**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.

Concept# Extensive-form game

Summary

In game theory, an extensive-form game is a specification of a game allowing (as the name suggests) for the explicit representation of a number of key aspects, like the sequencing of players' possible moves, their choices at every decision point, the (possibly imperfect) information each player has about the other player's moves when they make a decision, and their payoffs for all possible game outcomes. Extensive-form games also allow for the representation of incomplete information in the form of chance events modeled as "moves by nature". Extensive-form representations differ from normal-form in that they provide a more complete description of the game in question, whereas normal-form simply boils down the game into a payoff matrix.
Some authors, particularly in introductory textbooks, initially define the extensive-form game as being just a game tree with payoffs (no imperfect or incomplete information), and add the other elements in subsequent chapters as refinements. Whereas the rest of this article follows this gentle approach with motivating examples, we present upfront the finite extensive-form games as (ultimately) constructed here. This general definition was introduced by Harold W. Kuhn in 1953, who extended an earlier definition of von Neumann from 1928. Following the presentation from , an n-player extensive-form game thus consists of the following:
A finite set of n (rational) players
A rooted tree, called the game tree
Each terminal (leaf) node of the game tree has an n-tuple of payoffs, meaning there is one payoff for each player at the end of every possible play
A partition of the non-terminal nodes of the game tree in n+1 subsets, one for each (rational) player, and with a special subset for a fictitious player called Chance (or Nature). Each player's subset of nodes is referred to as the "nodes of the player". (A game of complete information thus has an empty set of Chance nodes.)
Each node of the Chance player has a probability distribution over its outgoing edges.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related courses (7)

Related people (6)

Related publications (34)

Related concepts (16)

Ontological neighbourhood

MGT-300: Game theory and strategic decisions

Game theory studies the strategic interactions between rational agents. It has a myriad of applications in politics, business, sports. A special branch of Game Theory, Auction Theory, has recently g

FIN-620: Game Theory

Game theory deals with multiperson strategic decision making. Major fields of Economics, such as Microeconomics, Corporate Finance, Market Microstructure, Monetary Economics, Industrial Organization,

ME-429: Multi-agent learning and control

Students will be able to formulate a multi-agent decision-making problem as a game and apply relevant mathematical theories and algorithms to analyze the interaction of the agents and predict the outc

Related lectures (19)

, , , , ,

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.

Cournot competition

Cournot competition is an economic model used to describe an industry structure in which companies compete on the amount of output they will produce, which they decide on independently of each other and at the same time. It is named after Antoine Augustin Cournot (1801–1877) who was inspired by observing competition in a spring water duopoly. It has the following features: There is more than one firm and all firms produce a homogeneous product, i.e., there is no product differentiation; Firms do not cooperate, i.

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.

Introduction to Game Theory

Covers game theory fundamentals, Nash equilibrium, and strategic interactions in multi-agent systems.

Game Theory: Decision Making in Interdependent Environments

Explores game theory, decision-making in interdependent environments, equilibrium concepts, and economic applications in management.

This paper proposes a safe reinforcement learning algorithm for generation bidding decisions and unit maintenance scheduling in a competitive electricity market environment. In this problem, each unit aims to find a bidding strategy that maximizes its reve ...

Efstratios Panteleimon Skoulakis

In this paper we provide a novel and simple algorithm, Clairvoyant Multiplicative Weights Updates (CMWU), for convergence to \textit{Coarse Correlated Equilibria} (CCE) in general games. CMWU effectively corresponds to the standard MWU algorithm but where ...

2022, , , ,

Blockchain systems often rely on rationality assumptions for their security, expecting that nodes are motivated to maximize their profits. These systems thus design their protocols to incentivize nodes to execute the honest protocol but fail to consider ou ...