Strategy (game theory) - Definition and Overview

A strategy in game theory is a sequence of activities and reactions, that fully determine an agents bahaviour in a game or a business situation. The mathematically precise description of behaviour is connected to computer programming and algorithms.

Examples of strategies

Tit for Tat

Strategies in game theory are of essential importance, since the prisoners dilemma was shown never to lead to cooperation unless multiperiod strategies are considered. A highly effective strategy is "Tit for Tat". It was found in a programming contest, with several algorithms competing for the highest utility score.

Roulette

There is a variety of betting strategies and tactics in the Roulette game. The most famous strategy is the doubling strategy:

1. Set 1€
2. If you loose: double your bet
3. Repeat 2. until you have a profit

[Probability illustration - Roulette with a Doubling System (http://hadm.sph.sc.edu/COURSES/ECON/Risk/riskdoubletest.html|)]

Hedging

Hegding is a strategy for financial investments, that searches for the lowest risk or optimal risk to performance ratio. Some kind of hedges are uniquely determined from simple parameters. The Black-Scholes equation demonstrates how a continuous stock buy and selling strategy can replicate an option without risk.

Mathematical tools

Theta calculus

Theta calculus is a mathematical frame work for the definition of strategies, processes and contracts. It is based on the foundations of operator theory and suggests a chronological notation of activities. All kinds of strategies and multiperiod games can be captured in terms of quantitative implications by a vocabulary of three elementary operators: waiting, transacting and deciding.