Game theory is fundamentally the science of strategy as 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.”
The games it studies range from chess to child rearing and from tennis to takeovers. But the games all share the common feature of interdependence. That is, the outcome for each participant depends on the choices (strategies) of all.
The Basics of Game Theory
The focus of game theory is the game, which serves as a model of an interactive situation among rational players. The key to game theory is that one player’s payoff is contingent on the strategy implemented by the other player. The game identifies the players’ identities, preferences, and available strategies and how these strategies affect the outcome. Depending on the model, various other requirements or assumptions may be necessary.
Impact of Game Theory on Economics and Business
Game theory has brought about a revolution in economics by addressing crucial problems in prior mathematical economic models.
In business, game theory is definitely beneficial for modelling competing behaviours between economic agents. Businesses often have several strategic choices that affect their ability to realize economic gain. For example, businesses may face dilemmas such as whether to retire existing products or start developing new ones, lower prices relative to the competition, or go about employing new marketing strategies. Economists often tend to use game theory to understand oligopoly firm behaviour. It helps to predict likely outcomes when firms engage in certain behaviours, such as price-fixing and collusion.
TYPES OF GAME THEORY
Although there are many types (e.g., symmetric/asymmetric, simultaneous/sequential, et al.) of game theories, cooperative and non-cooperative game theories are the most common. Cooperative game theory deals with how coalitions, or cooperative groups, interact when only the payoffs are known. It is a game between the coalitions of players rather than between individuals, and it questions how groups form and how they allocate the payoff among players.
Non-cooperative game theory deals with how rational economic agents deal with each other to achieve their own goals! The most common non-cooperative game happens to be the strategic game, in which only the available strategies and the outcomes that result from a combination of choices are listed down. A simplistic example of a real-world non-cooperative game is Rock-Paper-Scissors.
The Prisoner’s Dilemma
The Prisoner’s Dilemma is the most well-known example of game theory. Consider the example of two criminals arrested for a crime. Prosecutors have no hard evidence to convict them. However, to gain a confession, officials remove the prisoners from their solitary cells and question each one of them in separate chambers. Neither prisoner has the means to communicate with each other. Officials present four deals, often displayed as a 2 x 2 box. If both confess, they will each receive a five-year prison sentence. If Prisoner 1 confesses, but Prisoner 2 does not, Prisoner 1 will get three years and Prisoner 2 will get nine years. If Prisoner 2 confesses, but Prisoner 1 does not, Prisoner 1 will get 10 years, and Prisoner 2 will get two years. If neither confesses, each will serve two years in prison.
The most favourable strategy is then not to confess. However, neither is aware of the other’s strategy and without certainty that one will not confess, both will likely confess and receive a five-year prison sentence! The Nash equilibrium suggests that in a prisoner’s dilemma, both players will make the move that is best for them individually but worse for them collectively.
This is a simple game in which Player A must decide how to split a cash prize with Player B, who has no input into the Player A’s decision. While this is not a game theory strategy per se, it does provide some interesting insights into people’s behaviour. Experiments reveal about 50% keep all the money to them, 5% split it equally, and the other 45% give the other participant a smaller share.
In a volunteer’s dilemma, someone has to undertake a chore or a job for the common good. The worst possible outcome is realized if nobody volunteers. For example, consider a company in which accounting fraud is rampant, though top management is unaware of it. Some junior employees in the accounting department are aware of the fraud but hesitate to tell top management because it would result in the employees involved in the fraud being fired and most likely to be prosecuted!
The Centipede Game
The centipede game is an extensive-form game in game theory in which two players alternately get a chance to take the larger share of a slowly increasing money stash. It is arranged so that if a player passes the stash to his opponent who then takes the stash, the player receives a smaller amount compared to if he had taken the pot.
Limitations of Game Theory
The biggest issue with game theory is that, like most other economic models, it relies on the assumption that people are rational actors that are self-interested and utility-maximizing. We are social beings who do cooperate and care about the welfare of others, often at our own expense! Game theory cannot account for that fact that in some situations we may fall into Nash equilibrium, and other times we may not, depending on the social context and who the players are.
Decision Making Process
Game theory is concerned with decision-making in an interactive world such that the best decision of every decision-maker depends on what decisions others make! As a result, everyone in this interactive world, for advancing one’s own self-interest, will need to predict decisions of others.