Game Theory Quiz

Mathematical models of strategic interactions

• Game theory is the study of mathematical models of strategic interactions among rational agents.

• It has applications in all fields of social science, as well as in logic, systems science and computer science.

• Traditional methods of game theory addressed two-person zero-sum games, but advanced game theories now apply to a wider range of behavioral relations.

• Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann.

• Game theory was developed extensively in the 1950s and was explicitly applied to evolution in the 1970s.

• Game theory has been widely recognized as an important tool in many fields, with fifteen game theorists winning the economics Nobel Prize.

• Different types of games include cooperative/non-cooperative, symmetric/asymmetric, zero-sum/non-zero-sum, and simultaneous/sequential.

• Cooperative games are often analyzed through the framework of cooperative game theory, while non-cooperative game theory focuses on predicting individual players' actions and payoffs.

• Symmetric games are games where the payoffs for playing a particular strategy depend only on the other strategies employed, while asymmetric games have different strategies for each player.

• Zero-sum games are games in which choices by players can neither increase nor decrease the available resources, while non-zero-sum games have net results greater or less than zero.

• Simultaneous games are games where both players move simultaneously, while sequential games are games where players do not make decisions simultaneously.

• A game with perfect information means that all players, at every move in the game, know the previous history of the game and the moves previously made by all other players.Overview of Game Theory

• Game theory studies decision-making in situations where the outcome depends on the choices of multiple individuals.

• Bayesian games involve incomplete information, where players do not fully understand the characteristics of their opponents, and require understanding the player's preference for the draw.

• Combinatorial games, like chess and Go, have a strong combinatorial character and are solved using mathematical tools and proof methods.

• Continuous games allow players to choose a strategy from a continuous strategy set, and incentivize players to provide a larger amount of goods in a public good game than in discrete games.

• Differential games involve the evolution of the players' state variables governed by differential equations and have open-loop and closed-loop strategies.

• Evolutionary game theory studies players who adjust their strategies over time according to rules that are not necessarily rational or farsighted.

• Stochastic outcomes can be modeled using game theory by adding a randomly acting player who makes "chance moves".

• Metagames are games the play of which is the development of the rules for another game, the target or subject game.

• Pooling games are repeated plays with changing payoff tables that identify the invariance existence and robustness and predict variance over time.

• Mean field game theory is the study of strategic decision making in very large populations of small interacting agents.

• Game theorists use mathematical objects to deduce a set of equilibrium strategies for each player, and games can be presented in the extensive form or the normal form.Game Theory: An Overview

• Game theory is a branch of mathematics that studies decision-making in situations where two or more individuals or groups have competing interests.

• It is used to model and analyze a wide range of phenomena, including economics, political science, biology, and psychology.

• Normal form is a way of representing games, where each player chooses a strategy and receives a payoff based on the choices made by all players.

• Extensive form is another way of representing games, where players take turns making decisions and can see the choices made by other players.

• Characteristic function form is a game representation where separate rewards are not given, instead, the characteristic function decides the payoff of each player.

• Game theory has been applied to a wide range of human and animal behaviors, including economics, political science, biology, and psychology.

• Scholars have used game theory to develop theories of ethical or normative behavior and to prescribe such behavior.

• Game theory is used in mathematical economics and business for modeling competing behaviors of interacting agents.

• Game theory has extensive use in the field of managerial economics, such as analyzing strategic interactions between firms, analyzing cooperation between firms, and analyzing pricing strategies.

• Game theory is used in project management to model the decision-making process of players, such as investors, project managers, contractors, sub-contractors, governments and customers.

• Political scientists use game theory models to study fair division, political economy, public choice, war bargaining, positive political theory, and social choice theory.

• Game theory has been applied to explain the stability of any form of political government.

• Game theorists assume players act rationally, but in practice, human rationality and/or behavior often deviates from the model of rationality as used in game theory.Applications of Game Theory in Various Fields

• Game theory can model the prisoner's dilemma to explain why citizens do not replace the sovereign even if they would be better off collectively.

• Public and open debate in democracies sends clear and reliable information regarding their intentions to other states, which may explain democratic peace.

• War may result from asymmetric information, commitment problems, and issue indivisibilities, even if leaders are aware of the costs of fighting.

• In biology, game theory explains the evolution of sex ratios, animal communication, fighting behavior, and altruism with the idea of kin selection.

• Game theory provides a theoretical basis for multi-agent systems and is used in online algorithms, such as the k-server problem and algorithmic mechanism design.

• Philosophers have used game theory to develop accounts of convention, social norms, and interactive epistemology.

• Game theory is used in retail and consumer product pricing strategies, particularly for inelastic goods, such as during Black Friday.

• Game theory has been used to model and predict vaccination uptake in a society in epidemiology.

• Game theory has multiple applications in the field of AI/ML, such as multi-agent system formation, reinforcement learning, and mechanism design.

• Examples of well-known games include the prisoner's dilemma, the battle of the sexes, and the ultimatum game.