The theory behind the “game”

A and B are siblings. One day their parents bring a basket of variety of chocolates and instruct them that they are not allowed to eat more than 2 chocolates each, a week. Both being 12 year old their desire takes the best of them and one night after they knew their parents are deep asleep A and B sneak to the refrigerator and eat the chocolates more than their restricted limit. The next morning, their parents find out and remand the siblings and ask who is the culprit. Now in this scenario they have 3 options:

1. A and B both can confess to the crime they did and for their sincerity get grounded only for a week.
2. Either of them can pin it on the other and the one gets grounded for 2 weeks while the other escapes any sort of punishment.
3. A and B both deny to what they did and for to their insincerity face a month being grounded.

A desire led to an action with a common goal leading to an unfavourable (rarely favourable) outcome.

INTRO

Dated 1944, John von Neuman and Oskar Morgenstern published the mathematical formulation of this concept which has been stated as a “rare event” in the history of ideas. But in reality if one decides to trace the path of the Game Theory shall find the similar concepts proposed by Socrates, Aristotle, Plato, Hobbes, et al. to establish social-economic reforms for covenant of peace and stability of society.

At core, Game Theory is about forming strategies on the basis of learning from the recorded movements, actions and behaviours of participants in a given system, for maximum payoffs(maximum doesn’t really mean high amount more of the best suitable outcome in a given scenario). The aforementioned payoffs can be sometimes limit to just one entity and sometimes in the welfare of the entire system.

Game Theory has been realised as one the essential concepts of microeconomics as it studies and observes the direct and indirect impacts of the economical effects caused by the actions of a single entity. So on digging deeper one may realise that Game Theory has its branches across many domains for instance psychology, where in psychology they call it theory of social situations.

“This is such a common thing da, why does it have such an importance?”

Before proceeding further, some terms need to be put in context:

• Game: Any set of circumstances that has a result dependent on the actions of two of more decision-makers (players).
• Players: A strategic decision-maker within the context of the game.
• Strategy: A complete plan of action a player will take given the set of circumstances that might arise within the game.
• Payoff: The payout a player receives from arriving at a particular outcome. The payout can be in any quantifiable form, from dollars to utility.
• Information set: The information available at a given point in the game. The term information set is most usually applied when the game has a sequential component.
• Equilibrium: The point in a game where both players have made their decisions and an outcome is reached.
• Duopoly: Duo as it suggests, a situation where 2 companies together own all, or nearly all, of the market for a given product or service.
• Oligopoly: Oligopoly is a market structure with a small number of firms, none of which can keep the others from having significant influence. There is no precise upper limit to the number of firms in an oligopoly, but the number must be low enough that the actions of one firm significantly influence the others.

To observe Game Theory in its true nature we gotta focus our scopes on a competitive scenario. Sports for example. Sports being a beautiful phenomenon of team spirit and culture can turn a little darker if one participate goes rogue. Meaning, if a player thinks only about his performance and earnings his ideas and decisions may deflect from the collective positive outcomes desired by the team and the competition as a whole. The player may incline towards fixing or use performance enhancement drugs with an aim of personal desire-and-wants and may or may not have the desired outcome.

To get a better understanding we can consider a different strategy with a mere low-set example. 2 male friends who know each other for long get into the same college. And in the initial week they come across two attractive girls. Now if both individually decide to approach the same girl, the girl can shy and ignore both of them and at the same time the other girl feel offended for being the “second choice” and walk away as well. On the other hand, since both girls are equally attractive, one male would wait and see which girl the other male approaches and he will approach the other girl resulting in a win-win outcome practising the classic wing-man theory.

To further understand game theory, here are some of the more important concepts:

1. Prisoner’s Dilemma — refers to a situation where two completely rational individuals might not cooperate, even if it appears that it’s in their best interests to do so. Classic choice between self-interest and mutual interest.
2. Coordination game — a game in which the players benefit from working together. There’s no incentive for either party to cheat since it will result in a worse outcome than cooperating. (The above mentioned example of 2 male friends.)
3. Free Rider Problem (Tragedy of the Commons) — a problem in which every individual tries to reap the greatest benefit from a given resource, which harms others who can no longer enjoy the benefits. Examples: pollution, over-fishing, and ocean garbage.
4. Zero-Sum — the situation in which one person or group can win something only by causing another person or group to lose it. Examples: poker and gambling.
5. Principal-Agent Problem — when one person (the agent) is allowed to make decisions on behalf of another person (the principal). In this situation, the agent will not prioritise the best interest of the principal, but will instead pursue his own goals. Ex: politics
6. Nash Equilibrium — an optimal outcome where no player has an incentive to deviate from his chosen strategy after considering an opponent’s choice. Ex: traffic lights.
7. Grim Trigger — a strategy employed in a repeated non-cooperative game where you start by cooperating and continue to cooperate as long as everyone has cooperated in the past. If someone has defected, then you defect forever.
8. Schelling Points — a solution that people will tend to use in the absence of communication because it seems natural, special, or relevant to them. Example: meeting at noon at Grand Central
9. Keynesian Beauty Contest — an analogy for investing that suggests that investors may guess what other investors are going to think as opposed to what they think themselves.
10. Bounded Rationality — when given a choice, people will always follow a path that is simple and something they are used to (even if it’s not the most optimal outcome).
11. Byzantine Generals Problem — the situation where parties must agree on a single strategy in order to avoid complete failure, but where some of the involved parties are corrupt and disseminating false information or are otherwise unreliable. (This problem is built around an imaginary General who makes a decision to attack or retreat and must communicate the decision to his lieutenants. A given number of these actors are traitors & they cannot be relied upon to properly communicate orders.)

The Nash Equilibrium

Nash Equilibrium is an outcome reached that, once achieved, means no player can increase payoff by changing decisions unilaterally. It can also be thought of as “no regrets,” in the sense that once a decision is made, the player will have no regrets concerning decisions considering the consequences.

The Nash Equilibrium is reached over time, in most cases. However, once the Nash Equilibrium is reached, it will not be deviated from. After we learn how to find the Nash Equilibrium, take a look at how a unilateral move would affect the situation. Does it make any sense? It shouldn’t, and that’s why the Nash Equilibrium is described as “no regrets.” Generally, there can be more than one equilibrium in a game.

However, this usually occurs in games with more complex elements than two choices by two players. In simultaneous games that are repeated over time, one of these multiple equilibria is reached after some trial and error. This scenario of different choices overtime before reaching equilibrium is the most often played out in the business world when two firms are determining prices for highly interchangeable products, such as airfare or soft drinks.

Importance of Game Theory:

Game theory possesses the following merits:

1. Game theory shows the importance to duopolists of finding some way to agree. It helps to explain why duopoly prices tend to be administered in a rigid way. If prices were to change often, tacit agreements would not be found and would be difficult to enforce.

2. Game theory also highlights the importance of self-interest in the business world. In game theory, self-interest is routed through the mechanism of economic competition to bring the system to the saddle point. This shows the existence of the perfectly competitive market.

3. Game theory tries to explain how the duopoly problem cannot be determined. For this, it uses the solution without saddle point under constant-sum-two-person game. At the same time, the duopoly problem without a saddle point is solved by allowing each firm to adopt mixed strategies on a probability basis. In this way, the duopoly problem is shown to be always determined.

4. Further, game theory has been used to explain the market equilibrium when more than two firms are involved. The solution lies in either collusion or non-collusion. These are known as cooperative non-constant-sum game and non-cooperative non-constant-sum game respectively.

5. “Prisoner’s Dilemma” in game theory points towards collective decision making and the need for cooperation and common rules of road.

6. A player in game theory may be regarded as a single person or an organisation in the real world subject to decision making with a certain amount of resources. The strategy in game theory is a complete specification of what a player will do under each circumstance in the playing of the game. For example, the Director of a firm might tell his sales staff how he wants an advertising campaign to start and what should they do subsequently in response to various actions of competing firms.

7. The importance of the pay-off values lies in predicting the outcome of a series of alternative choices on the part of the player. Thus a perfect knowledge of the pay-off matrix to a player implies perfect predictions of all factors affecting the outcome of alternative strategies. Moreover, the minimax principle shows to the player the next course of action which would minimise the losses if the worst possible situation arose.

8. Again, game theory is helpful in solving the problems of business, labour and management. As a matter of fact, a businessman always tries to guess the strategy of his opponents so as to implement his plans more effectively. Similar is the case of management in trying to solve the problem of labour union’s bargaining for higher wages. Management might adopt the most profitable counter-strategy to tackle such problems. Further, producers might make decisions in which estimation of profits were to be balanced against the cost of production.

9. Last but not the least, there are certain economic problems which involve risk and technical relations. They can be handled with the help of the mathematical theory of games. Problems of linear programming and activity analysis can provide the main basis for economic application of the theory of games.

Dollars to donuts, game theory applications can be found in every walk of life and influence our economy. From cellphone device we decide to buy to the shampoo that was strategically kept on the middle shelf at the super-market. Even in politics, lobbyists apply game theory to manipulate vote to the desired law-maker and turn him into the most “electable” candidate. Economists and economic planners learn behaviour of economic agents and consumers and develop suitable financial models.

Limitations

1. Game theory is based on the knowledge of the actions and patterns. And the real world is more unsupervised data than supervised data. Meaning knowing every move/trend is not really practical. Hence recording and learning becomes next to impossible. Which makes implementation of the concept impossible.
2. Rationality over emotions. Game theory believes that the ‘participants’ of the system will act rationally rather than emotionally and makes predictions accordingly.
3. With increase in number of ‘participants’ it becomes more complex to develop models and provide inferences and plot the strategy.

FINAL SERVE

War-like simulations, where participants are provided with limited responses and choices, can be used to determine the patterns and behaviour of the economic agents. Recording these patterns and in turn connecting the dots a company can logically predict of a strategic move. For instance, if there are two companies who are neck-to-neck in a product industry, having similar products, by reading and learning about its past goals/targeted markets et al, can initiate a move and create an inertia and successfully manoeuvre the market and acquire the desired outcome.

Game theory is all about patterns. To study the patterns, and then take an action and see the response. A classic stimulus scenario. While having in mind that entire outcome is based on a prediction and a loose-end situation, it is also important to acknowledge that strategies and business model are based on such predictions backed by legitimate facts. While some managers and business personnel hesitate to comply with game theory, it is better be safe than sorry to give it a shot and observe its implementation. Game Theory will “help” to get a better grip at the market direction and trends, learning the consumer expenses patterns and movements and “help” to come up with better pricing models, products, ad campaigns and also give an insight for future research and development. Also in a growing competitive market, it is important to be aware of all the ongoing research, ideas and moves of the adversary companies so as to avoid losing the market share.

CONCLUSION

Albeit Game Theory has it’s fair share of limitation, we cannot neglect the fact that Game Theory is a reality. While being an innate nature in us humans it is also proven to be quantifiable and applied across many domains. Advertising, Branding, Production, Auction, Securities trading, Government decision-making process, Collaborative company services, Military, War, et al. game theory is applied for plotting models to secure the suitable needs and socio-economic welfare.