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Oligopolistic interdependent game theory
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?
Equilibria
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).
Analysis
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.
In conclusion
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 onemove simultaneous game i.e. the promotion of self-interest (in the guise of
the Nash equilibrium) over the benefits of stable cooperation.