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Cashmio Casino. Game theorists respond by comparing their assumptions to those used in physics. Thus while their assumptions do not always hold, they can treat game theory as a reasonable scientific ideal akin to the models used by physicists.
There is an ongoing debate regarding the importance of these experiments and whether the analysis of the experiments fully captures all aspects of the relevant situation.
Price , have turned to evolutionary game theory in order to resolve these issues. These models presume either no rationality or bounded rationality on the part of players.
Despite the name, evolutionary game theory does not necessarily presume natural selection in the biological sense.
Evolutionary game theory includes both biological as well as cultural evolution and also models of individual learning for example, fictitious play dynamics.
Some scholars see game theory not as a predictive tool for the behavior of human beings, but as a suggestion for how people ought to behave.
Since a strategy, corresponding to a Nash equilibrium of a game constitutes one's best response to the actions of the other players — provided they are in the same Nash equilibrium — playing a strategy that is part of a Nash equilibrium seems appropriate.
This normative use of game theory has also come under criticism. Game theory is a major method used in mathematical economics and business for modeling competing behaviors of interacting agents.
This research usually focuses on particular sets of strategies known as "solution concepts" or "equilibria". A common assumption is that players act rationally.
In non-cooperative games, the most famous of these is the Nash equilibrium. A set of strategies is a Nash equilibrium if each represents a best response to the other strategies.
If all the players are playing the strategies in a Nash equilibrium, they have no unilateral incentive to deviate, since their strategy is the best they can do given what others are doing.
The payoffs of the game are generally taken to represent the utility of individual players. 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.
Naturally one might wonder to what use this information should be put. Economists and business professors suggest two primary uses noted above : descriptive and prescriptive.
Sensible decision-making is critical for the success of projects. In project management, game theory is used to model the decision-making process of players, such as investors, project managers, contractors, sub-contractors, governments and customers.
Quite often, these players have competing interests, and sometimes their interests are directly detrimental to other players, making project management scenarios well-suited to be modeled by game theory.
Piraveenan  in his review provides several examples where game theory is used to model project management scenarios.
For instance, an investor typically has several investment options, and each option will likely result in a different project, and thus one of the investment options has to be chosen before the project charter can be produced.
Similarly, any large project involving subcontractors, for instance, a construction project, has a complex interplay between the main contractor the project manager and subcontractors, or among the subcontractors themselves, which typically has several decision points.
For example, if there is an ambiguity in the contract between the contractor and subcontractor, each must decide how hard to push their case without jeopardizing the whole project, and thus their own stake in it.
Similarly, when projects from competing organizations are launched, the marketing personnel have to decide what is the best timing and strategy to market the project, or its resultant product or service, so that it can gain maximum traction in the face of competition.
In each of these scenarios, the required decisions depend on the decisions of other players who, in some way, have competing interests to the interests of the decision-maker, and thus can ideally be modeled using game theory.
Piraveenan  summarises that two-player games are predominantly used to model project management scenarios, and based on the identity of these players, five distinct types of games are used in project management.
In terms of types of games, both cooperative as well as non-cooperative games, normal-form as well as extensive-form games, and zero-sum as well as non-zero-sum games are used to model various project management scenarios.
The application of game theory to political science is focused in the overlapping areas of fair division , political economy , public choice , war bargaining , positive political theory , and social choice theory.
In each of these areas, researchers have developed game-theoretic models in which the players are often voters, states, special interest groups, and politicians.
Early examples of game theory applied to political science are provided by Anthony Downs. In his book An Economic Theory of Democracy ,  he applies the Hotelling firm location model to the political process.
In the Downsian model, political candidates commit to ideologies on a one-dimensional policy space.
Downs first shows how the political candidates will converge to the ideology preferred by the median voter if voters are fully informed, but then argues that voters choose to remain rationally ignorant which allows for candidate divergence.
Game Theory was applied in to the Cuban missile crisis during the presidency of John F. It has also been proposed that game theory explains the stability of any form of political government.
Taking the simplest case of a monarchy, for example, the king, being only one person, does not and cannot maintain his authority by personally exercising physical control over all or even any significant number of his subjects.
Sovereign control is instead explained by the recognition by each citizen that all other citizens expect each other to view the king or other established government as the person whose orders will be followed.
Coordinating communication among citizens to replace the sovereign is effectively barred, since conspiracy to replace the sovereign is generally punishable as a crime.
Thus, in a process that can be modeled by variants of the prisoner's dilemma , during periods of stability no citizen will find it rational to move to replace the sovereign, even if all the citizens know they would be better off if they were all to act collectively.
A game-theoretic explanation for democratic peace is that public and open debate in democracies sends clear and reliable information regarding their intentions to other states.
In contrast, it is difficult to know the intentions of nondemocratic leaders, what effect concessions will have, and if promises will be kept.
Thus there will be mistrust and unwillingness to make concessions if at least one of the parties in a dispute is a non-democracy. On the other hand, game theory predicts that two countries may still go to war even if their leaders are cognizant of the costs of fighting.
War may result from asymmetric information; two countries may have incentives to mis-represent the amount of military resources they have on hand, rendering them unable to settle disputes agreeably without resorting to fighting.
Moreover, war may arise because of commitment problems: if two countries wish to settle a dispute via peaceful means, but each wishes to go back on the terms of that settlement, they may have no choice but to resort to warfare.
Finally, war may result from issue indivisibilities. Game theory could also help predict a nation's responses when there is a new rule or law to be applied to that nation.
One example would be Peter John Wood's research when he looked into what nations could do to help reduce climate change. Wood thought this could be accomplished by making treaties with other nations to reduce greenhouse gas emissions.
However, he concluded that this idea could not work because it would create a prisoner's dilemma to the nations. Unlike those in economics, the payoffs for games in biology are often interpreted as corresponding to fitness.
In addition, the focus has been less on equilibria that correspond to a notion of rationality and more on ones that would be maintained by evolutionary forces.
Although its initial motivation did not involve any of the mental requirements of the Nash equilibrium , every ESS is a Nash equilibrium.
In biology, game theory has been used as a model to understand many different phenomena. It was first used to explain the evolution and stability of the approximate sex ratios.
Fisher harv error: no target: CITEREFFisher help suggested that the sex ratios are a result of evolutionary forces acting on individuals who could be seen as trying to maximize their number of grandchildren.
Additionally, biologists have used evolutionary game theory and the ESS to explain the emergence of animal communication. For example, the mobbing behavior of many species, in which a large number of prey animals attack a larger predator, seems to be an example of spontaneous emergent organization.
Ants have also been shown to exhibit feed-forward behavior akin to fashion see Paul Ormerod 's Butterfly Economics. Biologists have used the game of chicken to analyze fighting behavior and territoriality.
According to Maynard Smith, in the preface to Evolution and the Theory of Games , "paradoxically, it has turned out that game theory is more readily applied to biology than to the field of economic behaviour for which it was originally designed".
Evolutionary game theory has been used to explain many seemingly incongruous phenomena in nature. One such phenomenon is known as biological altruism.
This is a situation in which an organism appears to act in a way that benefits other organisms and is detrimental to itself.
This is distinct from traditional notions of altruism because such actions are not conscious, but appear to be evolutionary adaptations to increase overall fitness.
Examples can be found in species ranging from vampire bats that regurgitate blood they have obtained from a night's hunting and give it to group members who have failed to feed, to worker bees that care for the queen bee for their entire lives and never mate, to vervet monkeys that warn group members of a predator's approach, even when it endangers that individual's chance of survival.
Evolutionary game theory explains this altruism with the idea of kin selection. Altruists discriminate between the individuals they help and favor relatives.
The more closely related two organisms are causes the incidences of altruism to increase because they share many of the same alleles.
This means that the altruistic individual, by ensuring that the alleles of its close relative are passed on through survival of its offspring, can forgo the option of having offspring itself because the same number of alleles are passed on.
Ensuring that enough of a sibling's offspring survive to adulthood precludes the necessity of the altruistic individual producing offspring. Similarly if it is considered that information other than that of a genetic nature e.
Game theory has come to play an increasingly important role in logic and in computer science. Several logical theories have a basis in game semantics.
In addition, computer scientists have used games to model interactive computations. Also, game theory provides a theoretical basis to the field of multi-agent systems.
Separately, game theory has played a role in online algorithms ; in particular, the k -server problem , which has in the past been referred to as games with moving costs and request-answer games.
The emergence of the Internet has motivated the development of algorithms for finding equilibria in games, markets, computational auctions, peer-to-peer systems, and security and information markets.
Algorithmic game theory  and within it algorithmic mechanism design  combine computational algorithm design and analysis of complex systems with economic theory.
Game theory has been put to several uses in philosophy. Responding to two papers by W. In so doing, he provided the first analysis of common knowledge and employed it in analyzing play in coordination games.
In addition, he first suggested that one can understand meaning in terms of signaling games. This later suggestion has been pursued by several philosophers since Lewis.
Game theory has also challenged philosophers to think in terms of interactive epistemology : what it means for a collective to have common beliefs or knowledge, and what are the consequences of this knowledge for the social outcomes resulting from the interactions of agents.
Philosophers who have worked in this area include Bicchieri , ,   Skyrms ,  and Stalnaker Since games like the prisoner's dilemma present an apparent conflict between morality and self-interest, explaining why cooperation is required by self-interest is an important component of this project.
This general strategy is a component of the general social contract view in political philosophy for examples, see Gauthier and Kavka harvtxt error: no target: CITEREFKavka help.
Other authors have attempted to use evolutionary game theory in order to explain the emergence of human attitudes about morality and corresponding animal behaviors.
These authors look at several games including the prisoner's dilemma, stag hunt , and the Nash bargaining game as providing an explanation for the emergence of attitudes about morality see, e.
Game theory applications are used heavily in the pricing strategies of retail and consumer markets, particularly for the sale of inelastic goods.
With retailers constantly competing against one another for consumer market share, it has become a fairly common practice for retailers to discount certain goods, intermittently, in the hopes of increasing foot-traffic in brick and mortar locations websites visits for e-commerce retailers or increasing sales of ancillary or complimentary products.
Black Friday , a popular shopping holiday in the US, is when many retailers focus on optimal pricing strategies to capture the holiday shopping market.
The retailer is focused on an optimal pricing strategy, while the consumer is focused on the best deal. In this closed system, there often is no dominant strategy as both players have alternative options.
That is, retailers can find a different customer, and consumers can shop at a different retailer. The open system assumes multiple retailers selling similar goods, and a finite number of consumers demanding the goods at an optimal price.
Amazon made up part of the difference by increasing the price of HDMI cables, as it has been found that consumers are less price discriminatory when it comes to the sale of secondary items.
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