This paper investigates interaction among residential electricity users and utility company in a distribution network with the capability of two-way communication provided by smart grid. The energy consumption scheduling of electricity users is formulated as a game-theoretic problem within a group where all players are not totally selfish. Considering altruistic behavior of human decision-making, altruistic player action to other players actions can be influenced by recognizing the well being of others. The proposed model captures the empathy of electricity users in energy consumption scheduling and how this behavior affect peak demand and electricity prices. Numerical results demonstrate that both residential users and utility company can benefit through the channel of empathy.
The cooperative game investigates coalition that may form between players as a result of external enforcement for cooperation and communication. In this type of game, users decide to cooperate with each other through communication to improve their payoffs. In fact, the main challenge is how to incentivize users to get together for cooperation or punish them to prevent non-cooperative behavior. In @cite_3 , a punishment mechanism was proposed to prevent selfish behaviors, which led to Pareto-optimal solution. A repeated game along with punishment mechanism detected by deviation from cooperative consumption were used to encourage cooperative behavior among building managers @cite_19 . Enforcing cooperation behavior with Extended Joint Action Learning method as decentralized reinforcement learning method was studied in @cite_0 . In this study, a joint reward function was introduced with the aim of finding actions which maximize this function within a multi agent system.
@cite_0 @cite_19 @cite_3
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We study a spectrum sharing problem in an unlicensed band where multiple systems coexist and interfere with each other. We first analyze a cooperative setting where all the systems collaborate to achieve a common goal. Under the assumptions that the systems communicate with Gaussian signals and treat interference as noise, we study the structure of the optimal power allocations. We show that any Pareto efficient vector of rates can be achieved with piece-wise constant power allocations. Moreover, if a strong interference condition among all the systems is satisfied, we show that frequency division multiplexing is optimal. We then consider a non-cooperative situation, where the systems act in a selfish and rational way, and investigate how the lack of cooperation can affect performance. Using game theory, we first analyze the possible outcomes of a one shot game, and observe that in many cases an inefficient solution results. We show that by extending the game definition to that of a repeated game, the possibility of building reputations and applying punishments allows to enlarge the set of achievable rates. We present examples that show that in many cases, the performance loss due to lack of cooperation is small. We also provide a converse theorem that proves that our results are tight and quantify the best achievable performance in a non-cooperative scenario One key question in cooperative game theory is that of coalitional stability. A coalition in such games is stable when no subset of the agents in it has a rational incentive to leave the coalition. Finding a division of the gains of the coalition (an imputation) lies at the heart of many cooperative game theory solution concepts, the most prominent of which is the core. However, some coalitional games have empty cores, and any imputation in such a game is unstable. We investigate the possibility of stabilizing the coalitional structure using external payments. In this case, a supplemental payment is offered to the grand coalition by an external party which is interested in having the members of the coalition work together. The sum of this payment plus the gains of the coalition, called the coalition's "adjusted gains", may be divided among the members of the coalition in a stable manner. We call a division of the adjusted gains a super-imputation, and define the cost of stability (CoS) as the minimal sum of payments that stabilizes the coalition. We examine the cost of stability in weighted voting games, where each agent has a weight, and a coalition is successful if the sum of its weights exceeds a given threshold. Such games offer a simple model of decision making in political bodies, and of cooperation in multiagent settings. We show that it is coNP-complete to test whether a super-imputation is stable, but show that if either the weights or payments of agents are bounded then there exists a polynomial algorithm for this problem. We provide a polynomial approximation algorithm for computing the cost of stability. In this work, we propose a game theoretic framework to analyze the behavior of cognitive radios for distributed adaptive channel allocation. We define two different objective functions for the spectrum sharing games, which capture the utility of selfish users and cooperative users, respectively. Based on the utility definition for cooperative users, we show that the channel allocation problem can be formulated as a potential game, and thus converges to a deterministic channel allocation Nash equilibrium point. Alternatively, a no-regret learning implementation is proposed for both scenarios and it is shown to have similar performance with the potential game when cooperation is enforced, but with a higher variability across users. The no-regret learning formulation is particularly useful to accommodate selfish users. Non-cooperative learning games have the advantage of a very low overhead for information exchange in the network. We show that cooperation based spectrum sharing etiquette improves the overall network performance at the expense of an increased overhead required for information exchange. Social dilemmas, where mutual cooperation can lead to high payoffs but participants face incentives to cheat, are ubiquitous in multi-agent interaction. We wish to construct agents that cooperate with pure cooperators, avoid exploitation by pure defectors, and incentivize cooperation from the rest. However, often the actions taken by a partner are (partially) unobserved or the consequences of individual actions are hard to predict. We show that in a large class of games good strategies can be constructed by conditioning one's behavior solely on outcomes (ie. one's past rewards). We call this consequentialist conditional cooperation. We show how to construct such strategies using deep reinforcement learning techniques and demonstrate, both analytically and experimentally, that they are effective in social dilemmas beyond simple matrix games. We also show the limitations of relying purely on consequences and discuss the need for understanding both the consequences of and the intentions behind an action.