Applying 'Game Theory' in bubble situation

What is Game Theory?
Game is a competitive activity involving skill, chance, or endurance on the part of two or more persons who play according to a set of rules, usually for their own amusement or for that of spectators and Game theory is the science of strategy. It attempts to determine mathematically and logically the actions that "players" should take to secure the best outcomes for themselves in a wide array of "games". Game theory was pioneered by renowned mathematician - John von Neumann. The realm of game theory goes beyond the analysis of simple games. In real world, there are many competitive situations where game theory can be applied. Game theory can be applied to devise strategy in area of sales price wars, energy regulation, labor- management negotiations, bidding at auction, arbitration, advertising, agricultural crop selection, conflict resolution and also stock markets and insurance among others.

Types of games
The essence of a game is the interdependence of player strategies. There are two distinct types of strategic interdependence: sequential and simultaneous. In the former, the players move in sequence, each aware of the others' previous actions. In the latter, the players act at the same time, each ignorant of the others' actions.

Sequential game can be analysed, by constructing a game tree map with all of the possibilities, then following the basic strategic rule: look ahead and reason back. Simultaneous game can be analysed considering all possible combinations. This can be most conveniently represented with a game table by listing the players and possible moves and outcomes.

An example of strategic interaction
Let us consider a simple and very famous example, called the Prisoner's Dilemma- two suspected felons (Lets say 'A' and 'B') are caught by the police, and interrogated in separate rooms. They are each told the following options:

• If you both confess, you will each go to jail for 10 years.

• If only one of you confesses, he gets only 1 year and the other gets 25 years.

• If neither of you confesses, you each get 3 years in jail

If suspect A keeps silent, then suspect B can get a better deal by confessing. If A confesses, B had better confess to avoid especially harsh treatment. Confession is B's dominant strategy. The same is true for A. Therefore, in equilibrium both confess. Both would fare better if they both stayed silent. Such cooperative behavior can be achieved in repeated plays of the game because the temporary gain from cheating (confession) can be outweighed by the long-run loss due to the breakdown of cooperation.

There are several notable features in this game. First notable feature is that the both players have a dominant strategy. A dominant strategy has payoffs such that, regardless of the choices of other players, no other strategy would result in a higher payoff. This greatly simplifies decisions, if you have a dominant strategy, use it, because there is no way to do better. Second notable feature is that the both players also have dominated strategies, with payoffs no better than those of at least one other strategy, regardless of the choices of other players. This also simplifies decisions, dominated strategies should never be used, since there is at least one other strategy that will never be worse, and could be better (depending on the choices of other players). A final observation here is that if both prisoners use their optimal strategies (confess), they do not reach an optimal outcome. This is an important theme; maximizing individual welfare does not necessarily aggregate to optimal welfare for a group.

Applying 'Prisoner's dilemma' in bubble situation
Stock prices occasionally rise well above their fundamental values until at some point the "bubble" bursts and the price drops quickly. In this situation, if you are holding a stock, which is over priced, you can apply strategy used in prisoner's dilemma.

Let us find out what are the options you have -

• If you and other players sell stock then price will come down significantly

• If only you sell and others doesn't sell then you will have limited profit

• If neither of you sell then price would go further and can get you more returns

In this situation, you should use dominant strategy i.e., sell your stock. It might be possible to fetch better returns by not selling stock but if your opponents use their dominant strategy then price will plummet and you will incur huge loss. Thus, in bubble market, the best strategy is to sell over priced stocks and take away whatever profits you have made before others start selling and the bubble bursts.