outcome occurs if everyone chooses a weakly dominated action, while the worst outcome occurs if everyone chooses the weakly dominant action. Secondly, the location of payoff-dominant equilibria behaves capriciously: two coordination games that look so much alike that even the consequences of unilateral deviations are the same may nevertheless have disjoint sets of payoff-dominant equilibria. Thirdly, a large class of games has no (pure or mixed) Nash equilibria. Following the proverb ``the grass is always greener on the other side of the hedge'', greener-grass games model constant discontent: in one part of the strategy space, players would rather switch to its complement. Once there, they'd rather switch back.coordination games; dominant strategies; payoff-dominance; nonexistence of equilibrium; tail events

The Possibility of Impossible Stairways and Greener Grass

In classical game theory, players have finitely many actions and evaluate outcomes of mixed strategies using a von Neumann-Morgenstern utility function. Allowing a larger, but countable, player set introduces a host of phenomena that are impossible in finite games. Firstly, in coordination games, all players have the same preferences: switching to a weakly dominant action makes everyone at least as well off as before. Nevertheless, there are coordina- tion games where the best outcome occurs if everyone chooses a weakly dominated action, while the worst outcome occurs if everyone chooses the weakly dominant action. Secondly, the location of payoff-dominant equilibria behaves capriciously: two coordination games that look so much alike that even the consequences of unilateral deviations are the same may nevertheless have disjoint sets of payoff-dominant equilibria. Thirdly, a large class of games has no (pure or mixed) Nash equilibria. Following the proverb \the grass is always greener on the other side of the hedge", greener-grass games model constant discontent: in one part of the strategy space, players would rather switch to its complement. Once there, they'd rather switch back.coordination games;dominant strategies;payoff-dominance;nonexistence of equi- librium;tail events

Game-theoretic infrastructure sharing in multioperator cellular networks

©2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.The introduction of fourth-generation wireless technologies has fueled the rapid development of cellular networks, significantly increasing the energy consumption and the expenditures of mobile network operators (MNOs). In addition, network underutilization during low-traffic periods (e.g., night zone) has motivated a new business model, namely, infrastructure sharing, which allows the MNOs to have their traffic served by other MNOs in the same geographic area, thus enabling them to switch off part of their network. In this paper, we propose a novel infrastructure-sharing algorithm for multioperator environments, which enables the deactivation of underutilized base stations during low-traffic periods. Motivated by the conflicting interests of the MNOs and the necessity for effective solutions, we introduce a game-theoretic framework that enables the MNOs to individually estimate the switching-off probabilities that reduce their expected financial cost. Our approach reaches dominant strategy equilibrium, which is the strategy that minimizes the cost of each player. Finally, we provide extensive analytical and experimental results to estimate the potential energy and cost savings that can be achieved in multioperator environments, incentivizing the MNOs to apply the proposed scheme.Peer ReviewedPostprint (author's final draft