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. Originally, it addressed two-person zero-sum games, in which each participant's gains or losses are exactly balanced by those of other participants. In the 21st century, game theory applies to a wide range of behavioral relations; it is now an umbrella term for the science of logical decision making in humans, animals, as well as computers.
Reinhard Justus Reginald Selten was a German economist, who won the 1994 Nobel Memorial Prize in Economic Sciences. He is also well known for his work in bounded rationality and can be considered one of the founding fathers of experimental economics.
Gérard Debreu was a French-born economist and mathematician. Best known as a professor of economics at the University of California, Berkeley, where he began work in 1962, he won the 1983 Nobel Memorial Prize in Economic Sciences.
Mechanism design is a field in economics and game theory that takes an objectives-first approach to designing economic mechanisms or incentives, toward desired objectives, in strategic settings, where players act rationally. Because it starts at the end of the game, then goes backwards, it is also called reverse game theory. It has broad applications, from economics and politics in such fields as market design, auction theory and social choice theory to networked-systems.
In game theory, a solution concept is a formal rule for predicting how a game will be played. These predictions are called "solutions", and describe which strategies will be adopted by players and, therefore, the result of the game. The most commonly used solution concepts are equilibrium concepts, most famously Nash equilibrium.
In economics and game theory, complete information is an economic situation or game in which knowledge about other market participants or players is available to all participants. The utility functions, payoffs, strategies and "types" of players are thus common knowledge. Complete information is the concept that each player in the game is aware of the sequence, strategies, and payoffs throughout gameplay. Given this information, the players have the ability to plan accordingly based on the information to maximize their own strategies and utility at the end of the game.
Social choice theory or social choice is a theoretical framework for analysis of combining individual opinions, preferences, interests, or welfares to reach a collective decision or social welfare in some sense. Whereas choice theory is concerned with individuals making choices based on their preferences, social choice theory is concerned with how to translate the preferences of individuals into the preferences of a group. A non-theoretical example of a collective decision is enacting a law or set of laws under a constitution. Another example is voting, where individual preferences over candidates are collected to elect a person that best represents the group's preferences.
In game theory, a Bayesian game is a game that models the outcome of player interactions using aspects of Bayesian probability. Bayesian games are notable because they allowed, for the first time in game theory, for the specification of the solutions to games with incomplete information.
Robert John Aumann is an Israeli-American mathematician, and a member of the United States National Academy of Sciences. He is a professor at the Center for the Study of Rationality in the Hebrew University of Jerusalem in Israel. He also holds a visiting position at Stony Brook University, and is one of the founding members of the Stony Brook Center for Game Theory.
Kenneth George "Ken" Binmore, is an English mathematician, economist, and game theorist, a Professor Emeritus of Economics at University College London (UCL) and a Visiting Emeritus Professor of Economics at the University of Bristol. As a founder of modern economic theory of bargaining, he made important contributions to the foundations of game theory, experimental economics, evolutionary game theory and analytical philosophy. He took up economics after holding the Chair of Mathematics at the London School of Economics. The switch has put him at the forefront of developments in game theory. His other interests include political and moral philosophy, decision theory, and statistics. He has written over 100 scholarly papers and 14 books.
In game theory, the purification theorem was contributed by Nobel laureate John Harsanyi in 1973. The theorem aims to justify a puzzling aspect of mixed strategy Nash equilibria: that each player is wholly indifferent amongst each of the actions he puts non-zero weight on, yet he mixes them so as to make every other player also indifferent.
László Rátz was a Hungarian mathematics high school teacher best known for educating such people as John von Neumann and Nobel laureate Eugene Wigner. He was a legendary teacher of "Budapest-Fasori Evangélikus Gimnázium", the Budapest Lutheran Gymnasium, a famous secondary school in Budapest in Hungary.
Risk dominance and payoff dominance are two related refinements of the Nash equilibrium (NE) solution concept in game theory, defined by John Harsanyi and Reinhard Selten. A Nash equilibrium is considered payoff dominant if it is Pareto superior to all other Nash equilibria in the game. When faced with a choice among equilibria, all players would agree on the payoff dominant equilibrium since it offers to each player at least as much payoff as the other Nash equilibria. Conversely, a Nash equilibrium is considered risk dominant if it has the largest basin of attraction. This implies that the more uncertainty players have about the actions of the other player(s), the more likely they will choose the strategy corresponding to it.
Equilibrium selection is a concept from game theory which seeks to address reasons for players of a game to select a certain equilibrium over another. The concept is especially relevant in evolutionary game theory, where the different methods of equilibrium selection respond to different ideas of what equilibria will be stable and persistent for one player to play even in the face of deviations of the other players. This is important because there are various equilibrium concepts, and for many particular concepts, such as the Nash equilibrium, many games have multiple equilibria.
Roger Bruce Myerson is an American economist and professor at the University of Chicago. He holds the title of the David L. Pearson Distinguished Service Professor of Global Conflict Studies at The Pearson Institute for the Study and Resolution of Global Conflicts in the Harris School of Public Policy, the Griffin Department of Economics, and the college. Previously, he held the title The Glen A. Lloyd Distinguished Service Professor of Economics. In 2007, he was the winner of the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel with Leonid Hurwicz and Eric Maskin for "having laid the foundations of mechanism design theory." He was elected a Member of the American Philosophical Society in 2019.
Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, or other computational methods. Proponents of this approach claim that it allows the formulation of theoretical relationships with rigor, generality, and simplicity.
Frank Horace Hahn FBA was a British economist whose work focused on general equilibrium theory, monetary theory, Keynesian economics and critique of monetarism. A famous problem of economic theory, the conditions under which money, which is intrinsically worthless, can have a positive value in a general equilibrium, is called "Hahn's problem" after him. One of Hahn's main abiding concerns was the understanding of Keynesian (Non-Walrasian) outcomes in general equilibrium situations.
Jean-François Mertens was a Belgian game theorist and mathematical economist.
Construction by Jean-François Mertens and Zamir implementing with John Harsanyi's proposal to model games with incomplete information by supposing that each player is characterized by a privately known type that describes his feasible strategies and payoffs as well as a probability distribution over other players' types.
