132,166 research outputs found
Against Game Theory
People make choices. Often, the outcome depends on choices other people make. What mental steps do people go through when making such choices? Game theory, the most influential model of choice in economics and the social sciences, offers an answer, one based on games of strategy such as chess and checkers: the chooser considers the choices that others will make and makes a choice that will lead to a better outcome for the chooser, given all those choices by other people. It is universally established in the social sciences that classical game theory (even when heavily modified) is bad at predicting behavior. But instead of abandoning classical game theory, those in the social sciences have mounted a rescue operation under the name of “behavioral game theory.” Its main tool is to propose systematic deviations from the predictions of game theory, deviations that arise from character type, for example. Other deviations purportedly come from cognitive overload or limitations. The fundamental idea of behavioral game theory is that, if we know the deviations, then we can correct our predictions accordingly, and so get it right. There are two problems with this rescue operation, each of them is fatal. (1) For a chooser, contemplating the range of possible deviations, as there are many dozens, actually makes it exponentially harder to figure out a path to an outcome. This makes the theoretical models useless for modeling human thought or human behavior in general. (2) Modeling deviations are helpful only if the deviations are consistent, so that scientists (and indeed decision makers) can make predictions about future choices on the basis of past choices. But the deviations are not consistent. In general, deviations from classical models are not consistent for any individual from one task to the next or between individuals for the same task. In addition, people’s beliefs are in general not consistent with their choices. Accordingly, all hope is hollow that we can construct a general behavioral game theory. What can replace it? We survey some of the emerging candidates
Compositional game theory
We introduce open games as a compositional foundation of economic game
theory. A compositional approach potentially allows methods of game theory and
theoretical computer science to be applied to large-scale economic models for
which standard economic tools are not practical. An open game represents a game
played relative to an arbitrary environment and to this end we introduce the
concept of coutility, which is the utility generated by an open game and
returned to its environment. Open games are the morphisms of a symmetric
monoidal category and can therefore be composed by categorical composition into
sequential move games and by monoidal products into simultaneous move games.
Open games can be represented by string diagrams which provide an intuitive but
formal visualisation of the information flows. We show that a variety of games
can be faithfully represented as open games in the sense of having the same
Nash equilibria and off-equilibrium best responses.Comment: This version submitted to LiCS 201
Quantum Game Theory
A systematic theory is introduced that describes stochastic effects in game
theory. In a biological context, such effects are relevant for the evolution of
finite populations with frequency-dependent selection. They are characterized
by quantum Nash equilibria, a generalization of the well-known Nash equilibrium
points in classical game theory. The implications of this theory for biological
systems are discussed in detail.Comment: 6 pages, 1 Postscript figur
Game theory of mind
This paper introduces a model of ‘theory of mind’, namely, how we represent the intentions and goals of others to optimise our mutual interactions. We draw on ideas from optimum control and game theory to provide a ‘game theory of mind’. First, we consider the representations of goals in terms of value functions that are prescribed by utility or rewards. Critically, the joint value functions and ensuing behaviour are optimised recursively, under the assumption that I represent your value function, your representation of mine, your representation of my representation of yours, and so on ad infinitum. However, if we assume that the degree of recursion is bounded, then players need to estimate the opponent's degree of recursion (i.e., sophistication) to respond optimally. This induces a problem of inferring the opponent's sophistication, given behavioural exchanges. We show it is possible to deduce whether players make inferences about each other and quantify their sophistication on the basis of choices in sequential games. This rests on comparing generative models of choices with, and without, inference. Model comparison is demonstrated using simulated and real data from a ‘stag-hunt’. Finally, we note that exactly the same sophisticated behaviour can be achieved by optimising the utility function itself (through prosocial utility), producing unsophisticated but apparently altruistic agents. This may be relevant ethologically in hierarchal game theory and coevolution
Escort Evolutionary Game Theory
A family of replicator-like dynamics, called the escort replicator equation,
is constructed using information-geometric concepts and generalized information
entropies and diverenges from statistical thermodynamics. Lyapunov functions
and escort generalizations of basic concepts and constructions in evolutionary
game theory are given, such as an escorted Fisher's Fundamental theorem and
generalizations of the Shahshahani geometry.Comment: Minor typo correctio
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