Background
In game theory, an open-loop equilibrium pertains to a type of equilibrium related to the structure of information within multi-stage games. It’s crucial for understanding strategic interaction when past decisions are hidden from opponents.
Historical Context
The concept of open-loop equilibrium emerged from mathematical analyses in the mid-20th century, paralleling advances in both solid state physics and strategic military planning which required robust multi-stage decision-making frameworks, before entering broader economic theory discussions.
Definitions and Concepts
An open-loop equilibrium is defined as:
- Open-Loop Equilibrium: The equilibrium of a multi-stage game where each player selects their entire strategy plan at the outset without the ability to revise these strategies based on the ongoing observation of opponents’ actions. Players do not have information on the choices made by others at previous decision nodes.
Contrast this with:
- Closed-Loop Equilibrium: In this type of equilibrium, players can observe the prior moves of their opponents, usually leading to sequential and adaptive strategies where past choices are common knowledge.
Major Analytical Frameworks
Classical Economics
Did not initially contemplate the complexities of multi-stage depth inherent in open-loop systems, as the relevant strategic feedback mechanisms of the time were typically single-shot considerations.
Neoclassical Economics
Incorporated game theoretical notions where open- and closed-loop frameworks became important in fields like oligopoly theory and auction design.
Keynesian Economic
Focused more on demand-driven output in the short and long term, intersecting less directly with these decision-structure concepts.
Marxian Economics
Kept game theoretic frameworks on the periphery, given its focus on class struggle and surplus value extraction, typically viewing economic battles as zero-sum class engagement rather than staged competitions.
Institutional Economics
Analyzed open-loop mechanisms within firmly structured institutions (government, legal systems), observing how strategic policies are committed despite evolving scenarios.
Behavioral Economics
As behavioral economists highlighted often irrational deviations from predicted norms, understanding static vs. advancing decision information flow is part of human strategic behavior complexity studies.
Post-Keynesian Economics
Emphasized within larger macro-economic frameworks where longer-term strategy implications consume differential game analysis reflective of open-loop equilibria.
Austrian Economics
Although focusing more on individual actions and free-market mechanisms, recognizing multistage game theory and inspecting it through the lens of subjective value holds importance.
Development Economics
Processes of economic development with limited feedback mechanisms due to information lags sometimes naturally fall into open-loop strategic analysis.
Monetarism
Though primarily focused on controlled money supplies and their economic services to influence an economy over time, scenarios exist where irrevocable policy games provide foundational stages for monetary plays.
Comparative Analysis
Understanding open-loop vs. closed-loop equilibria allows economists and policymakers to gauge the level of observable strategy interaction required in various economic designs. This insight is pivotal in designing regulatory frameworks, optimal tariff implementations, and tax policies where strategic anticipations are key.
Case Studies
- Arms Race Economics: Countries setting weapon development strategies without response capabilities.
- Pre-commitment in Monetary Policy: Central banks pre-set interest paths impacting economic predictions without flexible adjustments.
Suggested Books for Further Studies
- [Dynamic Noncooperative Game Theory by Tamer Basar and Geert Jan Olsder].
- [Game Theory and the Law by Douglas Baird, Robert Gertner and Randal Picker].
- [Strategy: An Introduction to Game Theory by Joel Watson].
Related Terms with Definitions
- Closed-Loop Equilibrium: An equilibrium where players observe past decisions of others, allowing strategy updates.
- Stackelberg Competition: A strategic game where leaders commit to quantities as followers adapt dynamically.
- Common Knowledge: Information that is known by all parties, and all parties know others also possess the information.
