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Register a new userStochastic Optimization of Service Provision with Selfish Users
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We develop a computationally efficient technique to solve a fairly general distributed service provision problem with selfish users and imperfect information. In particular, in a context in which the service capacity of the existing infrastructure can be partially adapted to the user load by activating just some of the service units, we aim at finding the configuration of active service units that achieves the best trade-off between maintenance (e.g. energetic) costs for the provider and user satisfaction. The core of our technique resides in the implementation of a belief-propagation (BP) algorithm to evaluate the cost configurations. Numerical results confirm the effectiveness of our approach.
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We study a class of games which model the competition among agents to access some service provided by distributed service units and which exhibit congestion and frustration phenomena when service units have limited capacity. We propose a technique, based on the cavity method of statistical physics, to characterize the full spectrum of Nash equilibria of the game. The analysis reveals a large variety of equilibria, with very different statistical properties. Natural selfish dynamics, such as best-response, usually tend to large-utility equilibria, even though those of smaller utility are exponentially more numerous. Interestingly, the latter actually can be reached by selecting the initial conditions of the best-response dynamics close to the saturation limit of the service unit capacities. We also study a more realistic stochastic variant of the game by means of a simple and effective approximation of the average over the random parameters, showing that the properties of the average-case Nash equilibria are qualitatively similar to the deterministic ones.
Blockchain and general purpose distributed ledgers are foundational technologies which bring significant innovation in the infrastructures and other underpinnings of our socio-economic systems. These P2P technologies are able to securely diffuse information within and across networks, without need for trustees or central authorities to enforce consensus. In this contribution, we propose a minimalistic stochastic model to understand the dynamics of blockchain-based consensus. By leveraging on random-walk theory, we model block propagation delay on different network topologies and provide a classification of blockchain systems in terms of two emergent properties. Firstly, we identify two performing regimes: a functional regime corresponding to an optimal system function; and a non-functional regime characterised by a congested or branched state of sub-optimal blockchains. Secondly, we discover a phase transition during the emergence of consensus and numerically investigate the corresponding critical point. Our results provide important insights into the consensus mechanism and sub-optimal states in decentralised systems.
We study the outcome of deferred acceptance when prospective medical residents can only apply to a limited set of hospitals. This limitation requires residents to make a strategic choice about the quality of hospitals they apply to. Through a mix of theoretical and experimental results, we study the effect of this strategic choice on the preferences submitted by participants, as well as on the overall welfare. We find that residents choices in our model mimic the behavior observed in real systems where individuals apply to a mix of positions consisting mostly of places where they are reasonably likely to get accepted, as well as a few reach applications to hospitals of very high quality, and a few safe applications to hospitals of lower than their expected level. Surprisingly, the number of such safe applications is not monotone in the number of allowed applications. We also find that selfish behavior can hurt social welfare, but the deterioration of overall welfare is very minimal.
The Bitcoin protocol prescribes certain behavior by the miners who are responsible for maintaining and extending the underlying blockchain; in particular, miners who successfully solve a puzzle, and hence can extend the chain by a block, are supposed to release that block immediately. Eyal and Sirer showed, however, that a selfish miner is incentivized to deviate from the protocol and withhold its blocks under certain conditions. The analysis by Eyal and Sirer, as well as in followup work, considers a emph{single} deviating miner (who may control a large fraction of the hashing power in the network) interacting with a remaining pool of honest miners. Here, we extend this analysis to the case where there are emph{multiple} (non-colluding) selfish miners. We find that with multiple strategic miners, specific deviations from honest mining by multiple strategic agents can outperform honest mining, even if individually miners would not be incentivised to be dishonest. This previous point effectively renders the Bitcoin protocol to be less secure than previously thought.
We consider a game-theoretical problem called selfish 2-dimensional bin packing game, a generalization of the 1-dimensional case already treated in the literature. In this game, the items to be packed are rectangles, and the bins are unit squares. The game starts with a set of items arbitrarily packed in bins. The cost of an item is defined as the ratio between its area and the total occupied area of the respective bin. Each item is a selfish player that wants to minimize its cost. A migration of an item to another bin is allowed only when its cost is decreased. We show that this game always converges to a Nash equilibrium (a stable packing where no single item can decrease its cost by migrating to another bin). We show that the pure price of anarchy of this game is unbounded, so we address the particular case where all items are squares. We show that the pure price of anarchy of the selfish square packing game is at least 2.3634 and at most 2.6875. We also present analogous results for the strong Nash equilibrium (a stable packing where no nonempty set of items can simultaneously migrate to another common bin and decrease the cost of each item in the set). We show that the strong price of anarchy when all items are squares is at least 2.0747 and at most 2.3605.
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