Strong Nash equilibrium

Résumé

In game theory a strong Nash equilibrium is a Nash equilibrium in which no coalition, taking the actions of its complements as given, can cooperatively deviate in a way that benefits all of its members. While the Nash concept of stability defines equilibrium only in terms of unilateral deviations, strong Nash equilibrium allows for deviations by every conceivable coalition. This equilibrium concept is particularly useful in areas such as the study of voting systems, in which there are typically many more players than possible outcomes, and so plain Nash equilibria are far too abundant. The strong Nash concept is criticized as too "strong" in that the environment allows for unlimited private communication. In fact, strong Nash equilibrium has to be Pareto-efficient. As a result of these requirements, Strong Nash rarely exists in games interesting enough to deserve study. Nevertheless, it is possible for there to be multiple strong Nash equilibria. For instance, in Approval voting,

Source officielle

https://en.wikipedia.org/wiki/Strong_Nash_equilibrium

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Designing Coalition-Proof Reverse Auctions Over Continuous Goods

Orcun Karaca

This paper investigates reverse auctions that involve continuous values of different types of goods, general nonconvex constraints, and second stage costs. We seek to design the payment rules and conditions under which coalitions of participants cannot influence the auction outcome in order to obtain higher collective utility. Under the incentive compatible Vickrey-Clarke-Groves mechanism, we show that coalition-proof outcomes are achieved if the submitted bids are convex and the constraint sets are of a polymatroid-type. These conditions, however, do not capture the complexity of the general class of reverse auctions under consideration. By relaxing the property of incentive compatibility, we investigate further payment rules that are coalition-proof without any extra conditions on the submitted bids and the constraint sets. Our results are verified with several case studies based on electricity market data.

2019

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Learning Generalized Nash Equilibria in a Class of Convex Games

We consider multiagent decision making where each agent optimizes its convex cost function subject to individual and coupling constraints. The constraint sets are compact convex subsets of a Euclidean space. To learn Nash equilibria, we propose a novel distributed payoff-based algorithm, where each agent uses information only about its cost value and the constraint value with its associated dual multiplier. We prove convergence of this algorithm to a Nash equilibrium, under the assumption that the game admits a strictly convex potential function. In the absence of coupling constraints, we prove convergence to Nash equilibria under significantly weaker assumptions, not requiring a potential function. Namely, strict monotonicity of the game mapping is sufficient for convergence. We also derive the convergence rate of the algorithm for strongly monotone game maps.

2019

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Payoff-Based Approach to Learning Nash Equilibria in Convex Games * *This research is partially supported by M. Kamgarpour’s European Union ERC Starting Grant, CONENE.

We consider multi-agent decision making, where each agent optimizes its cost function subject to constraints. Agents’ actions belong to a compact convex Euclidean space and the agents’ cost functions are coupled. We propose a distributed payoff-based algorithm to learn Nash equilibria in the game between agents. Each agent uses only information about its current cost value to compute its next action. We prove convergence of the proposed algorithm to a Nash equilibrium in the game leveraging established results on stochastic processes. The performance of the algorithm is analyzed with a numerical case study.

2017

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