When we hear the term “game,” we usually start thinking about amusements or sports. But in a branch of mathematics called “Game Theory,” the word ‘game’ has a much broader connotation. Game Theory is, in fact, the study of mathematical models and their interaction with the decision-makers. The game theory includes strategic thinking in which players make decisions by viewing various perspectives and by looking at the viewpoint of other participant players; also by analyzing their actions and reactions in particular situations.
The strategy corresponding to the Nash equilibrium is an optimal mixed strategy in ∆. Since game ∆ is fair (i.e. Its value is 0 and the sets of optimal strategies for the first and second player are the same), an optimal mixed strategy can be found by the solution of some linear feasibility problem. The rule of game is: Each of the players gets alternative turns. In each turn, a player selects either the first or last coin from the row, removes it. Permanently, and receives the value of the coin. Both the player plays in an optimal way, i.e., both want to maximize total winning money. Play heads-up limit Texas hold'em against an A.I designed to play game theory optimal poker. Don't forget to check out the stats page to see how you rank against other competitors.
Significance
The best use of game theory is to figure out the optimal solution from the best possible choices through the analysis of costs and benefits to each participant who competes with each other. The theory is applicable in different fields, like in business, psychology, biology, economics, political science, computers, etc. The practical implication of the theory lies in its use to support in explaining events and situations that occurred in the past and to determine different actions players may take in the future, etc. From the business point of view, game theory can be utilized by business managers to predict the strategic planning or thought process of their competitors and collaborators. It is considered a very powerful medium for forecasting or predicting the output of interactions between different participants or competitors in which reaction of one depends on the action of others.
Components or Elements of Game Theory
The game theory has mainly three components:
- Players: Game theory’s main element includes a set of players. Business managers and companies are considered as players.
Optimal Strategy Definition
- Strategies: Different strategies that players can use in the game. This also includes game rules that are set in a hierarchy to mention the arrangement of the best possible strategies and actions.
- Outcomes or results: This includes the possible strategies and expected payoffs as per outcomes. It is assumed that all the participants are already aware of these payoffs.
There are two main ways by which the game theory can be used, i.e., simultaneous games in which the players go ahead with their moves or actions simultaneously, irrespective of looking for information related to the moves or actions chosen by other players. The other one is a sequential game, which includes the dependency of the player’s moves or actions on the previous action’s results or another player’s choice.
Examples of Game Theory
Let’s have some real-life examples of Game Theory.
1. Bidding at Auction
Optimal Strategy Game Theory Example
An auction is considered as a sale activity in which different bidders bid for purchasing any good or service, and the same is sold to the bidder having the highest bid. Game theory is being used in bid auctions, especially for analysis of the first price sealed auction bidding. In this type of auction, bidders are supposed to submit bids in safe and sealed way. Different players are unaware of the value of goods or services of each other and try to devise a bidding strategy, irrespective of having complete information. The behavior of bidders and different other factors are being analyzed while making decisions during bid preparation.
2. Collective Bargaining or Negotiation Between Parties
Game theory plays an important role in different collective bargaining or negotiation activities among different parties or participants. For example, different negotiations take place between worker unions and the management during the situation of the strike of workers or lockout period to increase wages. Using game theory, both parties can arrive at the optimum solution of the issue, i.e., to increase wages by examining different options available for wages and benefits, which can maximize the welfare of both workers and management. Salary negotiation is also an example of the game theory application. The concept of game theory is used in other negotiations also like negotiations with suppliers while purchasing, compensation or incentive negotiations between management and suppliers or business partners, etc.
3. Decisions Related to New Products
Product-based decisions related to launching a new product in the market or to exit the launch of the product are also executed using game theory by businesses. Using game theory, business people can understand if the first-mover advantage is there or not, competitor’s possible moves related to new products and also deciding upon the strategies for defense, etc. Similarly, the concept of game theory is also being used in deciding whether entering a new market or exiting it.
4. Product Pricing Decisions
The applications of game theory are also being used widely in deciding upon the pricing strategies of both consumers and retailers. Retailers compete against each other to gain market share of customers and for this, they opt for different games or strategies, like offering attractive discounts on specific goods in order to increase sales of complementary products. For example, in the offseason, i.e., off-summer or off-winter season, garment shop vendors or retailers offer attractive sales on a certain stock of clothes in which they adopt optimal pricing strategies to attract maximum customers. In this, retailers use the game theory approach where retailers and consumers are the main players. The focus of retailers is on using the best pricing strategy while the preference of consumers is to choose the best deal in terms of discount and variety.
5. Stock Market Decisions
Using game theory, decisions regarding buying and selling shares in the stock market can be taken wisely. The investors make different stock market decisions by using different strategies of investment and by considering different players or investors. Game theory helps in predicting the decisions of other players related to investments, and based on these decisions, they can decide upon the strategies for themselves which maximize profit.
This course is an introduction to game theory and strategic thinking. Ideas such as dominance, backward induction, Nash equilibrium, evolutionary stability, commitment, credibility, asymmetric information, adverse selection, and signaling are discussed and applied to games played in class and to examples drawn from economics, politics, the movies, and elsewhere.
Course StructureThis Yale College course, taught on campus twice per week for 75 minutes, was recorded for Open Yale Courses in Fall 2007.
Game Theory Competitive Advantage