# game theory

(redirected from*Two-person zero-sum game*)

Also found in: Dictionary, Thesaurus, Medical, Encyclopedia, Wikipedia.

Related to Two-person zero-sum game: Constant sum game

## Game Theory

## game theory

a conceptual framework used by business strategists to analyse the consequences of particular competitive actions. It is typically employed in oligopolistic markets (dominated by a few large suppliers) where the fortunes of the firm are*interdependent*and the actions of one firm will have a big impact on the position of its rivals, and vice versa. To illustrate: consider the ‘pay-off matrix shown in Fig 44. in which two tobacco companies, Philip Morris (PM) and BAT have the options of ‘advertising’ or ‘not advertising’ their, respective, cigarette brands ‘Malboro’ and ‘Camel’. The ‘best’ course of action for BAT

*if PM advertises*is to advertise itself, securing a profit of £2bn;

*ifPM doesn't advertise*BAT's ‘best’ strategy is still to advertise, securing £4bn in this case. By circular reasoning, PM's ‘best’ strategy is to advertise. Thus, both companies advertise and secure £2bn each. Note, however, if the two companies could ‘agree’ not to advertise then they would each secure £3bn. See COLLUSION.

## game theory

a technique that uses logical deduction to explore the consequences of various strategies that might be adopted by competing game players. Game theory can be used in economics to represent the problems involved in formulating marketing strategy by small numbers of interdependent competitors.An oligopolist (see OLIGOPOLY) needs to assess competitors’ reactions to his own marketing policies to ensure that the ‘payoff from any particular marketing strategy may be estimated. For example, consider a struggle for market share between two firms (X and Y) where total market size is fixed, so that every percentage increase in the market share of one firm is necessarily lost to the other (that is, a ZERO-SUM GAME situation). Suppose company X has two strategy choices available, a price reduction (P) or a new advertising campaign (A), and that company Y has the same two strategies available. Any pair of strategies open to the two firms would result in a particular division of the market between them: if firm X were to adopt strategy P, and firm Y were to adopt its strategy P, then firm X would gain 50% of the market, leaving 50% for firm Y. This 50% market share is firm X's pay-off and all such market share information can be summarized in the form *of a * *. * *pay-off matrix * as in Fig. 80.

Each firm must decide on its own best strategy, using the information in the table. If firm X adopts a cautious approach then it would assume that in response to its strategy P, firm Y would counter with strategy A, reducing firm X's payoff from its strategy P to its minimum value 40% (underlined). Similarly, the fatalistic view of firm X's strategy A is that firm Y will counter with strategy P, reducing firm X's payoff from strategy A to its minimum value 55% (underlined). Following this pessimistic view, firm X can make the best of the situation by aiming at the highest of these (underlined) minimum payoffs, in this case 55% yielded by strategy A (a *maximin strategy). *

Firm Y could employ a similar strategy although for Y to assume the worst means that firm X receives a large market share so that firm Y, residually, receives very little. Thus, if firm Y employs its strategy P, its worst possible payoff is 45% of the market (55% going to firm X), and this is marked by circling 55% on the matrix. If firm Y were to employ its strategy A, its worst possible payoff would be 40% of the market (60% going to firm X) and this 60% is similarly marked by a circle. The best of these pessimistic payoffs for firm Y is the smallest of these circled figures, in this case 55% of the market going to firm X (a *minimax strategy). *

The outcome of this situation is that firm X will choose its strategy A and firm Y its strategy P, and neither would be inclined to alter its choice of strategy. This is known as a ‘Nash equilibrium’.

The above example shows a typical ‘prisoner's dilemma’ situation in which the non-cooperative pursuit of self-interest by the two firms makes them *both worse off. *

The example also depicts a simultaneous game between players where each player has no INFORMATION about the other player's move on which to base his decision. In sequential games, however, where the moves of the first player are observable to the second player before the second player must respond, coordination between players is more readily achieved. In such sequential games it is possible for each player to anticipate his rival's response. This makes it possible for game players to develop collusive or quasi-collusive solutions to their interdependence problem, which can make them *both better off. *

When game players are able to coordinate their strategies then they can act to expand the total market so that all players can enjoy increasing sales and profits - a NON-ZERO SUM GAME. See COLLUSION, CARTEL.

## game theory

The science of evaluating the relationships among parties and the optimal choices for participants in any given situation. Game theory is an important tool in negotiating. Two frequently encountered game theory models are the prisoner's dilemma and chicken.

• The prisoner's dilemma model involves parties trusting each other to make the best choice for all, without prearranging their plans, rather than making the best choice for an individ- ual. This is seen in the real estate world in quoting commissions, which involves informal, nonverbal negotiations among real estate agents. Although there is no price fixing going on, all brokers understand that if they cooperate and refuse to lower prices, they will all make a good living. If one or a few lower commission rates in order to capture a lot more business, those few will do well until all brokers lower their prices and get into a price war, after which all will do poorly.

• Chicken is the “sport” of two cars racing against each other, head-on, with the first one to swerve being labeled chicken and losing the match. The best way to win a game of chicken is to remove your ability to swerve and to let the other side know that you no longer have any freedom to move—no freedom of negotiation, in other words. For example, the com- mon use of the chicken theory is to tell a seller that you do not have, and cannot borrow, enough money to meet the asking price. The seller will have to reduce the price, or you will have to find another property.