Game On: Introduction to Game Theory in Economics
Welcome to the first blog of our series on game theory, a mathematical model that has transformed the way we understand strategy in economics. At its core, game theory is about the strategic interactions between individuals or entities and analyses how choices are made in competitive environments ranging from businesses vying for market share, governments negotiating treaties, or consumers deciding between products. In this series, we will go through its fundamental concepts and applications in economics, demonstrating the role it plays in strategic decision-making.
The application of game theory in economics was pioneered by mathematician John von Neumann and economist Oskar Morgenstern in the mid-twentieth century after their publication of Theory of Games and Economic Behavior. The model began to be applied to various real-world scenarios ensuing the publication, further popularising it beyond academia. In 1950, mathematician John Nash, not to be confused with John von Neumann, developed a more widely applicable criterion for mutual consistency of players' strategies known as the Nash equilibrium. This was ground-breaking, allowing economists to predict outcomes in competitive environments, such as markets and negotiations, and has broad applications across various fields, including oligopoly theory, auction design, and resource management.
To understand the basics of game theory, there are several key concepts to grasp. Each game model consists of the players, payoffs, strategies, and sometimes a Nash equilibrium. First, we have the players or agents: individuals or entities that participate in a game, making decisions that influence the outcomes based on their chosen strategies. Then there are the payoffs, also known as utility, which represent how much a player stands to gain or lose by playing the game. A common misconception is that the payoff must be a monetary value, but in games like the famous Prisoner’s Dilemma, the most preferred option would have the highest value; in this case, it is the most lenient sentence for the prisoner. To make it easier and simpler to understand, let’s look at the example below.
In this game, each participant secretly writes down either the letter A or C as a "grade bid." Your form will be randomly paired with another, and neither you nor your partner will know each other's choices. Grades are assigned as follows:
If you choose A and your partner chooses C, you receive an A and they receive a C.
If both choose A, you both get a B-.
If you choose C and your partner chooses A, you receive a C and they get an A.
If both choose C, you both receive a B+.
Taken from Polak, B. (2007). Summaries & Lessons of First Class. Yale University.
To determine the strategy of a rational person, we first need to understand the payoffs associated with each outcome, which depend on individual preferences and moral sentiments of all players involved. Game theory does not dictate these payoffs; rather, it provides insights into optimal strategies once they are established. For instance, if all players are self-interested ("evil gits") and prefer higher grades, the potential payoffs could be defined as follows:
Taken from Polak, B. (2007). Summaries & Lessons of First Class. Yale University.
Here, the values in the matrix are translated from the alphabetical grade to the value of utility I or my pair receives if given the corresponding grade. In this case, since my payoff from strategy α, 0 or 3, is strictly higher than that from strategy β, -1 or 1, regardless of others' choices, my strategy α strictly dominates my strategy β, and therefore we have a dominant strategy in this game. A Nash Equilibrium is defined as a strategy when a player cannot benefit by unilaterally changing their strategy from one to any other strategy. Mainly applied to non-cooperative games, it shows how individual strategies can lead to collective outcomes, both positive and negative ones. So in the above matrix, the Nash Equilibria would be (0,0) and (1,1). However, when using the same logic above to consider the strategies of my pair, their dominant strategy is also α. Hence the most probable outcome of the game is that both parties receive 0 payoff.
Moving on to the actual applications in economics, game theory can be applied to almost every strategic interaction between two parties. It plays a major role in helping one understand the roles of agents and the outcomes of their strategies. In an oligopoly where dominant firms are interdependent in pricing policies and other decisions, game theory can become handy to analyse how firms may act in the context of this interdependence. For example, a reason why oligopolies have trouble upholding collusive agreements to generate monopoly profits can be explained with game theory. While firms would generally be better off collectively if they cooperate, each individual firm has an even stronger incentive to increase their market share and cheat their competitors to achieve it. Since the incentive to defect is strong, some firms may even opt out of a collusive agreement if they don’t believe potential defectors can be punished effectively and fairly. In addition, outcomes where no party has incentives to deviate from agreements can be identified by finding the Nash Equilibrium.
Furthermore, game theory is also largely used in the study of situations in mergers and acquisitions (M&A). From drafting up a deal to closing it, firms have to predict the behaviour of their competitors or targeted firms to achieve the best possible outcome from the whole process. The most common use of game theory in M&A is for describing transactions in the context of company valuation. With different valuation techniques, a foundation for negotiations can be built, subsequently beginning the bargaining processes to find a common satisfactory price for the firms involved.
To sum it up, game theory is one of the many models used by academics and enterprises to analyse different possibilities in an interaction with another agent, predicting the outcomes and implications. Decision-making in all kinds of situations would be much more unforeseeable and vague without a proper framework to approach it. In the upcoming posts, several more types of game models will be introduced, along with the theory’s applications in anticipating competitors’ behaviours, negotiation dynamics, and antitrust analysis.
Sources:
https://en.wikipedia.org/wiki/Game_theory
Dutta, P. K. (1999). Strategies and games: Theory and Practice. MIT Press.
Polak, B. (2007). Summaries & Lessons of First Class. Yale University. https://oyc.yale.edu/sites/default/files/summary%20of%20first%20class.pdf
Lumen Learning. (2018). Boundless economics. Open Textbook Library. Retrieved from https://socialsci.libretexts.org/Bookshelves/Economics/Economics_(Boundless)
