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Lecture

Game Theory: Learning in Finite Action Games

Description

This lecture discusses the learning dynamics in finite action games, focusing on the importance of game theoretic analysis. It begins with a motivation for understanding the problem and how game theory can provide solutions. The instructor outlines the agenda, which includes exploring different types of equilibria such as correlated and coarse correlated equilibria. The lecture recaps best-response dynamics and their convergence properties, emphasizing the challenges in finding pure and mixed Nash equilibria. An example of a Stop & Go game illustrates the concepts, highlighting the utilities and potential outcomes for players. The discussion extends to correlated equilibria, explaining how they differ from Nash equilibria and their implications for social welfare. The instructor also introduces coarse correlated equilibria, providing definitions and examples to clarify the concepts. The lecture concludes with a focus on computational methods for finding these equilibria, emphasizing their tractability compared to traditional Nash equilibria, and sets the stage for further exploration of learning algorithms in game theory.

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Instructor

Maryam Kamgarpour

Maryam Kamgarpour holds a Doctor of Philosophy in Engineering from the University of California, Berkeley and a Bachelor of Applied Science from University of Waterloo, Canada. Her research is on safe decision-making and control under uncertainty, game theory and mechanism design, mixed integer and stochastic optimization and control. Her theoretical research is motivated by control challenges arising in intelligent transportation networks, robotics, power grid systems and healthcare. She is the recipient of NASA High Potential Individual Award, NASA Excellence in Publication Award, and the European Union (ERC) Starting Grant.

Official source

Related concepts (32)

Nash equilibrium

In game theory, the Nash equilibrium, named after the mathematician John Nash, is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is assumed to know the equilibrium strategies of the other players, and no one has anything to gain by changing only one's own strategy. The principle of Nash equilibrium dates back to the time of Cournot, who in 1838 applied it to competing firms choosing outputs.

Strategy (game theory)

In game theory, a player's strategy is any of the options which they choose in a setting where the outcome depends not only on their own actions but on the actions of others. The discipline mainly concerns the action of a player in a game affecting the behavior or actions of other players. Some examples of "games" include chess, bridge, poker, monopoly, diplomacy or battleship. A player's strategy will determine the action which the player will take at any stage of the game.

Correlated equilibrium

In game theory, a correlated equilibrium is a solution concept that is more general than the well known Nash equilibrium. It was first discussed by mathematician Robert Aumann in 1974. The idea is that each player chooses their action according to their private observation of the value of the same public signal. A strategy assigns an action to every possible observation a player can make. If no player would want to deviate from their strategy (assuming the others also don't deviate), the distribution from which the signals are drawn is called a correlated equilibrium.

Evolutionarily stable strategy

An evolutionarily stable strategy (ESS) is a strategy (or set of strategies) that is impermeable when adopted by a population in adaptation to a specific environment, that is to say it cannot be displaced by an alternative strategy (or set of strategies) which may be novel or initially rare. Introduced by John Maynard Smith and George R. Price in 1972/3, it is an important concept in behavioural ecology, evolutionary psychology, mathematical game theory and economics, with applications in other fields such as anthropology, philosophy and political science.

Game theory is the study of mathematical models of strategic interactions among rational agents. It has applications in all fields of social science, as well as in logic, systems science and computer science. The concepts of game theory are used extensively in economics as well. The traditional methods of game theory addressed two-person zero-sum games, in which each participant's gains or losses are exactly balanced by the losses and gains of other participants.