The game theory was first realized in 1928 when John von Neumann
published his papers where he analysed the Brouwer’s fixed-point theorem
of the possible outcome to the players of the zero-sum game when any of them
cheats. Later Ockar Morgenstern joined him and together they published Theory
of Games and Economic Behavior book. But first the main point in the
theorem was that the player’s behaviour would be to cooperate, and based on it
there were strategies developed. In the 1950th the Prisoners' Dilemma
came onto the scene introduced by notable mathematicians Merrill M. Flood and
Melvin Dresher. Around 1950, John Nash developed a criterion for mutual
consistency of players' strategies, known as Nash equilibrium,
applicable to a wider variety of games than the criterion proposed by von
Neumann and Morgenstern. This equilibrium is sufficiently general to allow for
the analysis of non-cooperative games in addition to
cooperative ones. 1 The main ideas behind the game theory would be that this is
always better to cooperate to produce mutually beneficial outcomes. However,
each player is tempted to pursue his or her individual interests. Cooperation
requires that both players compromise, and forego their individual maximum
payoffs. Yet, in compromising, each player risks complete loss if the opponent
decides to seek his or her own maximum payoff. Rather than risking total loss,
players tend to prefer the less productive outcome. 2
The playoff matrix works like in the following video:
This
is the shortest explanation why the matrix D would be preferred to the matrix
A.
Though
this is not always the best to cheat and really depends on possible outcome in
each situation. If the possible earnings or loses are not significant
fortunately many would prefer not to cheat. Now let’s look at where it is used.
Game theory has been used to study a wide variety of
human and animal behaviors. It was initially developed in economics
to understand a large collection of economic behaviors, including behaviors of
firms, markets, and consumers. The use of game theory in the social sciences
has expanded, and game theory has been applied to political, sociological, and
psychological behaviors as well. In the politics the example is Cold War. During the Cold War the opposing
alliances of NATO
and the Warsaw Pact
both had the choice to arm or disarm. From each side's point of view disarming
while the opponent continues to arm would have led to military inferiority. If
both sides chose to arm, neither could afford to attack each other, but at the
high cost of maintaining and developing a nuclear arsenal. If both sides chose
to disarm, war would be avoided and there would be no costs. If your opponent
disarmed while you continue to arm, then you achieve superiority. Although the
'best' overall outcome is for both sides to disarm, the rational course for
both sides is to arm. This is indeed what happened, and both sides poured
enormous resources in to military research and armament for the next thirty
years until the dissolution of the Soviet Union
broke the deadlock.3
In environmental studies, the PD is evident
in crises such as global climate change. It is argued all countries will
benefit from a stable climate, but any single country is often hesitant to curb
CO2
emissions. The immediate benefit to an individual country to maintain current
behavior is perceived to be greater than the purported eventual benefit to all
countries if behavior was changed, therefore explaining the current impasse
concerning climate change.3
Now
let’s look at the collusions and cartels. They have lots in common cartel is
distinguished as formal agreement between competitors6 and collusion
is an agreement between two or more persons, sometimes illegal and therefore
secretive7. Though the collusions are prohibited in most countries
there is evidence about cartels in between countries. The most recognized one
is OPEK. As long as the members of cartel are following the agreement all of
them are better off. But if any of the members tried to cheat the well-being of
all members is falling down dramatically. In the single country market there
are also some other constrains for the Prisoners Dilemma.The knowledge
that the game will be played again leads players to consider the consequences
of their actions; one's opponent may retaliate or be unwilling to cooperate in
the future, if one's strategy always seeks maximum payoffs at the expense of
the other player.2 This leads to collusive behaviour of the firms on
the market in terms of keeping the promise. They do act in their best interests
but do realise that it requires keeping in mind the interests of the other
players and respecting them. For
the proof of this idea please watch the last two minutes of the
following video:
Sources:
- http://en.wikipedia.org/wiki/Game_theory
- http://www.beyondintractability.org/bi-essay/prisoners-dilemma
- http://en.wikipedia.org/wiki/Prisoner's_dilemma
- http://connect.mcgraw-hill.com/connect/hmEBook.do?setTab=sectionTabs
- http://www.youtube.com
- http://en.wikipedia.org/wiki/Cartel
- http://en.wikipedia.org/wiki/Collusion
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