Exploring 'compellingness' in mechanism design

Consider an auction. You have two types of main protagonists or agents: a seller (or auctioneer) and many potential buyers. There are, of course, certain ground rules. For instance, one objective may be to design the auction ...

Researcher solves nearly 60-year-old game theory dilemma

To understand how driverless vehicles can navigate the complexities of the road, researchers often use game theory—mathematical models representing the way rational agents behave strategically to meet their goals.

Increasing crop yields by breeding plants to cooperate

A simple breeding experiment, combined with genetic analysis, can rapidly uncover genes that promote cooperation and higher yields of plant populations, according to a new study published November 29 in the open access journal ...

Study shows how moral behavior pays off in the end

Selfless behavior and cooperation cannot be taken for granted. Mohammad Salahshour of the Max Planck Institute for Mathematics in the Sciences (now at Max Planck Institute of Animal Behavior), has used a game theory-based ...

Why do we learn to reward cooperation?

Researchers at the Max Planck Institute in Plön show that reputation plays a key role in determining which rewarding policies people adopt. Using game theory, they explain why individuals learn to use rewards to specifically ...

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Game theory

Game theory is a branch of applied mathematics that is used in the social sciences (most notably economics), biology, engineering, political science, international relations, computer science, and philosophy. Game theory attempts to mathematically capture behavior in strategic situations, in which an individual's success in making choices depends on the choices of others. While initially developed to analyze competitions in which one individual does better at another's expense (zero sum games), it has been expanded to treat a wide class of interactions, which are classified according to several criteria. Today, "game theory is a sort of umbrella or 'unified field' theory for the rational side of social science, where 'social' is interpreted broadly, to include human as well as non-human players (computers, animals, plants)" (Aumann 1987).

Traditional applications of game theory attempt to find equilibria in these games. In an equilibrium, each player of the game has adopted a strategy that they are unlikely to change. Many equilibrium concepts have been developed (most famously the Nash equilibrium) in an attempt to capture this idea. These equilibrium concepts are motivated differently depending on the field of application, although they often overlap or coincide. This methodology is not without criticism, and debates continue over the appropriateness of particular equilibrium concepts, the appropriateness of equilibria altogether, and the usefulness of mathematical models more generally.

Although some developments occurred before it, the field of game theory came into being with the 1944 book Theory of Games and Economic Behavior by John von Neumann and Oskar Morgenstern. This theory was developed extensively in the 1950s by many scholars. Game theory was later explicitly applied to biology in the 1970s, although similar developments go back at least as far as the 1930s. Game theory has been widely recognized as an important tool in many fields. Eight game theorists have won Nobel prizes in economics, and John Maynard Smith was awarded the Crafoord Prize for his application of game theory to biology.

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