Negotiation Games (Routledge Advances in Game Theory)
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In a general equilibrium model no individual is considered a player; all are regarded as individual maximizers. When an attempt is made to consider a closed economic model as a noncooperative game, considerable difficulties are encountered in describing the strategies of the players. This can be seen im-mediately by considering the bilateral monopoly problem; each individual does not really know what he is in a position to buy until he finds out what he can sell.
In order to model this type of situation as a game, it may be necessary to consider strategies which do not clear the market and which may cause a player to become bankrupt—i. Shapley and Shubik in Shubik have successfully modeled the closed two-sided two- commodity market without side payments and have shown that the noncooperative equilibrium point converges from below the Pareto-optimal surface to the competitive equilibrium point.
They also have considered more goods and markets on the assumption of the existence of a transferable but not necessarily comparable utility. When there are more than two commodities and one market, the existence of a unique competitive equilibrium point appears to be indispensable in defining the strategies and payoffs of players in a noncooperative game.
No one has succeeded in constructing a satisfactory general market model as a noncooperative game without using a side-payment mechanism. The important role played by the side-payment commodity is that of a strategy decoupler. In summary, it appears that, in the limit, at least three considerably different game-theoretic solutions are coincidental with the competitive equilibrium solution.
This means that by considering different solutions we may interpret the com petitive market in terms of decentralization, fair division, the power of groups, and the attenuation of power of the individual. There has been no indication of a limiting behavior for these solutions as numbers grow; on the contrary, it is conjectured that in general the solutions proliferate. When, however, numbers are few, as in cartel arrangements and in international trade, these other solutions provide insights, as Nyblen has shown in his work dealing with stable sets When conditions other than those needed for the existence of a competitive equilibrium hold, such as external economies or diseconomies, joint ownership, increasing returns to scale, and interlinked tastes, then the different solutions in general do not converge.
There may be no competitive equilibrium; the core may be empty; and the definition of a non-cooperative game when joint property is at stake will call for a statement of the laws concerning damages and threats. Similarly, even though the conditions for the existence of a competitive equi librium are satisfied, the various solutions will be different if there are few participants. When the competitive equilibrium does not exist, we must seek another criterion to solve the problem of distribution or, if possible, change the laws to rein-troduce the competitive equilibrium.
The other solutions provide different criteria. However, if a society desires, for example, to have its distribution system satisfy conditions of decentralization and fair division, or of fair division and limits on power of groups, it may be logically impossible to do so. Davis and Whinston , Scarf , and Shapley and Shubik have investigated applications of game theory to external economies, to increasing returns to scale, and to joint ownership.
In the case of joint ownership the relation between economics and politics as mechanisms for the distribution of the proceeds from jointly owned resources is evident. Leaving aside questions of transferable utility, there is a considerable difference between an econ omy in which there is only barter or a passive shadow price system and one in which the government, and possibly others, have important monetary strategies.
Faxen has considered financial policy from a game-theoretic viewpoint. There have been some diverse applications of game theory to budgeting and to management science, as can be seen in the articles by Bennion and Shubik Nyblen has attempted to apply the von Neumann and Morgenstern concept of stable set to problems of macroeconomics.
He notes that the Walrasian system bypasses the problem of individual power by assuming it away. He observes that in game theory certain simple aggregation procedures do not hold; thus, the solutions to a four-person game obtained by aggregating two players in a five-person game may have little in common with the solutions to the original five-person game. He outlines an institutional theory of the rate of interest based upon a standard of behavior and primarily at a descriptive level links the concepts of discriminatory solution and excess to inflation and international trade. Aumann, Robert J.
Econometrica — Dresher, Lloyd S. Bennion, E. Davis, Otto A. Fellner, William J.
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New York: Knopf. Griesmer, James H. 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. 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 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. 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.
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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.