Game Theory

Opening Statement

We read a lot about economics in newspapers, but you rarely read about game theory. This may be because, as yet, it's still pretty theoretical.

Economists study how societies allocate resources between competing uses. Conventionally, they study how this is achieved by the movement of prices paid in markets bringing supply and demand into equilibrium. The standard model assumes the buyers and sellers in those markets are each so small they have no effect on the prices being paid. In reality, many markets are dominated by a few big companies which do have the ability to influence the price. So game theory began as an alternative way of studying the behavior of the many ''oligopolies'' that characterize modern economies.

The Game Theory

Game theory is the study of how people and businesses behave in a strategic situations. By ‘strategic’ we mean a situation in which each person, when deciding what actions to take, must consider how others might respond to that action. Because the number of firms in an oligopolistic market is small, each firm must act strategically. Each firm knows that its profit depends not only on how much it produces but also on how much the other firms produce. In making its production decision, each firm in an oligopoly should consider how its decision might affect the production decisions of all other firms.

Economists use game theory to describe, predict, and explain people's behavior. They've used it to study auctions, bargaining, merger pricing, oligopolies, and much else.

A little History

Game theory was originally developed by the Hungarian-born American mathematician John von Neumann and his Princeton University colleague Oskar Morgenstern, a German-born American economist, to solve problems in economics. In their book The Theory of Games and Economic Behaviour (1944), von Neumann and Morgenstern asserted that the mathematics developed for the physical sciences, which describes the workings of a disinterested nature, was a good model for economics. They observed that economics is much like a game, wherein players anticipate each other’s moves, and therefore require a new kind of mathematics, which they called the game theory.

The Prisoner's Dilemma

The classic example of game theory is the Prisoner Dilemma a situation where two prisoners are being questioned over their guilt or innocence of a crime.

Two prisoners, A and B, suspected of committing a robbery together, are isolated, and urged to confess. Each is concerned only with getting the shortest possible prison sentence for himself; each must decide whether to confess without knowing his partner’s decision. Both prisoners, however, know the consequences of their decisions:

• If both confess, both go to jail for five years
• If neither confesses, both go to jail for one year (for carrying concealed weapons)
• If A confesses while B does not, the confessor goes free (for turning state’s evidence) and the silent one goes to jail for 20 years.
• And if B confesses while A does not, the confessor goes free (for turning state’s evidence) and the silent one goes to jail for 20 years.

 

Superficially, the analysis of prisoners dilemma is very simple. Although A cannot be sure what B will do, he knows that he does best to confess when B confesses (he gets five years rather than 20) and also when B remains silent (he serves no time rather than a year), B will reach the same conclusion. So the solution would seem to be that each prisoner does best to confess and go to jail for five years. Paradoxically, however, the two robbers would do better if they both adopted the apparently irrational strategy of remaining silent; each would then serve only one year in jail. The irony of prisoners' dilemma is that when each of two (or more) parties act selfishly and do not cooperate with the other (that is, when he confesses), they do worse than when they act unselfishly and cooperate together (that is, when they remain silent).

Nash Equilibrium

 

Nash equilibrium is a concept within game theory where the optimal outcome of a game is where there is no incentive to deviate from the initial strategy. More specifically, the Nash equilibrium is a concept of game theory where the optimal outcome of a game is one where no player has an incentive to deviate from their chosen strategy after considering an opponent's choice.

 

Overall, an individual can receive no incremental benefit from changing actions, assuming other players remain constant in their strategies. A game may have multiple Nash equilibrium or none at all.

 

Example - 

 

Imagine that two manufacturers dominate the toaster industry both company A and company B make 1 million toasters a year for a price of $30 each and earn a profit of 10 million dollars annually. 

Company A knows that the market is bigger than this and decides to increase its production from 1 million toasters to 2 million toasters each year at a reduced price of 27 dollars, in this scenario its profit increases to 14 million dollars

 

However, company B also knows that if it boosts production its competitor A will follow and they also increase their production from 1 million toasters to 2 million toasters

 

Because of the increase in supply of toasters in the market the price will be reduced from 27 dollars to 24 dollars and company’s profit will reduce from 14 million dollars to 8 million dollars that is lower than it is now at current production level. ( 10 million dollars )

 

 As it turns out the two companies are already at a state of Nash equilibrium given the competing firms expected response neither businesses can make more money by unilaterally deciding to boost production this example illustrates why game theorists look at decisions not in isolation but as a part of the system of interactions.

 

The reason why Nash equilibrium is considered such an important concept of game theory relates to its applicability. The Nash equilibrium can be incorporated into a wide range of disciplines, from economics to the social sciences.

 

To quickly find the Nash equilibrium or see if it even exists, reveal each player's strategy to the other players. If no one changes their strategy, then the Nash equilibrium is proven.

 

 Oligopoly and Game Theory

In an oligopoly, firms are interdependent; they are affected not only by their own decisions regarding how much to produce but by the decisions of other firms in the market as well. Game theory offers a useful framework for thinking about how firms may act in the context of this interdependence.

More specifically, game theory can be used to model situations in which each actor, when deciding on a course of action, must also consider how others might respond to that action.

Game theory can explain why oligopolies have trouble maintaining collusive arrangements to generate monopoly profits. While firms would be better off

collectively if they cooperate, each individual firm has a strong incentive to cheat and undercut their competitors in order to increase market share. 

Thank You

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