The game semantics of game theory

We use a reformulation of compositional game theory to reunite game theory with game semantics, by viewing an open game as the System and its choice of contexts as the Environment. Specifically, the system is jointly controlled by $n \geq 0$ noncooperative players, each independently optimising a real-valued payoff. The goal of the system is to play a Nash equilibrium, and the goal of the environment is to prevent it. The key to this is the realisation that lenses (from functional programming) form a dialectica category, which have an existing game-semantic interpretation. In the second half of this paper, we apply these ideas to build a compact closed category of `computable open games' by replacing the underlying dialectica category with a wave-style geometry of interaction category, specifically the Int-construction applied to the cartesian monoidal category of directed-complete partial orders

Evolutionary Game Theory

Articl

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

Game theory

game theory

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

Are Individuals Fickle-Minded?

Game theory has been used to model large-scale social events — such as constitutional law, democratic stability, standard setting, gender roles, social movements, communication, markets, the selection of officials by means of elections, coalition formation, resource allocation, distribution of goods, and war — as the aggregate result of individual choices in interdependent decision-making. Game theory in this way assumes methodological individualism. The widespread observation that game theory predictions do not in general match observation has led to many attempts to repair game theory by creating behavioral game theory, which adds corrective terms to the game theoretic predictions in the hope of making predictions that better match observations. But for game theory to be useful in making predictions, we must be able to generalize from an individual’s behavior in one situation to that individual’s behavior in very closely similar situations. In other words, behavioral game theory needs individuals to be reasonably consistent in action if the theory is to have predictive power. We argue on the basis of experimental evidence that the assumption of such consistency is unwarranted. More realistic models of individual agents must be developed that acknowledge the variance in behavior for a given individual

The Mythology of Game Theory

Non-cooperative game theory is at its heart a theory of cognition, specifically a theory of how decisions are made. Game theory\u27s leverage is that we can design different payoffs, settings, player arrays, action possibilities, and information structures, and that these differences lead to different strategies, outcomes, and equilibria. It is well-known that, in experimental settings, people do not adopt the predicted strategies, outcomes, and equilibria. The standard response to this mismatch of prediction and observation is to add various psychological axioms to the game-theoretic framework. Regardless of the differing specific proposals and results, game theory uniformly makes certain cognitive assumptions that seem rarely to be acknowledged, much less interrogated. Indeed, it is not widely understood that game theory is essentially a cognitive theory. Here, we interrogate those cognitive assumptions. We do more than reject specific predictions from specific games. More broadly, we reject the underlying cognitive model implicitly assumed by game theory