Lecture

Dynamic Games: Theory and Applications

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In course

ME-429: Game theory for multiagent decision-making

Students will be able to formulate a multi-agent decision-making problem in static and dynamic environments as a game and apply relevant mathematical theories and algorithms to analyze the interaction of the agents and predict the outcome of the decision-m ...

Description

This lecture focuses on dynamic games, exploring their structure and applications. The instructor begins by reviewing concepts from previous lectures, including correlated and coarse-correlated equilibria. The discussion transitions to dynamic games, emphasizing the shift from tree models to loop models. The instructor explains how feedback games can be represented in extensive form, detailing the evolution of states based on players' actions. The lecture covers the importance of information structures, distinguishing between open-loop and perfect state-feedback models. The instructor illustrates the dynamics of non-zero sum dynamic games using a three-truck platoon example, highlighting the players' objectives and the state evolution. The concept of subgame-perfect Nash Equilibrium is introduced, along with backward induction as a method for finding these equilibria. The lecture concludes with a brief overview of dynamic programming and its relevance to solving optimal feedback laws in multi-player scenarios, setting the stage for further exploration in subsequent sessions.

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

Ontological neighbourhood

Economics

Microeconomics: Game theory

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.

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.

Zero-sum game

Zero-sum game is a mathematical representation in game theory and economic theory of a situation that involves two sides, where the result is an advantage for one side and an equivalent loss for the other. In other words, player one's gain is equivalent to player two's loss, with the result that the net improvement in benefit of the game is zero. If the total gains of the participants are added up, and the total losses are subtracted, they will sum to zero.

Backward induction

Backward induction is the process of reasoning backwards in time, from the end of a problem or situation, to determine a sequence of optimal actions. It proceeds by examining the last point at which a decision is to be made and then identifying what action would be most optimal at that moment. Using this information, one can then determine what to do at the second-to-last time of decision. This process continues backwards until one has determined the best action for every possible situation (i.e.

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.

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