Put yourself in the shoes of Walter White from Breaking Bad a professor-turned-drug-lord and you have an accomplice Jesse! You are under investigation by the DEA Drug Enforcement Administration after they managed to trace the whole gamut of illegal activities you were involved in over the period of last two years. But they have insufficient proof and hence they require a testimony from either of you to go ahead with the prosecution. Both of you are interrogated separately and do not come in any kind of contact whatsoever.
Perfect information A game of imperfect information the dotted line represents ignorance on the part of player 2, formally called an information set An important subset of sequential games consists of games of perfect information.
A game Game theory in the economics of one of perfect information if all players know the moves previously made by all other players. Most games studied in game theory are imperfect-information games.
Games of incomplete information can be reduced, however, to games of imperfect information by introducing " moves by nature ". Examples include chess and go. Games that involve imperfect information may also have a strong combinatorial character, for instance backgammon.
There is no unified theory addressing combinatorial elements in games. There are, however, mathematical tools that can solve particular problems and answer general questions. These methods address games with higher combinatorial complexity than those usually considered in traditional or "economic" game theory.
A related field of study, drawing from computational complexity theoryis game complexitywhich is concerned with estimating the computational difficulty of finding optimal strategies. The practical solutions involve computational heuristics, like alpha-beta pruning or use of artificial neural networks trained by reinforcement learningwhich make games more tractable in computing practice.
Determinacy Games, as studied by economists and real-world game players, are generally finished in finitely many moves.
Pure mathematicians are not so constrained, and set theorists in particular study games that last for infinitely many moves, with the winner or other payoff not known until after all those moves are completed.
The focus of attention is usually not so much on the best way to play such a game, but whether one player has a winning strategy. The existence of such strategies, for cleverly designed games, has important consequences in descriptive set theory. Discrete and continuous games[ edit ] Much of game theory is concerned with finite, discrete games, that have a finite number of players, moves, events, outcomes, etc.
Many concepts can be extended, however. Continuous games allow players to choose a strategy from a continuous strategy set. For instance, Cournot competition is typically modeled with players' strategies being any non-negative quantities, including fractional quantities.
Differential games[ edit ] Differential games such as the continuous pursuit and evasion game are continuous games where the evolution of the players' state variables is governed by differential equations. The problem of finding an optimal strategy in a differential game is closely related to the optimal control theory.
In particular, there are two types of strategies: A particular case of differential games are the games with a random time horizon. Therefore, the players maximize the mathematical expectation of the cost function.
It was shown that the modified optimization problem can be reformulated as a discounted differential game over an infinite time interval. Evolutionary game theory[ edit ] Evolutionary game theory studies players who adjust their strategies over time according to rules that are not necessarily rational or farsighted.
Such rules may feature imitation, optimization or survival of the fittest. In biology, such models can represent biological evolutionin which offspring adopt their parents' strategies and parents who play more successful strategies i.
In the social sciences, such models typically represent strategic adjustment by players who play a game many times within their lifetime and, consciously or unconsciously, occasionally adjust their strategies. These situations are not considered game theoretical by some authors.
Although these fields may have different motivators, the mathematics involved are substantially the same, e. For some problems, different approaches to modeling stochastic outcomes may lead to different solutions. For example, the difference in approach between MDPs and the minimax solution is that the latter considers the worst-case over a set of adversarial moves, rather than reasoning in expectation about these moves given a fixed probability distribution.
The minimax approach may be advantageous where stochastic models of uncertainty are not available, but may also be overestimating extremely unlikely but costly events, dramatically swaying the strategy in such scenarios if it is assumed that an adversary can force such an event to happen.
General models that include all elements of stochastic outcomes, adversaries, and partial or noisy observability of moves by other players have also been studied.
The " gold standard " is considered to be partially observable stochastic game POSGbut few realistic problems are computationally feasible in POSG representation. Metagames seek to maximize the utility value of the rule set developed. The theory of metagames is related to mechanism design theory.
The term metagame analysis is also used to refer to a practical approach developed by Nigel Howard. Subsequent developments have led to the formulation of confrontation analysis.
Pooling games[ edit ] These are games prevailing over all forms of society. Pooling games are repeated plays with changing payoff table in general over an experienced path and their equilibrium strategies usually take a form of evolutionary social convention and economic convention. Pooling game theory emerges to formally recognize the interaction between optimal choice in one play and the emergence of forthcoming payoff table update path, identify the invariance existence and robustness, and predict variance over time.
The theory is based upon topological transformation classification of payoff table update over time to predict variance and invariance, and is also within the jurisdiction of the computational law of reachable optimality for ordered system.Game Theory in Economics As an introduction to Game Theory, an important concept in Economics, let’s take an example.
Put yourself in the shoes of Walter White from Breaking Bad (a professor-turned-drug-lord) and you have an accomplice (Jesse!) in your sweet little crime. Game theory analysis has direct relevance to the study of the conduct and behaviour of firms in oligopolistic markets – for example the decisions that firms must take over pricing and levels of production, and also how much money to invest in research and development spending.
A prototypical paper on game theory in economics begins by presenting a game that is an abstraction of a particular economic situation.
One or more solution concepts are chosen, and the author demonstrates which strategy sets in the presented game are equilibria of the appropriate type. Game theory The politics, economics, science and statistical analysis of the games we play and watch Turkish despite There is little evidence that football helps racial integration.
BREAKING DOWN 'Game Theory' The focus of game theory is the game, which serves as a model of an interactive situation among rational players. Economics of Game Theory Game study is the study of strategic interaction where one player’s decision depends on what the other player does.
What the opponent does also depends upon what he thinks the first player will do.