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According to Salvatore (2006:386), game theory allows economists to study oligopolistic interdependent decision-making. Simply put, through the application of game theory, we can portray complex strategic situations in a highly simplified setting through the creation of formalised models to analyse the potential outcomes. Such outcomes could be conflict (or competition) and cooperation (or collusion) that, in turn, will influence the oligopolistic firm's choice of best strategy when faced by these outcomes. Therefore, these games allow us to view the strategic interaction between the economic agents or players. Wilkinson (2005:332-376) says that economic issues involve strategic interaction e.g. the behaviour of Pepsi and Coca-Cola in imperfectly competitive markets. Salvatore (2006:386) divides game theory into two branches: cooperative and non-cooperative. In the case of the latter, ‘players' cannot make binding arrangements or agreements, and the focus of the analysis is on the individual who is concerned with maximising his position i.e. doing as well as possible for himself. In the case of the former, i.e. cooperative game theory, binding arrangements or agreements are allowed and the focus of the analysis is the group, association or coalition. However, for this assignment, I will focus mainly on non-cooperative game theory.
Elements in the game
Wilkinson (2005:332-376) points out that game theory is made up of four elements;
Players: each decision-maker in the game is called a player, a term that can be applied to an individual, firm or even a nation state. In addition, each player has the ability to choose among a set of possible actions.
Strategies: each course of action open to a player is known as strategy. However, if the strategy proves to be better than all the other strategies i.e. regardless of the actions of the other players, it is known as the dominant strategy (Salvatore, 2006:388-388). Conversely, if the strategy is worse than the others, regardless of the actions of the other players, it is known as the dominated strategy.
Payoffs: this is the outcome or consequence of each strategy at the end of the game. Payoffs can be measured in terms of utility or usefulness to the firm, or in monetary considerations i.e. profits and losses. Finally, it is assumed that players are able to rank the payoffs in order to make the best decision.
Information: do the players have perfect knowledge i.e. if the players know what happens every time a decision needs to be made (e.g. as in chess) or imperfect knowledge i.e. the contrary of the previously mentioned point?
According to Wilkinson (2005:332-376), there are two equilibrium concepts that are often used in game theory i.e. the dominant strategy equilibrium and the Nash equilibrium. As pointed out earlier, the dominant strategy is the best response vis-à-vis the other players' responses. However, if the strategies being pursued by all the players are dominant, this will create a solution known as dominant strategy equilibrium (DSE). Another such solution for game theory can be facilitated by a process known as an iterative deletion of dominated strategies (IDDS). For instance, the elimination of all the actions that players will not consider, will, by default, leave the player with those strategies the others will consider. Of course, such game scenarios are heavily reliant on the players playing rationally. The third solution in game theory is the Nash equilibrium (a solution concept developed by Noble prize winner John Nash) that requires that each player pursues his/her best strategy with zero deviation in response to a particular strategy combination formulated by the other players. Salvatore (2006:386), points out that in this situation the dominant strategy adopted in the Nash equilibrium may not have the best outcome for the players or society in the real world. Salvatore further points out that the Nash equilibrium is an important element in game theory, as there are situations that arise where there is no dominant strategy, except the best strategy being played out that will lead to an equilibrium that may represent a bad outcome for the individual players.
The Prisoner's dilemma (PD)
The PD is a classic problem in game theory that was modified by Albert W. Tucker (cited in Wilkinson, 2005:332-376) to incorporate the notion of prison sentence payoffs. PD is a simultaneous-move, one-shot game operating in an imperfect information environment i.e. we do not know what the other player has decided to do or will do. The scenario is as follows: two people are arrested for a crime: however, the District Attorney has little evidence but is eager to get a confession. Then the DA separates the two suspects and tells them individually: “If you confess and your companion does not, I can promise you a six-month sentence, whereas your companion will get ten years. However, if you both confess, you'll each get a three-year sentence.” Each suspect knows that if neither confesses, they will be tried for a lesser crime and will each receive a two-year sentence (see table below).
The characteristics and outcomes of the PD are that each player can play two possible strategies either cooperate (i.e. collude) or defect (i.e. cheat or compete). The reason for this is simple, namely, because in this game (as in all game theory) the only concern of each player here is to maximise his own payoff, with zero concern for the other players' payoff. The upshot of this is that an agreement by both suspects not to confess will result in the lowest amount of jail time. This represents what economists call a nonzero-sum game in which the interests of the players are not in direct conflict, thus producing opportunities for both players to gain, this can be demonstrated by the ‘don't confess' option in the game. However, although this would be the rational course of action, each player has the same dominant strategy i.e. to defect from any form of cooperation. This can be demonstrated by the table above where we can see that the strategy to ‘confess' strictly dominates 'not to confess” for both A and B. Therefore, the ‘confess' strategy is strictly dominant because it will be played by both players and represents the Nash equilibrium, as the outcome achieved is based on rational self interest that creates an incentive to ‘cheat', because the players simply do not trust one another. Whereas, the ‘not confess' is strictly dominated by the confess strategy even though it offers the best outcome.
Consequences of the PD
As the dominant strategy of each player was to defect from cooperation, the resulting outcome of these strategies (or equilibria) for both players was worse than the cooperative outcome had it been chosen. What PD tells us is that optimal or dominant strategy adopted by players may be the best response to counter other players' strategies, but not necessarily the best outcome. And if the players could agree on strategies that were different from the Nash equilibrium (i.e. a solution which is sub-optimal because it is based on self-interest), best outcome would be attained through collusion or the setting up of a cartel to increase profits. As pointed out at the beginning of this assignment, game theory applies to the oligopoly market structure where there are a few sellers of a product. And as there are only a few sellers of the product or service, the actions of each seller will often affect the other because of mutual interdependence. Oligopolies know that if they cooperate they can achieve satisfactory outcome that does not put the other members of the oligopoly at a disadvantage. This can be demonstrated by the example of U.S. Steel (USX today) (which was considered to be price leader in the steel industry) that was able to raise its product price on the tacit understanding that the other steel producers would match the price soon after. The importance of this is that U.S. Steel‘s strategy was one of cooperation not self-interest (sub-optimal) and resulted in an orderly price increase, without either exposing the other producers to U.S. government antitrust legislation that makes overt collusion illegal in the U.S., or running the risk of a dangerous price war (Salvatore, 2003:128). However, because self-interest is a strong human emotion, the incentive to choose a sub-optimal strategy is strong as the Nash equilibrium bears out.
The study of game theory allows economists to study interdependence of oligopoly market structures. The Prisoners' Dilemma is one of many games that business can ‘play' e.g. tit-for-tat or the Battle of the Sexes to name but a few (http://www.mbs.edu/home/jgans/mecon/value/Segment%205_3.htm). The importance of such games is to identify the dominant or optimal strategy that allows the firm to realise its goals. The importance of the PD is that it can also identify the sub-optimal strategy that may frustrate the best outcome e.g. through collusion, cartel members can agree to cooperate to extract the most profit from the market and share it. However, if a firm acts independently of tacit agreements, it could spark of a ruinous price war as in the case of the US airline fare wars (Salvatore, 2006:394). As a game, the PD offers an interesting outcome for consideration, namely, the consequences of a one-move simultaneous game i.e. the promotion of self-interest (in the guise of the Nash equilibrium) over the benefits of stable cooperation.