Game Theory

Business Club
Game Theory

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Krutarth Dharmesh Shah, Nikita Kishore , Piyush Kedia
29th October, 2017

Introduction

We, as humans, are social animals. We have multiple interactions with other people everyday, regarding all sorts of issues. As we live in a common society, and share limited resources, all decisions of our lives are directly / indirectly influenced by the actions of other stakeholders in the same domain. Our collective actions influence the outcome which we face.

Game Theory is basically a branch of science which deals with creating models for strategic interaction and decision making between two or more parties. Basically, game theory deals with situations where the fallout of a particular problem for one side, is dependent on the actions of all sides involved in the problem.

Initially, game theory was applied in the field of games and economics, but now it has gone on to be used in biology, industries, politics etc. There have been multiple Economics Nobel Laureates from the field of Game theory, and it has been an area of major research in the last century.

Basic Terminology

Let's define the basic terms in Game Theory.

Game

Any situation / set of circumstances which has two or more decision makers(players) involved, where the result is dependent on the actions of all the decision makers.

Player

A participant in a game, whose decisions influence what benefit he derives from the game. The aim of the player is to maximize that benefit.

Strategy

A strategy is a plan of action, which a player in a game may pursue / plan to pursue, depending on the circumstances under which the game is being played. Strategy may change over the course of the game.

Payoff

A numerical value which estimates the relative/absolute benefit a player may get from a particular outcome of a game. The payoff is quantifiable in some cases, like money or number, but in other cases, it can be evaluated on utility.

Information set

An information set is the total information available to the player in a game at any instant in the duration of the game. The information set is mostly used when sequential games are involved.

Equilibrium

Equilibrium is reached in a game when all players have made their decisions, and an outcome has come into effect.

Assumptions

There are numerous factors influencing the decisions and outcome of a game. The more the factors, the harder it becomes to predict the course of play, and the effect of factors. Thus, we assume a few things in order to proceed to analyze the situations.

1. We assume that, in a game, all players behave rationally. This means they take all decisions based on the available information, past history and a rational outlook. In the real world, though, people often become illogical and take brash decisions.
2. It is assumed that every player in a game wants the maximum payoff available, and this will influence his decisions to a great extent.
3. Game theory assumes, and expects, games to be completely descriptive. This means, all possible outcomes are defined and covered, and payoffs for each player are defined for each outcome. The description is supposed to answer all “what if”s .

Types of Games

• Cooperative /non cooperative

A game is cooperative if the players are able to form binding commitments externally enforced (e.g. through contract law). A game is non-cooperative if players cannot form alliances or if all agreements need to be self-enforcing

• Symmetric /asymmetric

A symmetric game is a game where the payoffs for playing a particular strategy depend only on the other strategies employed, not on who is playing them. If the identities of the players can be changed without changing the payoff to the strategies, then a game is symmetric. The standard representations of chicken, the prisoner's dilemma, and the stag hunt are all symmetric games.

• Zero-sum / Non-zero-sum game

Zero-sum games are a special case of constant-sum games, in which choices by players can neither increase nor decrease the available resources. In zero-sum games the total benefit to all players in the game, for every combination of strategies, always adds to zero. Poker is one of the best examples of zero sum games. Non-zero-sum games may turn out to be a bit beneficial for all parties.

• Simultaneous / Sequential

Simultaneous games are games where both players move simultaneously, or if they do not move simultaneously, the later players are unaware of the earlier players' actions (making them effectively simultaneous). Sequential games (or dynamic games) are games where later players have some knowledge about earlier actions.