We model the competition over mining resources and over several cryptocurrencies as a non-cooperative game. Leveraging results about congestion games, we establish conditions for the existence of pure Nash equilibria and provide efficient algorithms for finding such equilibria. We account for multiple system models, varying according to the way that mining resources are allocated and shared and according to the granularity at which mining puzzle complexity is adjusted. When constraints on resources are included, the resulting game is a constrained resource allocation game for which we characterize a normalized Nash equilibrium. Under the proposed models, we provide structural properties of the corresponding types of equilibrium, e.g., establishing conditions under which at most two mining infrastructures will be active or under which no miners will have incentives to mine a given cryptocurrency.
We model the competition over several blockchains characterizing multiple cryptocurrencies as a non-cooperative game. Then, we specialize our results to two instances of the general game, showing properties of the Nash equilibrium. In particular, leveraging results about congestion games, we establish the existence of pure Nash equilibria and provide efficient algorithms for finding such equilibria.
Abstract-Access to online contents represents a large share of the Internet traffic. Most such contents are multimedia items which are user-generated, i.e., posted online by the contents' owners. In this paper we focus on how those who provide contents can leverage online platforms in order to profit from their large base of potential viewers.Actually, platforms like Vimeo or YouTube provide tools to accelerate the dissemination of contents, i.e., recommendation lists and other re-ranking mechanisms. Hence, the popularity of a content can be increased by paying a cost for advertisement: doing so, it will appear with some priority in the recommendation lists and will be accessed more frequently by the platform users.Ultimately, such acceleration mechanism engenders a competition among online contents to gain popularity. In this context, our focus is on the structure of the acceleration strategies which a content provider should use in order to optimally promote a content given a certain daily budget. Such a best response indeed depends on the strategies adopted by competing content providers. Also, it is a function of the potential popularity of a content and the fee paid for the platform advertisement service.We formulate the problem as a differential game and we solve it for the infinite horizon case by deriving the structure of certain Nash equilibria of the game.
The Youtube recommendation is one the most important view source of a video. In this paper, we focus on the recommendation system in boosting the popularity of videos. We first construct a graph that captures the recommendation system in Youtube and study empirically the relationship between the number of views of a video and the average number of views of the videos in its recommendation list. We then consider a random walker on the recommendation graph, i.e. a random user that browses through videos such that the video it chooses to watch is selected randomly among the videos in the recommendation list of the previous video it watched. We study the stability properties of this random process and we show that the trajectory obtained does not contain cycles if the number of videos in the recommendation list is small (which is the case if the computer's screen is small).
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