# Game theory

Custom Student Mr. Teacher ENG 1001-04 8 October 2016

## Game theory

Game theory is a broad field of study that involves examining ways in which strategic decisions are derived. The study is applied in areas where strategic interactions among rational players produce outcomes with respect to the preferences of those players (Fudenberg & Tirole 1991). Game theory is a branch of applied mathematics that is mostly used in the social sciences situations like, economics, psychology, political science, and philosophy.

The theory is also used in other fields like, biology, engineering, political science, international relations and computer science. Game theory can be classified as; non-cooperative (or strategic) games and co-operative (or coalitional) games (Fernandez & Bierman 1998). Non-cooperative games are involved with how intelligent individuals interact with one another in an effort to achieve their own goals. Co-operative games are where players co-operate in their moves (strategies) to achieve the desired common goals.

‘Strategic-form’ or ‘normal form’ games and ‘extensive form’ games. ‘Strategic form’ games are games where actions by players are taken simultaneously and order of the play is irrelevant to the game’s outcome. ‘Extensive form’ games are games where actions are taken by the players in a sequence and order of play is relevant to a game’s outcome. They are usually presented in a tree diagram. Symmetric and Asymmetric games; Asymmetric games are where the payoffs for playing a particular move depend only on the other player’s strategies.

Symmetric game is where identities of the players can be changed without changing the payoff to the strategies. Zero-sum games and non-zero sum games; Zero-sum games are where the total benefits to all players add up to zero (Camerer 2003). In non-zero sum games, the total benefits do not necessarily adds up to zero. Discrete and continuous games; discrete games have finite number of players, moves, events and outcomes. Continuous games have infinite numbers.

The basic elements of game theory are; an agent (an entity with preferences/options), game (All situations in which at least one agent can only act to maximize his utility through anticipating responses to his actions by one or more other agents), utility (amount of benefits/welfare an agent derives from occurrence of an event), payoff (an ordinal utility number assigned to a player at event of a certain outcome), outcome (an assignment of a set of payoffs, one to each player in the game), strategy (player’s plan on which action to take to achieved his/her desired payoff) and trees and matrices (ways of representing games that is based on order of play) (Fernandez & Bierman 1998). Game theory is based on the following assumptions: Players in a game are able to make their own preferences i. e. they are free agents.

Players are economically rational and they can, assess outcomes, calculate paths to outcomes and choose actions that they think will yield their preferred outcomes. Agents’ purpose is to maximize their utility. Game outcome depends on the actions taken by the players (Camerer 2003). Game theory has been used to explain in different fields to explain varied phenomena. In economics, game theory has been employed to explain business behaviors and economic conditions. Economic theories have embraced game theory in explaining and exhibiting certain economic behaviors. Economists have used other related theories in trying to understand rational interaction of strategic economic decisions that are made by people.

These theories are closely linked to game theory and they include, decision theory, general equilibrium theory and mechanism design theory. Decision theory is a game theory of a single player against nature that focuses on preferences and the formation of beliefs (Fernandez & Bierman 1998). The theory is used to demonstrate how best to acquire information before making a decision. Equilibrium theory is a branch of game theory that deals with trade and production and mostly with where there are relatively large number of individual consumers and producers (Fudenberg & Tirole 1991). It is widely used in the macroeconomic analysis of broad based economic policies like monetary and fiscal policies, stock markets analysis, interest and exchange rates studies.

Mechanism design theory is built on game theory but have special focus on the consequences of different types of rules (strategies). Example of a game theory is price game used by companies in a duopolistic market to increase their market share. In a duopoly market, two firms control the market and they use factors like prices, quality products and services, promotions, branding and promotion to compete over the market share (Samuelson 2008). When market share of one company increases, the other company’s share decreases. Firms in sectors that sells homogeneous products (e. g. energy sector), uses pricing strategy to win increase their market share.

Taking example of two oil companies in a duopolistic market in current oil price surge, the companies are faced with problem of adjusting their prices upwards since this will adversely affect the demand of their oil products and thus reduce their revenues. Increase in crude oil prices has been experienced in the world, and oil and petroleum companies have to increase their retail prices upwards to realize earnings from their venture. Companies also have objective of increasing the volume of their sales, by increasing the market share of their products. Since petroleum companies trades homogeneous products, the main marketing tool to increase their market share is price. For two companies in a duopoly market, if one company increases its prices, and other maintains or even reduces, the former loses market share to the latter.

Both companies face the following possibilities from their moves; reduction of market share of their products and hence their future revenues and profit or reduction in their profit margin or loss and hence shrink of their financial performance and growth in the future. Therefore each of the firms is faced with dilemma of which move to take in this situation of sharp increase in their raw materials. The two firms have the following strategic problem; to ensure profitability of their companies amid high cost of their sales, and pressure to maintain their prices at competitive price over their rivals in order to increase demand of their products.

These are conflicting goals that management of each company must resolve by making strategic price decisions. Pricing strategies for the two firms are either to increase the price that would results to increase in revenue and retain its market share, reduce price which results to increase in market share of its products or maintain the price (Ibid 2008). Each company want to maximize its utility in the pricing moves i. e. to select a move that will see its market share maintained or increased and also ensure profitability of the company. Each strategy that the companies may take have implications on the other i. e. move by one firm affects the other firm.

Example, in case of one firm decreasing its prices, this will affects negatively market share of the other as the demand of the former company’s product increases. Therefore, each company is expected to take choice that will result to its favor. Since the two firms are competing for success in their business, there is no cooperation expected while making this very important pricing choice. However, both firm being the only supplier in the market, they can cooperate and set their price mutually in a way that will ensure that no company will lose out to the other. Such arrangements are common in oligopolistic markets, where producers when faced by price pressure mutually agree to set their prices at the same level that will maintain the market share levels.

In this game, each player (company) prefers to increase its market share over the other over maintaining the current market share. Therefore, they are taking conflicting moves to win over the other. The information about the available strategic choices is available to both firms. Both firms also know the current market share of their products and prices of the rival group. Each company has information about the strengths of the other company and knows how much they can support low prices in the price wars. They also know that the cost of crude oil has increased in the world market and that price was the tool to increase their revenues and growth. The only information both companies do not have is which choice their rival make and when.

Companies will not make price changes at the same time; therefore the company that will make price changes after the other will have advantage over the other as it has prior information that is very important in making the pricing decisions. This game is an extensive game and the moves are in a sequence order. Therefore, timing of their moves is very important as it will give the second company advantage to make a well informed move. Using a hypothetical case, we take example of one company making first move and then the other follows. Using the game tool we can get the possible outcomes and solutions in an economic situation like ours. The payoffs assigned to each possible result indicate situations where a company can benefit (high payoffs) or lose out to the other competing company (low payoffs).

Using a hypothetical example of oil companies BP Inc and Shell Plc as companies that operates in a monopolistic market, we can examine outcomes of pricing moves made by the two companies. The game can be used to give solutions to the price problem in a tight monopolisic market. The pricing game is based on the following assumptions: both BP Inc and Shell Plc are rational entities and in their moves their objectives are to increase their market share. Both firms make a sequential move on pricing that take extensive form (Fudenberg & Tirole 1991). Shell Plc makes their decision after the BP Inc makes their pricing move. There is perfect market information symmetry (all company has all market information).

Other factors that affect influence market share of the companies are constant. Strategies employed are price increment, price reduction or maintaining the price level. Payoffs (utility functions) for the moves are assigned as: Company that increases its market share over the other gets 5, company that losses its market share to the other gets -5. The payoffs represent the companies gain or loss in market share. The range for payoff is from -5 to 5, with both the lowest and the highest value representing the highest gain and the highest loss. The medium values represent an outcome of moderate change in the market share of the companies. The game can be represented in a tree diagram as follows: BP Inc

P^ Pv P¦ Shell P^ Pv P¦ P^ Pv P¦ P^ Pv P¦ (0, 0) (-5, 5) (-2, 4) (5, -5) (3, 3) (4, 2) (4, 0) (2, 4) (2, 2) If BP Inc increases its prices ( P^) due to increased world crude oil prices, and shell Plc increases (P^) too the outcome will be (0, 0) i. e. their market share would not change but their sales may reduce due to decreased demand. If Shell Plc reduces (Pv) the prices after BP Inc has increased its prices, the pay offs are (-5, 5) i. e. BP Inc will loss its market share at a rate that is same as one Shell Plc will increase its market share.

In the scenario that BP Inc will raise its prices and Shell maintains its prices (P¦), the payoffs are (-2, 4) i. e. market share for BP will reduce (Pv) but at low rate compared to Shell increment rate will be. On the other hand, if BP Inc reduces its prices first and then Shell raises its prices, the outcome will be (5, -5) i. e. market share for BP will increase at a rate that’s same as the one Shell Plc will lose its share. If both firms reduces their prices, the payoff is going to be (3, 3) i. e. their market share will not change but their sales will be better (higher revenue than if prices are higher). However, if BP reduces its prices but Shell maintains its price, the pay off will be (4, 2) i. e.

BP’s market share will increase comparatively higher than Shell’s. In the last scenario, in case BP maintains its price level but Shell Plc increases its price the outcome payoff will be (4, 0) i. e. BP’s share will increase over Shell’s at relatively higher rate. But if BP maintains its prices and Shell reduces its prices, the pay off will be (2, 4) i. e. Shell Plc will increase its market share at a higher rate than BP Inc. In the last possible scenario, if both BP and Shell maintains their prices, the payoff will be (2, 2) i. e. there is not going to be changes in the market share, though both firms will have higher sales than if they raise their prices.

The game theory provides the solution that the second (shell) should take a move to reduce its price, if BP increases as it will greatly increase its market share. Also it can get increased market share and profit if it maintains its prices, after BP increases its prices. To the company that makes the first move, the best solution is to maintain the price level as it will have higher payoffs without risking the move by the Shell. These options are the only one that will increase their market share and profitable growth. The price game theory can be used to understand economic changes in duopolistic markets. The game can be used in making strategic pricing and marketing decisions.

The approach is important to economic theorists in describing the economic rationale that relates to commodity prices, demand and supply dynamics (Guala 2005). Despite the usefulness of game theory, there are some challenges to this theory. The assumptions on which the theory is based sometimes do not hold (Fernandez & Bierman 1998). Game theorist assumption that players always act in a way to directly maximize their utility sometimes is violated by human behaviors i. e. in practice, human behavior often deviates from this model. This is because of the following factors that need to be considered; irrationality, new models of deliberation, and different motives ().

In real life some people tend to respond irrationally in a situation where they are ideally expected to respond rationally. Also different people are motivated by different things and thus tend to respond differently in the same situation. To this end some theorists take game theory as tool for suggesting how people should respond but not as a tool to predict human behaviors and that game theory is used to explain strategic reasoning rather than strategic behaviors. Other limitations of the theory are based on the assumptions that prices changes are the only factors that will affect the demand of the oil products and consequently the market share. In real life there are rational factors that affect the market share of a product or a company.

Quality of products and services, brand strength, promotions and other marketing strategies influences the demand of a product and its market share. Companies may also be motivated by other factors other than increasing market share when making pricing decisions. The theory also does not assign specific values to specify to what percentage a company gain or lose the market share. Since it’s an economic analysis it should give outcomes that can be easily understood and that make economic sense. However, the theory is very important in giving the general description of how individuals are expected to respond given a certain economic conditions.

In the economic field the theory has been instrumental in explaining behaviors of firms and individuals’ producers and consumers. The theory is also very important in understanding how strategic decisions relate. Reference: Camerer, C. (2003). Behavioral Game Theory: Experiments in Strategic Interaction. Princeton: Princeton University Press Fernandez, L F. ; Bierman, H S. (1998), Game Theory with Economic Applications, Addison-Wesley Fudenberg, D. , and Tirole, J. (1991). Game Theory. Cambridge, MA: MIT Press Guala, F. (2005). The Methodology of Experimental Economics. Cambridge: Cambridge University Press Samuelson, L. (2005). Economic Theory and Experimental Economics. Journal of Economic Literature 43:65-107.

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