Cooperative game theory

In game theory, a cooperative game (or coalitional game) is a game with competition between groups of players ("coalitions") due to the possibility of external enforcement of cooperative behavior (e.g. through contract law). Those are opposed to non-cooperative games in which there is either no possibility to forge alliances or all agreements need to be self-enforcing (e.g. through credible threats). Cooperative games are often analysed through the framework of cooperative game theory, which focuses on predicting which coalitions will form, the joint actions that groups take and the resulting collective payoffs. It is opposed to the traditional non-cooperative game theory which focuses on predicting individual players' actions and payoffs and analyzing Nash equilibria. Cooperative game theory provides a high-level approach as it only describes the structure, strategies and payoffs of coalitions, whereas non-cooperative game theory also looks at how bargaining procedures wi

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In cooperative game theory, the core is the set of feasible allocations or imputations where no coalition of agents can benefit by breaking away from the grand coalition. One can think of the core co

Non-cooperative game theory

A non-cooperative game is a form of game under the topic of game theory. Non-cooperative games are used in situations where there are competition between the players of the game. In this model, there

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Bandit Online Learning of Nash Equilibria in Monotone Games

We address online bandit learning of Nash equilibria in multi-agent convex games. We propose an algorithm whereby each agent uses only obtained values of her cost function at each joint played action, lacking any information of the functional form of her cost or other agents' costs or strategies. In contrast to past work where convergent algorithms required strong monotonicity, we prove that the algorithm converges to a Nash equilibrium under mere monotonicity assumption. The proposed algorithm extends the applicability of bandit learning in several games including zero-sum convex games with possibly unbounded action spaces, mixed extension of finite-action zero-sum games, as well as convex games with linear coupling constraints.

2021

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

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.

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