Extensive Form

Background

The extensive form is a fundamental concept in game theory that represents games as a decision tree. This form provides a more detailed insight into the sequential and strategic interactions between players, encapsulating decision nodes, strategies, information sets, and pay-offs.

Historical Context

Game theory, including concepts such as extensive form, has evolved significantly since the early 20th century. It was majorly developed by mathematicians like John Von Neumann and Oskar Morgenstern in their seminal work “Theory of Games and Economic Behavior” (1944). The extensive form diagram they introduced laid the groundwork for advancing non-cooperative game theory.

Definitions and Concepts

Extensive Form: A representation of a game that systematically captures every possible sequence of moves, decision points, possible strategies from each player, the information each player has at every decision point (information sets), and the associated rewards and pay-offs.
Decision Nodes: Points in the extensive form tree where players make decisions.
Strategies: A complete plan of actions a player will take given the different possible decisions they will need to make.
Information Sets: Groupings of decision nodes where the player cannot differentiate between nodes within the same set due to lack of information.
Pay-Offs: The rewards a player gets from following a particular strategy, influenced by both their decisions and those of other players.

Major Analytical Frameworks

Classical Economics

Classical economics doesn’t directly discuss extensive form as it traditionally focuses more on market outcomes than on strategic interplays between individuals or firms that can be better analyzed using game theory concepts.

Neoclassical Economics

While neoclassical economics adopts mathematical tools and marginal analysis, extensive form finds utility primarily in the realm of non-cooperative games within this framework, especially in oligopoly and auction settings.

Keynesian Economic

Keynesian economics, dealing with macroeconomic phenomena, utilizes fewer game-theoretic constructs like extensive form since its focus is on aggregate demand, consumption, and employment rather than on individual strategic interactions.

Marxian Economics

Marxian economics, with its focus on class struggle and surplus value, does not typically employ extensive form within its primary analytical tools but could use extensive form to explore strategic behavior in labor-capital relations.

Institutional Economics

Institutional economists can find utility in extensive form to examine the evolutionary dynamics of institutions and strategic interactions within them.

Behavioral Economics

Behavioral economists use extensive game forms to investigate how real (as opposed to theoretically rational) players behave in strategic settings, incorporating insights into human psychology.

Post-Keynesian Economics

Post-Keynesian economists focus more on issues of uncertainty and path dependency using broader frameworks, seeing less direct application of extensive form.

Austrian Economics

Austrian economics, which emphasizes individual actions and subjective values, might use extensive form to analyze sequences of entrepreneurial decision-making.

Development Economics

Development economists could apply extensive form to investigate strategic interactions between different agents in development contexts like micro-credit scenarios or cooperative farming strategies.

Monetarism

Monetarists focus on the role of money supply and may see limited use of extensive game forms, which are more microeconomic focused, though they could be used to model strategic bank behavior.

Comparative Analysis

Utilizing the extensive form conveys several advantages over the simple pay-off matrix. It’s particularly beneficial because it highlights the sequential aspects of decision-making and the interdependency of strategies, therefore broadly applicable across several fronts of microeconomic and strategic analyses.

Case Studies

Tree structure representations of different forms of auctions (e.g., Dutch and English auctions).
Strategic interactions in oligopoly models such as Cournot and Stackelberg competition.
Analysis of bidding strategies in procurement games.

Suggested Books for Further Studies

“Game Theory: Analysis of Conflict” by Roger B. Myerson
“An Introduction to Game Theory” by Martin J. Osborne
“The Theory of Games and Economic Behavior” by John von Neumann and Oskar Morgenstern

Normal Form Game: A representation of a simultaneous-move game using a payoff matrix.
Strategic Form Game: Another name for a normal form game, emphasizing the strategy choices of players.
Nash Equilibrium: A situation where no player can benefit by unilaterally changing their strategy, given the strategies of other players.
Subgame Perfect Equilibrium: A refinement of Nash Equilibrium applicable in extensive form games, where players’ strategies constitute a Nash Equilibrium in every subgame.